Ratio Calculator

What this calculator does

So, you have two ratios that are equal, and you know three of the four numbers involved but not the fourth. This tool finds the missing one. You set up the two ratios as an equation, leave one box blank, and it solves for the value that makes them equal.

The layout shows two fractions side by side with an equals sign between them. Fill in three of the four positions, leave one empty, and press Calculate.

How to use it

1. Enter three of the four values across the two ratios.
2. Leave exactly one box blank, the value you want to find.
3. Press Calculate.

It needs precisely three numbers with one gap. If you fill in all four, or leave more than one blank, it will ask you to leave just one empty.

What a proportion is

A proportion is a statement that two ratios are equal. Written as fractions, it looks like one fraction equals another, such as 3 over 4 equals 6 over 8. Both sides represent the same relationship between two quantities, just at a different scale. When one of the four numbers is unknown, the equality still pins it down completely, because there is only one value that keeps the two ratios matching. Solving a proportion is finding that value, and it is one of the most useful moves in everyday arithmetic.

How it solves: cross-multiplication

The tool uses cross-multiplication, the standard technique for proportions. In an equation of two fractions, the product of one numerator and the opposite denominator equals the product of the other numerator and its opposite denominator. Multiplying across the two known corners and dividing by the third number gives the missing one. So if three of the four are known, a single multiply and divide delivers the fourth. The tool figures out which position is blank and applies the right arrangement automatically, giving a decimal to three places when the answer is not a whole number.

Where proportions come up

Proportions are everywhere once you start looking. Scaling a recipe up or down is a proportion: if a recipe for four needs 200 grams of flour, the amount for six keeps the same ratio. Reading a map uses proportions, converting a distance on paper to a distance on the ground. Currency conversion, mixing paint or fuel, working out unit prices, resizing an image without distorting it: all of these are the same "if this, then how much of that?" question, which is exactly what solving a proportion answers.

A worked example

Suppose you set up 3 over 4 equals 6 over a blank box. Three of the four numbers are known: 3, 4, and 6. Cross-multiplying, you take 4 times 6, which is 24, and divide by 3, which gives 8. So the missing value is 8, and the proportion reads 3 over 4 equals 6 over 8. Both sides reduce to the same ratio, confirming the answer.

Questions people ask

What does this tool solve?

A proportion, meaning two equal ratios. Given three of the four numbers, it finds the fourth that keeps the ratios equal.

How many boxes do I leave blank?

Exactly one. Fill in three values and leave the one you want to find empty.

How does it work it out?

By cross-multiplication: multiply the two known diagonal numbers and divide by the third to get the missing value.

Why is my answer a decimal?

When the missing value is not a whole number, the tool gives it to three decimal places.

What if I just want to reduce a ratio?

That is a different job. The ratio simplifier calculator reduces a single ratio to its lowest terms.

References

On proportions and ratios. A proportion states that two ratios are equal, which lets a missing term be found by cross-multiplication.

1. Eric W. Weisstein, "Proportional," from MathWorld, a Wolfram resource, on proportional quantities and the constant ratio between them.
2. Eric W. Weisstein, "Ratio," from MathWorld, a Wolfram resource, on the ratio of two numbers as a quotient.