Proportion Calculator

How to use this proportion calculator.

To solve fractions for unknown x using this proportion solver, follow the below steps:

  • Input the values
  • Make sure one input should be unknown (x).
  • Hit the " calculate " button

After pressing the button, you will get the value of unknown x and a step-by-step solution by cross multiplication and proportion method.

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What is Proportion?

“ Proportion is the statement that identifies the fact that two ratios have equal values. For instance, consider the following.”

\(\dfrac{a}{b} = \dfrac{u}{v}\)

The above mathematical statement shows that the value of a/b (“a” divided by “b”) is the same as the value of u/v (“u” divided by “v”).  Suppose that if the value of \(\Big(\dfrac{a}{b}\Big)\)  is 10 then \(\Big(\dfrac{u}{v}\Big)\)  would have a value of 10 as well.

A proportion between two ratios can be expressed using 2 forms.

1.    The fraction form

The proportion between a,b and u,v would appear as follows if the fraction layout is used.

In the fraction form, a forward slash sign “/” is used between each pair of numbers.

2.    Ratio Form

The proportion \(c,d\) and \(e,f\) would appear in the following way if the ratio layout is used.

\(c:d = e:f\)

In the ratio form, a colon sign “:” appears between every pair of variables instead of the forward slash. 

Proportion Formula

The proportion formula is given below for pairs of variables \((a,b)\) and \((c,d)\)

\(\text{Proportion} = \dfrac{a}{b} = \dfrac{c}{d}\)

The proportion concept is used to determine the value of the unknown variable X. Consider that the value of X needs to be determined in the equation given below.

\(\dfrac{36}{6} = \dfrac{X}{10}\)

The solution is given as follows

\(6 = \dfrac{X}{10}\)

\(X = 6 \times10\)

Understanding the steps of calculation

Here are the steps which have been performed in the above question

Here, we have two ratios and one of them has an unknown value “x”. Through proportion concepts, the value of X has to be determined. Here you need to know the terms “extremes” and “means”. In the above example, we have four values  \(\Big(\dfrac{100}{10}\Big)\) and  \(\dfrac{36}{6} = \dfrac{X}{10}\) Extremes are the values that form a downward slope (36 and 10 in this case). However, the values making an upward slope are (6 and X).

Multiply the two extreme values and two mean values with each other respectively. This would give you the following equation. \(\dfrac{36}{6} = \dfrac{X}{10}\)

Cross Multiplication for Solving Proportions

When you are solving a proportion, the concept of cross-multiplication is applied. What is cross multiplication? When you have two ratios with values expected to be equal, certain steps of simplification are performed. The first of these steps is cross-multiplication. For instance, consider that we have the following two ratios which are considered to be equal.

  •  \(\dfrac{c}{p}\)
  •    \(\dfrac{d}{q}\)

As these two ratios are equal, they can be used in the form of proportion. In other words, we can write the following statement to elaborate on this point.

\(\dfrac{c}{p} = \dfrac{d}{q}\)

Now, we need to perform cross-multiplication to proceed with the process of calculating proportion. In the above sets of ratios, “c” will be multiplied by “q” and “d” will be multiplied by “p”. This form of multiplication is called cross-multiplication because values are multiplied in the form of two diagonals which appears like a cross. Let us proceed with the implication steps.

\(c \times q = p \times d\)

Cross Multiplication to check the proportion between two unknown variables

If you have two unknown variables, the cross-multiplication concept can be used to check the proportion between two unknown variables. For instance, consider that we have the following ratios

  • \(\dfrac{A}{8}\)
  •    \(\dfrac{B}{4}\)

Let us consider that these two ratios are equal which means that they are in proportion. Hence, the following statement would be constructed after equating them.

\(\dfrac{A}{8} = \dfrac{B}{4}\)

Performing the cross-multiplication step. This would give us

\(A \times4 = B \times 8\)

\(4A = 8B\)

Now, divide the right-hand side of the equation to determine the value of A in terms of B

\(A = \dfrac{8B}{4}\)

According to the above resultant statement, the value of A would be two times the value of B. If “B” has a value of 4, A would be 8.

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Proportion Calculator

What is a proportion – proportion definition, constant of proportionality – values being directly and inversely proportional, how to solve proportions – proportion examples, the golden ratio, law of multiple proportions – proportional relationships in chemistry, directly proportional tax definition.

The proportion calculator helps compute identical proportions. Before we can use the calculator, it's important to understand what a proportion is and how to solve proportions by hand. To help you understand these topics we present to you a proportion definition and the concept of the constant of proportionality. After reading this text, you will be able to tell whether two parameters are directly proportional or inversely proportional.

