Ratio calculator
Pick what you need, type the numbers, and get the answer with exact arithmetic. Decimals and fractions such as 1.5 or 3/4 are fine; the tool clears them before simplifying.
Runs in your browser: nothing you enter is sent anywhere.
How to use it
- Choose the mode.
- Enter A and B. For scaling or solving, also enter C.
- Read the headline result. The rows beneath give the exact decimal values and the scale factor.
How it works
Simplifying cross-multiplies the two terms into whole numbers and divides by the GCD, all in exact fractions, so 0.1:0.3 gives 1:3 without floating-point noise. Scaling and solving use the factor C / A: the new B is B × C / A. Percentages divide each term by A + B.
Worked example
A recipe uses 12 cups of flour to 8 cups of water, a ratio of 12:8.
- Simplified: 12:8 = 3:2.
- To use 30 cups of flour, the scale factor is 30 / 12 = 2.5, so water becomes 8 × 2.5 = 20, giving 30:20.
- As percentages, flour is 12/20 = 60% and water 40%.
Tips
- Keep both terms in the same unit before comparing, such as grams with grams.
- Results with a repeating decimal, like 2/3, are shown to eight decimal places.
- A ratio of 0:5 simplifies to 0:1, and 5:0 to 1:0.
Frequently asked questions
How do you simplify a ratio?
Divide both terms by their greatest common divisor. For 12:8 the GCD is 4, so the ratio is 3:2. If the terms are decimals or fractions, the tool first multiplies both by the same number to make whole numbers, so 1.5:2.5 becomes 3:5.
How do you solve A:B = C:D for D?
Cross-multiply. A × D = B × C, so D = B × C / A. For 3:4 = 9:D, D = 4 × 9 / 3 = 12. The scale factor is C / A, here 3, and it multiplies B as well.
How do I turn a ratio into percentages?
Add the terms and divide each by the total. In 3:1 the total is 4, so the parts are 3/4 = 75% and 1/4 = 25%.
Can a ratio have more than two terms?
Yes, as in 2:3:5, but this calculator handles two-term ratios. For a longer ratio, work in pairs or divide every term by the GCD of all of them.
Is 3:2 the same as 1.5?
As a size comparison yes, because 3 ÷ 2 = 1.5. A ratio and a fraction differ in meaning, though. 3:2 compares part to part, while 3/5 compares one part to the whole 3 + 2.