How it works
A proportion states that two ratios are equal. Cross-multiplying both sides and rearranging gives x = (B × C) ÷ A.
The calculation is one multiply and one divide. For 2 : 5 = 6 : x, A is 2, B is 5 and C is 6: multiply B by C to reach 30, then divide by A to get 15. Keep each ratio in the order the problem states it, because swapping A and B turns the proportion into its reciprocal and answers a different question.
A percentage is the same proportion with 100 as one of the terms, which is why 25 : 100 = 8 : x and the statement that 8 out of 25 is 32% are two ways of writing a single calculation; the guide to percentages works through that link.
Formula: A : B = C : x, so x = (B × C) ÷ A
Examples
Scaling a recipe
If 2 cups of flour need 3 eggs, how many eggs for 6 cups? 2 : 3 = 6 : x gives x = (3 × 6) ÷ 2 = 9.
Turning a share into a percentage
8 out of 25 is the same share as x out of 100, so write 25 : 100 = 8 : x. x = (100 × 8) ÷ 25 = 800 ÷ 25 = 32, which reads as 32%. The Percentage Calculator reaches 32% from the same two numbers without setting up the proportion.
Finding a unit price from a pack size
A 250 g pack costs 3.40, so 250 : 3.40 = 100 : x gives the price of 100 g. Entering the decimals as they stand, x = (3.40 × 100) ÷ 250 = 1.36.
Common uses
- Rescaling a recipe or a mixture when one ingredient quantity changes
- Finding the price of a smaller quantity from a pack price and a pack size
- Splitting an amount between two people in a stated ratio such as 2 : 3
- Converting a part of a total into a percentage by using 100 as the other term
Things to keep in mind
- A cannot be zero, since it is the calculation's denominator.
- Enter values of zero or more: like the Ratio Calculator, this treats A, B and C as quantities being compared, which is not meaningful for a negative value.
- B and C can both be zero: 2 : 5 = 0 : x and 2 : 0 = 5 : x each give x = 0, since a zero quantity stays zero on both sides of the equality.
- Decimals are accepted, so 0.75 : 1 = 30 : x gives 40, the same answer as 3 : 4 = 30 : x; only A has to be above zero.
- Results are kept to 12 significant digits and displayed to 10 decimal places, so a repeating decimal such as 2 ÷ 3 is shown as 0.6666666667 rather than as an exact fraction.