Finally, we talk about some real-life proportion examples. You will see that proportional relationships are present everywhere in the world that surrounds us . Scientists use the law of multiple proportions while performing chemical reactions and accountants (or basically any taxpayer) should be familiar with the proportional tax definition to know how much money they have to pay to the state.

A proportion is a relationship between two quantities. It displays what portion of one part is contained in the whole. The result is typically seen as a fraction, but can also be represented with a colon, or as a decimal or percent. If your preference is in the percent-based display, we encourage you to visit our percentage calculator , it might also be a better choice for solving proportions with 100 100 100 as the denominator. It still follows the proportion definition but also enables you, for example, to calculate what percent of your birthday cake was eaten by your uncle 😊.

Just as a fraction is made up of two parts, a numerator and a denominator , the same holds true for a proportion. The upper number of proportion is the numerator, and the bottom part of the proportion is the denominator. To illustrate this, let's look at an example.

Suppose, that there is a cake cut into 12 slices. 5 of the 12 slices have been eaten (by that cheeky uncle). You want to know the proportion of slices remaining compared to the entire cake. You have 12 − 5 = 7 12-5 = 7 12 − 5 = 7 slices remaining, so the proportion is 7 / 12 7/12 7/12 . If you wish to rewrite this proportion using a colon, you could write it as 7 : 12 7:12 7 : 12 . Note that this proportion calculator will not represent the proportion in the latter form.

What is the process if we want to simplify or scale the proportion up to a larger, yet equivalent proportion? The next section on how to solve proportions explains this process.

The constant of proportionality connects ratios or products of two quantities. Sometimes it goes under the name of the coefficient of probability. We can write it in the form of an equation. If two variables are directly proportional , then the formula for the constant of proportionality looks like this:

where c c c is the constant of proportionality, while x x x and y y y are the two variables in a directly proportional relationship. If two variables are inversely proportional , then the coefficient of proportionality formula is:

where c c c is the constant of proportionality, while x x x and y y y are the two variables in an inversely proportional relationship.

It may sound like a very theoretical concept at first, but you will be surprised by the number of real-life applications of these constants. We use them so often that we don't realize that they are, mathematically speaking, constants of proportionality. Speed (or velocity) could be one of the most well-known examples. It is the ratio between distance and time. We can write it like this:

Where v v v is the velocity, s s s is the distance, and t t t stands for time.

Looks familiar, doesn't it? Yes, it is the same formula as for the constant of proportionality of two directly proportional variables . As this relationship is (by proportion definition) constant, then if we change one variable, the second one will also have to change. This way, by knowing our speed, we can also calculate the distance we will cover in 1 minute, 1 hour, 1 day, or any other period. With the value of time gradually increasing, the distance covered will also rise proportionally. The other way around, when the distance becomes shorter, then the time value will also have to decrease to maintain the constant ratio. Other popular examples of constants of proportionality of two directly proportional variables are concentration and density. In both of these examples, the directly proportional variables are mass and volume.

Now, we will talk about an example of the constant of proportionality of two inversely proportional variables. Let's stick with the theme of traveling. This time, let's have a look at the formula for the distance:

This equation seems to be more similar to the formula of the constant of proportionality of two inversely proportional variables , doesn't it? If the distance (constant) stays the same, then the change in velocity or time will cause a change of the other variable. As we are talking about an inversely proportional relationship, then an increase in velocity leads to a reduction in travel time. We observe this process in real life. A car traveling at a higher speed will reach its destination in a shorter period. In turn, if we want to prolong the travel time (e.g., to admire the countryside or to save on gas), then the velocity will have to decrease. The constant ratio has to be preserved. In the last paragraphs of this text, you will find some other real-life proportion examples and instructions on how to solve them.

Suppose that we have the same proportion of 7 / 12 7/12 7/12 but we want to scale it up to a larger, equivalent ratio with a denominator of 96 96 96 . To do this, we set up two equivalent proportions and solve for the missing part. The process of solving the proportion is as follows:

  • Set up both fractions, labeling the missing part with any variable of your choice.
  • Put an equal sign between the two ratios. Note that ratio and proportion are the same things.
  • Isolate the variable by using cross multiplication, which is multiplying the denominator of one proportion by the numerator of the other and vice versa.
  • Solve for the variable.
  • Use the proportion calculator to check your answer. Now you know everything about solving proportions.

Solving the above example, we get:

We urge you to use the proportion calculator if you are solving proportions with larger numbers or those involving decimals.

The proportions can be used to adjust the amount of ingredients in a recipe for a larger number of guests. If you want to make pancakes, our pancake recipe calculator will tell you exactly what you have to prepare for a certain number of people.

