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).
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- What is a proportion?
- How to solve proportions?
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
- 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 1m3/s you can fill a 600m3 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.
FAQs
A proportion is just an expression setting two ratios equal to each other, using different absolute numbers in the fractions. Proportions are written like ratios are, for example, a/b = c/d or a:b = c:d.
How do I solve a proportion? ›
The 3 ways to solve a proportion are: vertically, horizontally and diagonally (cross-multiplication). The vertical method is used if one of the ratios has a common multiple between the two quantities. The horizontal method is used if there is a common multiple between both numerators or denominators.
How to know if it is proportion or not? ›
Ratios are proportional if they represent the same relationship. One way to see if two ratios are proportional is to write them as fractions and then reduce them. If the reduced fractions are the same, your ratios are proportional.
What is a proportional relationship calculator? ›
Proportion Calculator is a free online tool that displays whether the given proportions are equal or not. BYJU'S online proportion calculator tool makes the calculation faster, and it displays the true or false in a fraction of seconds.
How to find the unknown value in a proportion? ›
To do so, we would:
- Identify the known ratio, where both values are known.
- Identify the ratio with one known value and one unknown value.
- Use the two ratios to create a proportion.
- Cross-multiply to solve the problem.
Consider two ratios a:b = b:c then as per the rule of proportion product of the mean term is equal to the product of extremes, this means b2 = ac, hence b = √ac is called mean proportion.
How to calculate sample proportion? ›
The sample proportion P is given by P=X/N, where X denotes the number of successes and N denotes the size of the sample in question. This sample proportion reflects that particular sample, and other samples of the population may result in different sample proportions.
What is an example of a proportion? ›
Proportions. A proportion is a type of ratio that relates a part to a whole. For example, in the class with with 20 men and 80 women, the total class size is 100, and the proportion of men is 20/100 or 20%. The proportion of women is 80/100 or 80%.
What is the rule for solving proportions? ›
What is the rule for solving proportions? The product of the means is equal to the product of the extremes.
What is the proportion method in math? ›
A proportion is an equation in which two ratios are set equal to each other. For example, if there is 1 boy and 3 girls you could write the ratio as: 1 : 3 (for every one boy there are 3 girls) 1 / 4 are boys and 3 / 4 are girls. 0.25 are boys (by dividing 1 by 4)
Approach: If four numbers a, b, c and d are in proportion then a:b = c:d. The solution is to sort the four numbers and pair up the first 2 together and the last 2 together and check their ratios this is because, in order for them to be in proportion, the product of means has to be equal to the product of extremes.
What does a proportion equation look like? ›
The proportional relation equation is y = k x . The letters y and x are the variables, which can change, and the letter k is the constant of proportionality. The constant of proportionality is the constant ratio between the y and x variables.
How to calculate proportion? ›
The proportion formula is used to depict if two ratios or fractions are equal. We can find the missing value by dividing the given values. The proportion formula can be given as a: b::c : d = a/b = c/d where a and d are the extreme terms and b and c are the mean terms.
How do you know if a proportion is true or not? ›
Identifying True Proportions
Express each ratio as a simplified fraction. 3. If the simplified fractions are the same, the proportion is true; if the fractions are different, the proportion is false.
How to find proportion in a table? ›
You can tell if a table shows a proportional relationship by calculating the ratio of each pair of values. If those ratios are all the same, the table shows a proportional relationship. Let's try it! Determine if the table shows a proportional relationship.
How to solve proportion problems? ›
One of the most common methods is cross-multiplication:
- First multiply across the diagonal line with two known numbers. ...
- Now divide your answer by the last remaining number in the proportion: 300 ÷ 6 = 50 {\displaystyle 300\div 6=50} .
- x = 50 {\displaystyle x=50} and the complete proportion is.
A proportion calculator is a tool designed to solve equations where two ratios are set to be equal. It can calculate unknown variables when three values are known.
What is the proportion equation? ›
A proportion is an equation in which two ratios are set equal to each other. For example, if there is 1 boy and 3 girls you could write the ratio as: 1 : 3 (for every one boy there are 3 girls) 1 / 4 are boys and 3 / 4 are girls. 0.25 are boys (by dividing 1 by 4)
What is the formula for proportionality? ›
The formula for a proportional equation is y = kx. The letters y and x are the variables in the equation. The letter k represents the constant of proportionality, which remains the same.
What is the formula for calculating direct proportion? ›
What is a Direct Proportion Equation? The equation of direct proportionality is y = kx, where x and y are the given quantities and k is any constant value.
Hence the third proportion to 4 and 8 is 16.
