Ratio
calculator.
Simplify a ratio of two or three terms, solve a proportion for the missing value, or divide an amount in a given ratio. Decimals and fractions are handled exactly.
12 : 18 simplifies to 2 : 3.
- As 1 : n
- 1 : 1.5
- Shares of the total
- 40% / 60%
divide every term by the greatest common divisor (after clearing decimals and fractions)Parts of
a whole.
- Simplify: clear decimals and fractions, then divide every term by the greatest common divisor.
- Solve A : B = C : x with x = B × C ÷ A.
- Split a total: each part = total × its term ÷ the sum of the terms.
How do you simplify a ratio?
Divide every term by their greatest common divisor. 12 : 18 has a GCD of 6, so it simplifies to 2 : 3. With decimals, scale up first: 1.5 : 2.25 : 0.75 becomes 150 : 225 : 75, which simplifies to 2 : 3 : 1.
How do you solve a proportion?
A proportion says two ratios are equal. If 3 cups of flour make 4 servings, then 4 : 3 = 9 : x for 9 servings, and x = 3 × 9 ÷ 4 = 6.75 cups. Cross-multiplying gives the same result: 4x = 27.
Splitting an amount in a ratio
Add the terms to find how many equal shares there are, then give each person their number of shares. $1,000 in the ratio 2 : 3 is 5 shares of $200, so $400 and $600.
Worked examples.
Simplify 12 : 18
A class has 12 girls and 18 boys.
2 : 3 (40% / 60%).
Load this exampleA ratio with decimals
1.5 : 2.25 : 0.75.
2 : 3 : 1.
Load this exampleSolve a proportion
A recipe uses 3 cups of flour for 4 servings. How much for 9 servings?
6.75 cups (4 : 3 = 9 : 6.75).
Load this exampleSplit an amount
Split $1,000 between partners in the ratio 2 : 3.
$400 and $600.
Load this exampleWhat this calculator
does not do.
- Terms must be positive; up to three terms.
- Split amounts are not rounded to currency, so tiny rounding may be needed when paying out.
Common questions.
Is 2 : 3 the same as 2/3?
Not quite. 2 : 3 compares two parts, so the first part is 2/5 of the whole, not 2/3.
How do I write a ratio as 1 : n?
Divide every term by the first. 4 : 10 becomes 1 : 2.5; the calculator shows this form for every ratio.
- Math is Fun, Ratios — ratios, simplifying and sharing
Exact rational arithmetic with BigInt. Tests include decimal and fraction terms, three-term ratios, proportions with repeating answers, and 300 randomized scaled ratios that must simplify back to coprime terms with the same value.
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