There is a special ratio that occurs in nature and construction that is achieved when two quantities have the same proportion as the proportion of their sum to the larger of the two quantities. This is known as the golden ratio , which has a value of approximately 1.618 . We know that it sounds very complicated, but things will get clearer shortly. The formula for the golden ratio, given two quantities a a a and b b b is:

The golden ratio calculator is handy to compute this ratio.

The golden ratio can be seen in architecture and in general with shapes, such as the rectangle. A rectangle is golden if, with the given width w = a w = a w = a and length l = a + b l = a + b l = a + b , the ratio ( a + b ) / a = a / b (a+b)/a = a/b ( a + b ) / a = a / b yields the value of approximately 1.618. The golden ratio is the limit of the ratios of consecutive Fibonacci numbers and a non-terminating decimal. Thus we use the approximate value of 1.618. The golden rectangle calculator will compute the length and width that achieves the golden rectangle.

In geometry, the proportion calculator comes in handy when working with similar polygons. By definition, two polygons are said to be similar if their sides are in proportion. The most common application of this is with triangles. The law of sines for triangles is based on the fact that there is a proportional relationship between the sides and angles of a triangle.

The ability to solve proportions may also come in handy when dealing with chemical reactions. The law of multiple proportions is one of the most fundamental rules of stoichiometry, discovered by the British chemist John Dalton. It is the methodology of calculating the amounts of reactants and products of chemical reactions. For help with this, check out our theoretical yield calculator . Dalton's full statement looks like this:

If two elements form more than one compound between them, then the ratios of the masses of the second element which combine with a fixed mass of the first element will be ratios of small whole numbers.

Less scientifically speaking, if we divide masses of atoms of different elements forming a single particle (e.g., CO₂ – carbon dioxide), we always receive a constant ratio specific for this particle. The result will consist very often of small numbers.

Let's show it on an example and calculate the ratio for the sulfuric acid – H₂SO₄ :

  • First, we have to count the numbers of atoms of particular elements forming the sulfuric acid. We have 2 atoms of hydrogen H, 1 atom of sulfur S, and 4 atoms of oxygen O.
  • Secondly, we need to calculate the total mass of atoms of each element. Single hydrogen atom weighs 1 u (u stands for atomic mass unit), one atom of oxygen weighs 16 u, and one atom of sulfur has a mass of 32 u.
Joint mass of hydrogen atoms is: 2 × 1   u = 2   u 2 \times 1 \ \mathrm u = 2 \ \mathrm u 2 × 1   u = 2   u , The total mass of oxygen in the sulfuric acid particle is: 4 × 16   u = 64   u 4 \times 16 \ \mathrm u = 64 \ \mathrm u 4 × 16   u = 64   u , There is only one atom of sulfur in this particle, so the weight of sulfur is equal to 32   u 32 \ \mathrm u 32   u .
  • The last thing to do is to divide all numbers one by another. The only condition is that we have to maintain all numbers as whole numbers. We cannot create fractions. It will look like this:
  • And that’s it! We have received a ratio of small numbers for a particle of sulfuric acid.

Thanks to this knowledge we can tell that if we have 1 g (or any any other unit of mass) of hydrogen we need to add 16 g of sulfur and 32 g of oxygen to be sure that all atoms of each element will take part in the reaction and that there will not be any leftovers.

We have a task for you! Check (by using our proportions calculator) how many grams of hydrogen and oxygen can react fully with 352 grams of sulfur creating sulfuric acid (you can find the answer at the end of this text).

There are some other examples of proportional relationships in chemistry. The molarity shows the relationship between a number of moles of a certain solute (a dissolved substance) and a volume of solution. Some amateur chemists may be interested in the ABV (alcohol by volume), representing the relation between the volume of alcohol and the total volume of a drink.

After a quick visit to the world of chemistry, now it is time to see whether we can find our beloved proportions in finances. In fact, we can! Some of the taxes that we pay are proportional taxes. It means that the tax rate is fixed and everyone has to pay the same percentage of their income (or any other value undergoing proportional taxation).

Let’s illustrate it with an example. The proportional tax rate is 15%. Person X has an income of 15,000$ so the tax that he or she will have to pay at the end of the tax year will be equal to:

In turn, person Y earns 125,000$. However, the proportional tax definition requires the rate to be fixed, so to calculate the tax that he or she will have to pay we can use a similar formula:

Although the amount of tax paid by the person Y is greater than the tax of person X, it is the same part of their income as a whole, namely 15/100 or 15%.

Another type of tax (probably the most popular one) is a progressive tax. It is similar to the proportional tax as you also have to pay a certain percent of your income. The difference is that this percentage (or tax rate) changes with an increase of income. In progressive tax, there are specific tax rates for certain ranges of income value. For example, people of income under 100,000$ may have to pay 20% of their earnings, while people with an income over 100,000$ may have a tax rate of 25%.

