Ratio Calculator

How to simplify a ratio

Divide every term of the ratio by the same number until they are the smallest possible whole numbers.

• Whole numbers: divide both terms by their greatest common divisor (GCD). 12 : 18 divided by 6 is 2 : 3.
• Decimals: first scale the numbers to whole numbers, then divide by the GCD. 1.5 : 2.5 is the same as 15 : 25, which simplifies to 3 : 5.
• Three terms: divide by the GCD of all three. 2 : 4 : 6 simplifies to 1 : 2 : 3.

The calculation uses whole-number arithmetic, so decimals cause no rounding errors. A ratio that contains 0 works (0 : 5 simplifies to 0 : 1). A ratio where every term is 0 cannot be simplified and shows an error.

Ratio value and share

• Ratio value = a ÷ b. For 3 : 5 it is 3 ÷ 5 = 0.6 (not available if b is 0).
• Share of the whole = each term ÷ the sum of all terms. For 3 : 5, a is 37.5% and b is 62.5%.

How to solve a proportion

In a proportion a : b = c : d, the cross products are equal: a × d = b × c. The missing number is

• a = b × c ÷ d b = a × d ÷ c c = a × d ÷ b d = b × c ÷ a

Leave the box you want to find empty and fill in the other three. If you fill in all four, the calculator checks whether the two ratios are equal.

If the answer does not divide evenly, the calculator shows it rounded to 6 decimal places and also as an exact fraction. If it divides evenly, the value shown is exact.

Examples

• 1.5 : 2.5 → 3 : 5 (ratio value 0.6)
• 2 : 4 : 6 → 1 : 2 : 3
• 2 : 3 = 4 : □ → □ = 3 × 4 ÷ 2 = 6
• Scaling a recipe: 200 g of flour goes with 130 g of water. How much water for 500 g of flour? 200 : 130 = 500 : □ → □ = 325 g

Notes

• Numbers must be 0 or more, with up to 9 digits before the decimal point and 6 decimal places. Negative numbers are not accepted.
• In a proportion, if the number you divide by is 0 (for example, a when you are finding d), the missing number cannot be found, and the reason is shown.
• A proportion only describes a proportional relationship (when a doubles, b also doubles). It does not apply to relationships that are not proportional.
• To work with fractions, use the Fraction Calculator. To find what percent one number is of another, use the Percentage Calculator.

Frequently asked questions

What is the difference between a ratio and a ratio value?

A ratio such as 3 : 5 compares two numbers. The ratio value is that comparison as a single number: 3 ÷ 5 = 0.6.

What happens if the answer to a proportion does not divide evenly?

For 3 : 7 = 1 : □, the missing number is 7 ÷ 3, which does not divide evenly. The calculator shows 2.333333 (rounded to 6 decimal places) and the exact fraction 7/3.

Can a ratio be left as decimals?

A ratio can be written with decimals, but the "simplest ratio in whole numbers" uses the smallest whole numbers. 1.5 : 2.5 and 3 : 5 are the same ratio.