Answer to the question: By the law of multiple proportions, 352 grams of sulfur can react fully with 22 grams of hydrogen and 704 grams of oxygen, creating sulfuric acid.

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Proportion Calculator

Enter an unknown variable (x) and 3 values in the input boxes below to find the proportion between two ratios using proportions calculator.

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Table of Contents:

What are proportions?

Steps to solve proportions, how to solve proportions, frequently asked questions .

Give Us Feedback

Proportion calculator is an online tool that solves two fractions for the variable x. It evaluates the equality between two fractions with cross multiplication.

Proportion is a statement which tells us that two ratios are equal. The symbol of proportion is ‘::’ and ‘=’.

For example, two ratios are in proportion if they are equal to each other.

Proportions

To solve the proportions first set the two proportions/ratios equivalent to each other with the one missing part that is represented by the unknown variable such as “x, y, z”. Follow the below steps to solve the proportions.

  • Set the two fractions across the equal sign and place the one variable according to your choice.
  • Apply the cross multiplication on both sides of the equal sign by multiplying the numerator of one side with the denominator of the other or vice versa and separating the variables or constant by an equal sign.
  • Simply the variable side by multiplying or dividing the coefficient according to the situation with the other side of the equal sign that is attached to the variable.

Alternatively, to verify your answer or overcome by the long process of calculations use our Proportion Calculator which provides answers in seconds with detailed steps.

Solving proportions is easier than you think. Let’s solve a proportion with an example.

If ratio of pizzas to burgers is 3/5 in a party, how many of burgers will be there if there are total of 15 burgers.

Step 1: Construct a proportion using the given values and x .

Step 2: Apply cross multiplication to the above equation.

5x = 3 × 15

So, there will be 9 pizzas with 15 burgers.

Use proportion solver above to solve fractions.

What is the proportion?

A proportion is a relation or equation that compares two different ratios and tells how the two ratios are equal to each other. For example: if the total class size is 100, with 20 boys and 80 girls, then the proportion of boys is 20/100 which is 20% while the proportion of girls is 80/100 which equals 80%.

Is proportion a type of ratio?

Yes , proportion is the type of because both are used in the intent of the comparison of fractions of numbers or quantities. A ratio is the comparison of two numbers or quantities while proportion is the comparison of the two ratios.

What are the types of Proportion?

There are three types of proportions such as direct proportion, inverse proportion, and Continuous proportion.

  • Direct proportion is the proportion of the two ratios in which the values of one side ratio increase if the value of the other also increases, and vice versa.
  • Inverse proportion is the comparison of two ratios in which the denominator of one ratio decreases then the numerator of the other increases, and vice versa. For example, as one doubles, the other one halves.
  • Continuous proportion is the comparison of ratios, if the consequent and antecedent of two ratios are not the same then multiply the term that converted the ratios into the continued proportion.
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  • The ratio of girls to boys is 5:4. There are 110 girls. How many boys are there?
  • The ratio of girls to boys is 7:5. There are 120 girls. How many boys are there?

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Proportion Calculator

Use this calculator to easily solve proportion equations. Enter any three numbers in the denominators and enumerators for the two proportions and the fourth will be calculated for you to make Proportion 1 and Proportion 2 equal (having the same constant of proportionality ).

  • What is a proportion?
  • How to solve proportions?
  • Example calculation
  • What is constant of proportionality?

    What is a proportion?

From mathematics, a proportion is simply two ratios in an equation, for example 1/2 = 50/100, 75/100 = 3/4, 9/10 = 90/100. If one variable is a product of the other variable and a constant, the two variables are called directly proportional - in this case x/y is a constant ratio. If the product of two variables is a constant, the two are inversely proportional - in this case x·y is a constant.

Proportions are used in problems involving changing numbers while keeping a ratio constant . For example, if the price of a hamburger has risen by 10%, you might express this as a proportion: old price / 100 = new price / 110, so if you know the old price you can solve the proportion equation to find the new price. If the old price was $5, then $5/100 = x/110, then x = $5 / 100 * 110 = $5.5. While you can certainly do such calculations using our proportions calculator above, percentage math is easier using our percent calculator .

Proportions are also often used in unit conversion, where the difference between units of the imperial and metric system are proportionally constant. Scaling and resizing often require the calculation of proportions, such as if you know the desired width of an image, photo or video, you can figure out the required height to preserve the aspect ratio. Similarly, to read distances on a map you need to be able to solve proportions.

    How to solve proportions?

Solving proportional equations is fairly trivial, if you know the basic equation transformation laws - multiplying and dividing both sides by the same number is all that is required. Of course, with the help of our proportion calculator all the work is done for you.

    Example calculation

Say you have the proportion 4/5 = 12/x and need to find x. To solve for x, you need to first multiply both sides by x, resulting in x · 4/5 = 12. Then you divide both sides by 4/5, getting x = 12 / (4 / 5) = 12 / 4 * 5 = 3 * 5 = 15. Therefore, 4 is to 5 as 12 is to 15.

    What is constant of proportionality?

In solving proportions you can encounter the term "constant of proportionality", also known as the "unit rate" or "constant of proportional variation". It expresses the relationship of two variables (say x and y) when they are multiplicatively connected to a constant so that either their ratio or their product yields a constant. So we either have c = x / y or c = x · y where c is then the constant of proportionality between x and y.

With direct proportionality we have c = x / y which we can also express that as c / 1 = x / y and solve for c using the calculator above. If y = 5 for x = 20, then we have c / 1 = 20 / 5 hence c = 4. With inverse proportionality c = x · y which we can also express that as c / x = y / 1 and again solve for c. If y = 2 for x = 10, then we have c / 10 = 2 / 1 hence c = 20.

Common examples of direct proportionality include:

  • the circumference of a circle and its diameter (the constant is known as π)
  • the distance travelled by a moving object under constant speed is proportional to the time (the constant is the speed, you can explore this topic using our speed, distance & time calculator
  • the relationship between the net force acting on an object and its acceleration . This relationship is governed by Newton's second law and the constant of proportionality is the object's mass.

Examples of proportionality varying inversely include:

  • the number of people working on a given set task, if each has the same productivity , is inversely proportional to the time it will take to complete that task. The constant is the individual productivity - how long it would take a single worker to compelte the entire work.
  • the number of identical pipes you need to fill the volume of a swimming pool in a given number of minutes. The constant is the time it takes a single pipe to fill in the pool. E.g. if you have 2 pipes (x) each with a debit of 1m 3 /s you can fill a 600m 3 pool in 5 minutes (y). However, you only need 1 minute if you have 5 times the number of pipes (10 in total). The constant (c) in this case is 10, that is it takes 10 minutes for a single pipe to fill in the entire pool ( calculation ).

Our proportions calculator can be used to construct and check many more examples.

Cite this calculator & page

If you'd like to cite this online calculator resource and information as provided on the page, you can use the following citation: Georgiev G.Z., "Proportion Calculator" , [online] Available at: https://www.gigacalculator.com/calculators/proportion-calculator.php URL [Accessed Date: 19 Sep, 2024].

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About Proportion Calculator

What is a proportion, understanding the formula of proportion:.

The essence of a proportion lies in its formula, which allows us to equate two ratios and solve for an unknown value. The basic formula for proportion is represented as:

\[ \frac{a}{b} = \frac{c}{d} \]

  • (a) and (b) are values from the first ratio.
  • (c) and (d) are values from the second ratio.

To solve for a missing value in a proportion, you can cross-multiply and then solve for the unknown variable. For instance, if you know (a), (b), and (c) but want to find (d), you can rearrange the formula:

\[ d = \frac{b \times c}{a} \]

Our Proportion Calculator not only gives you the result but also provides a step-by-step breakdown using this formula, ensuring you understand the calculation process thoroughly.

Watch the 1-min video to learn how to use the Proportion Calculator

  • Proportion (mathematics) - Wikipedia
  • Worked example: Solving proportions - Khan Academy

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Proportion Calculator

Common proportion:, ratio calculator: master the little secrets of proportion calculation easily.

Have you ever been troubled by solving proportion problems? Now, with our ratio calculator , everything becomes simple! This little tool is not only suitable for students and teachers but also for anyone who wants to quickly solve proportion problems.

What are proportions?

proportions might sound a bit abstract, but it's everywhere. Whether it's mixing ingredients while cooking or comparing prices while shopping, proportions are at work. Simply put, a proportion is a mathematical method that tells us that two rates are equal.

How to Use the Ratio Calculator?

Using the ratio calculator is as simple as counting. Enter the three values you know and one unknown variable (such as x), click the mouse, and the answer comes out!

Handy Tips for Solving Proportions Manually

Although there is a ratio calculator, understanding how to solve proportions manually is also very useful. Here's a little example:

  • Write down the proportion: for example, 9/16 = 1080/X.
  • Cross-multiplication: 9X = 16 × 1080.
  • Find the value of X: X = 17280 ÷ 9 = 1920.

Ratio Calculator is your little math assistant, making complex proportion problems a breeze. Moreover, understanding the calculation of proportions can make you more flexible in life. For more learning and life tips, welcome to visit our website. Our proportion calculator is always ready to help you, making math no longer difficult!

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Proportion Calculator

Enter an unknown variable (x) and 3 values in the input boxes below to find the proportion between two ratios using proportions calculator.

share-it

Table of Contents:

What are proportions?

How to solve proportions.

Proportion calculator is an online tool that solves two fractions for the variable x. It evaluates the equality between two fractions with cross multiplication.

Proportion is a statement which tells us that two ratios are equal. The symbol of proportion is ‘::’ and ‘=’.

For example, two ratios are in proportion if they are equal to each other.

Proportions

Solving proportions is easier than you think. Let’s solve a proportion with an example.

If ratio of pizzas to burgers is 3/5 in a party, how many of burgers will be there if there are total of 15 burgers.

Step 1: Construct a proportion using the given values and x .

Step 2: Apply cross multiplication to the above equation.

5x = 3 × 15

So, there will be 9 pizzas with 15 burgers.

Use proportion solver above to solve fractions.

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Proportion Calculator

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Quick-Start Guide

The calculator uses cross multiplication to convert proportions into equations which are then solved using ordinary equation solving methods. Be sure to enter something in each input box before clicking solve. Use the following as a guide:

Any lowercase letter may be used as a variable.

Exponents are supported on variables using the ^ (caret) symbol. For example, to express x 2 , enter x^2. Note: exponents must be positive integers, no negatives, decimals, or variables. Exponents may not be placed on numbers, brackets, or parentheses.

Parentheses and Brackets

Parentheses ( ) and brackets [ ] may be used to group terms as in a standard equation or expression.

Multiplication, Addition, and Subtraction

For addition and subtraction, use the standard + and – symbols respectively. For multiplication, use the * symbol. A * symbol is not necessiary when multiplying a number by a variable. For instance: 2 * x can also be entered as 2x. Similarly, 2 * (x + 5) can also be entered as 2(x + 5); 2x * (5) can be entered as 2x(5). The * is also optional when multiplying parentheses, example: (x + 1)(x – 1).

Order of Operations

The calculator follows the standard order of operations taught by most algebra books – Parentheses, Exponents, Multiplication and Division, Addition and Subtraction. The only exception is that division is not supported; attempts to use the / symbol will result in an error.

Division, Square Root, Radicals, Fractions

The above features are not supported.

Special Note

If either side of the proportion has a numerator and denominator that share a common factor with a variable, the calculator will report an erroneous solution. Example: 1/2 = x/x will cause the calculator to report 0 as a solution, even though there is no solution.

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Proportion Calculator

This proportion calculator can solve ratios in case a value is missing or even two values are missing from the given proportion or can evaluate as true or false any proportions.

Other Tools You May Find Useful

■ Decimal Calculator

■ Ratio Calculator

■ Fraction Calculator

■ Derivative Calculator

How does this proportion calculator work?

This math tool allows you solve ratios in any of the following situations:

  • By specifying two numbers (A and B in the first fraction area)  from the four numbers of the proportion (decimals are allowed) it will display the complete and true ratio by filling in the right values for the rest of two numbers (C and D);
  • In case you input three numbers out of the four of the proportion (A, B AND either C or D) (decimals are allowed) it will display the ratio meaning that is returns the value for the number missing (C or D by case);
  • Whenever you input all the components of the proportion it checks if the proportion is true or false.

The formulas used by this proportion calculator are:

  • if you enter only A and B in order to determine the C and D figures, it multiplies both A and B by 2 in order to return true ratio values for C and D.
  • if you complete the A, B and C to find the D value, it solves the expression in which D = C * (B / A). The same goes in case you input D and try to discover the C number.
  • When all numbers are given (A, B, C, D) in order to assess whether the proportion is true or false it will calculate the value of the division of A by B (A/B), and the value of the division of C by D then compares it. If the two resulting values are equal then the ratio is TRUE, otherwise is FALSE.

Few examples of calculations

1. A = 4, B = 9 then C = 8 and D = 18

2. A = 7, B = 13 and C = 6 then D = 11.1428571429

3. A = 28, B = 34 and D =15 then C= 12.3529411765

4. A = 13, B = 15, C = 2 and D = 33 then 13 : 15 = 2 : 33 is FALSE.

5. A = 11, B = 7, C = 29 and D = 18.4545454545 then 11 : 7 = 29 : 18.4545454545  is TRUE.

free{}calculator

Proportion calculator, what is proportion .

Proportion is a mathematical concept that compares two or more values to each other. It is used to determine the relationship between two or more values and is expressed as a ratio or a fraction. Proportion is used in many areas of mathematics, including geometry, algebra, and statistics. It is also used in everyday life to compare sizes, amounts, and other values.

What is Proportion Calculator ?

A Proportion Calculator is a tool used to solve proportion problems. It can be used to find the missing value in a proportion, given the other values. It can also be used to find the ratio of two numbers.

How to Calculate Proportion ?

Proportion is the comparison of two numbers or ratios. To calculate a proportion, divide one number by the other. For example, if you have two numbers, 10 and 20, the proportion would be 10/20, which is equal to 0.5.

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Proportion Calculator

Calculate proportion, simple proportion calculator.

Simple proportion is a mathematical method that allows solving problems involving directly or inversely proportional quantities. For example, if 5 liters of juice yield 10 glasses, how many glasses can you get with 8 liters of juice? The simple proportion helps to find the answer in a simple and quick way.

To apply the simple proportion, you need to identify four related values, with one of them being unknown. These values should be organized in a table with two columns and two rows, leaving the unknown value represented by x. Then, perform a cross-multiplication between the values and isolate the unknown value.

The simple proportion can be direct or inverse. The direct simple proportion is used when the quantities are directly proportional, meaning that when one increases, the other also increases in the same proportion, or when one decreases, the other also decreases in the same proportion. The inverse simple proportion is used when the quantities are inversely proportional, meaning that when one increases, the other decreases in the same proportion, or when one decreases, the other increases in the same proportion.

To facilitate the calculation of simple proportion, there are online calculators that allow you to input the available data and get the result automatically. Some calculators also show the solution steps and the formula used.

How to calculate direct simple proportion?

To calculate direct simple proportion, follow these steps:

  • Identify the two quantities involved in the problem and determine if they are directly proportional.
  • Organize the four values related to each other in a table with two columns and two rows, leaving the unknown value represented by x.
  • Perform a cross-multiplication between the values and equate the products.
  • Isolate the unknown value x and solve the equation.

The formula for direct simple proportion is:

x = (b x c) / a

Where x is the unknown value, a and b are the values from the first row of the table, and c is the value from the second row of the table that is in the same column as x.

How to calculate inverse simple proportion?

To calculate inverse simple proportion, follow these steps:

  • Identify the two quantities involved in the problem and determine if they are inversely proportional.

The formula for inverse simple proportion is:

x = (a x c) / b

What are directly proportional quantities?

Directly proportional quantities are those that vary in the same ratio, meaning that when one increases, the other also increases in the same proportion, or when one decreases, the other also decreases in the same proportion. For example, the price of a product and the quantity purchased are directly proportional, as buying more units results in a higher payment.

What are inversely proportional quantities?

Inversely proportional quantities are those that vary in the inverse ratio, meaning that when one increases, the other decreases in the same proportion, or when one decreases, the other increases in the same proportion. For example, travel time and average speed are inversely proportional, as higher speed results in less time needed to cover a certain distance.

References:

  • Simple and Compound Proportion - Toda Matéria
  • Simple and Compound Proportion
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  • Proportion Calculator

This online Proportion Calculator is used to solve proportion problem and find the missing value in a proportion, given three known values.

Solving proportions

Proportion is defined as a statement that two ratios are equal. For example, 1/3 = 5/15 . This can also be written in the form 1:3 = 5:15 . When two ratios are of equal value, then the values are said to be in equal proportion. The symbol of proportion is “ :: ” or “ = ”.

In case three numbers of a general proportion A/B = C/D are known, the forth number can be easily found using straightforward calculations. This process is called solving a proportion.

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Check out our other math calculators such as Golden Ratio Calculator or Cube Root Calculator .

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Helping with Math

Proportion Calculator

A proportion calculator is a tool that helps you solve proportion problems. A proportion is a statement that two ratios are equal.

Enter Information:

What is Proportion?

In mathematics, proportion refers to the relationship between two ratios that are equal to each other. A proportion is a statement of equality between two ratios, which are usually written as fractions . It expresses the relationship between the part and the whole or between two parts. The general form of a proportion is:

Where a and b are the first ratio, and c and d are the second ratio. The proportion states that the first ratio is equal to the second ratio. Proportions can be used to solve various problems related to ratios and proportions in different fields such as mathematics, science, and finance.

Proportion Formula

The proportion formula is:

  • a and b are the first pair of proportional values
  • c and d are the second pair of proportional values

This can also be written as:

a : b = c : d

The cross- multiplication property can also be used to find the missing value in a proportion. For example, if we know a, b, and c, we can find d using the formula:

d = (b * c) / a

Cross Multiplication for Solving Proportions

Cross multiplication is a method used to solve proportions, particularly those involving two ratios that are equal to each other. The steps for using cross multiplication to solve a proportion are as follows:

  • Write the proportion as two equal fractions, with one fraction on each side of the equal sign.
  • Cross-multiply by multiplying the numerator of one fraction by the denominator of the other fraction.
  • Simplify the resulting equation by multiplying or dividing both sides by the same factor, if necessary.
  • Solve for the variable by isolating it on one side of the equation.

Here’s an example:

Solve for x: 3/5 = 9/x

  • Write the proportion: 3/5 = 9/x
  • Cross-multiply: 3x = 45
  • Simplify: divide both sides by 3, x = 15
  • Check: substitute x = 15 back into the original equation to make sure both sides are equal: 3/5 = 9/15 = 3/5

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Ratio Calculator

The ratio calculator readily finds an equivalent form of the ratios and performs various operations on them including simplifying ratios, making them larger and smaller, with calculations shown.

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An online ratio calculator helps you to determine identical ratios by giving three out of four parts of two ratios. Also, this ratios calculator works best to find the fifth & sixth parts from the three ratios by giving any four parts. Our ratio solver performs the following seven operations on both two & three ratios. Also, you can try our online proportion calculator that helps you to solve the proportion problems easily with different methods.

What Is a Ratio?

“Ratio is defined as the comparison of two quantities in mathematics” Our ratio finder finds the exact comparison among numbers to quantify the relationship between them.

How To Calculate Ratio?

The ratio comprises two parts, the numerator & denominator just the same as the fraction. If we have two ratios and want to calculate the ratio for the missing value in the ratio, simply follow the given steps:

  • Write ratios in the form of fractions and put any variable (x or y) in the missing value
  • Set the fractions equal to each other
  • Now cross-multiply the given ratios to form fractions
  • Solve for the missing variable
  • Finally, try the ratio calculator to verify your answer

You can get assistance to our online fraction calculator to add, subtract, multiply or divide the two or three fraction. Here we have a manual example to clear the understanding:

Important Cases:

Our calculator helps you to find results for the following ratio problems:

Missing Value:

Suppose we have the ratio as:

Product of extremes = Product of means

x = 6.66…

x = 6.67 (Round off)

Comparison of Ratios:

If you are given two ratios:

3:5 & 5:9

Here we have:

3:5 = 3/5 = 0.6

5:9 = 5/9 = 0.55

Hence proved that:

3:5 > 5:9

Reducing a Ratio:

Suppose we have the given ratio as:

To reduce this ratio, we have to find a common factor for both numbers:

4 = 2*2 6 = 2*3

Common Factor = 2

Now we have:

So the new reduced ratio is 2:3

You can also verify the results by inputting all these values in our ratio calculator.

Scaling a Ratio:

Consider the same ratio in the above case i.e. 4:6 and increase it by a factor of 6

The final increased ratio is:

We encourage you to use our ratio calculator if you’re going to solve the complex ratios of large numbers.

Working of Online Ratio Calculator:

Our calculator is an accurate tool to simplify & find the unknown value in the ratio. You just have to stick to the following points for calculating ratios:

  • First of all, hit the tab to choose how many ratios you want to do the calculations. It is either A: B or A:B:C
  • Very next, select the method of calculation from the dropdown of this calculator
  • Then, enter the fields according to the selected input parameters
  • Tap Calculate
  • Missing value ( s )
  • Simplification of ratio
  • Visual representation of the ratio (Pie-chart)

What Is The Golden Ratio?

When the two quantities have the same ratio as the ratio of their sum to the larger of the two quantities, then the ratio is termed as golden ratio. For example, the quantities expressed in x & y, then the golden ratio between x & y is (x+y)/x = x/y

Ratio Calculator

Use this online tool to solve for the unknown value in the proportion.

What is a Ratio?

Using the ratio calculator.

Resort to the help of this amazing ratio calculator when you have you settle ratio/proportion problems and check equivalent fractions. Despite the fact that you cannot enter a ratio of 4/5 into this calculator, it accepts values such as 4:5, for example, 4/3 should be written as 4:3. Moreover, our ratio calculator is also able to write down the list of equivalent ratios and process decimal numbers.

How to Calculate Ratios

You may also want to try our Aspect Ratio Calculator.

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Title: fast analysis of the openai o1-preview model in solving random k-sat problem: does the llm solve the problem itself or call an external sat solver.

Abstract: In this manuscript I present an analysis on the performance of OpenAI O1-preview model in solving random K-SAT instances for K$\in {2,3,4}$ as a function of $\alpha=M/N$ where $M$ is the number of clauses and $N$ is the number of variables of the satisfiable problem. I show that the model can call an external SAT solver to solve the instances, rather than solving them directly. Despite using external solvers, the model reports incorrect assignments as output. Moreover, I propose and present an analysis to quantify whether the OpenAI O1-preview model demonstrates a spark of intelligence or merely makes random guesses when outputting an assignment for a Boolean satisfiability problem.
Subjects: Computation and Language (cs.CL); Disordered Systems and Neural Networks (cond-mat.dis-nn); Artificial Intelligence (cs.AI)
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  25. Fast Analysis of the OpenAI O1-Preview Model in Solving Random K-SAT

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