A ratio compares two quantities: 12 boys to 18 girls, 1 part cement to 2 parts sand, a 16:9 screen. Ratios with the same proportion are equivalent, so 12:18, 6:9 and 2:3 all describe the same relationship. This ratio calculator reduces a ratio to lowest terms, solves the proportion A : B = C : ? when you need to scale a recipe or a mix, and shows the ratio as 1 : n and as percentage shares of the total.
Mixing ratios are common on building projects. For concrete quantities see the concrete slab calculator, and for lawn product rates the lawn fertilizer calculator. To work with fractions directly, use the fraction calculator.
How to use the ratio calculator
- Enter the two terms of the ratio, A and B. Decimals are allowed, for example 1.5 : 2.5.
- Read the simplified ratio.
- To scale, enter C, the new value for the first term. The calculator finds the matching second term.
- The unit ratio and percentage shares help when a mix is specified as "1 to n" or as parts of a total.
Formula
The proportion rule comes from cross-multiplying: A × D = B × C. Decimal ratios are first multiplied by a power of ten so both terms are whole numbers.
Worked example
A class has 12 boys and 18 girls.
- GCD(12, 18) = 6, so the ratio simplifies to 2 : 3.
- If another class with the same ratio has 30 boys, the number of girls is 18 × 30 ÷ 12 = 45.
- Unit ratio: 1 : 1.5.
- Shares: 12 ÷ 30 = 40% boys and 60% girls.
Part-to-part vs part-to-whole
A ratio of 2 : 3 is part-to-part. The whole has 2 + 3 = 5 parts, so the first quantity is 2/5 (40%) of the total, not 2/3. This matters when a mix is specified by parts. A mortar mix of 1 part cement to 3 parts sand, for example, means cement is one quarter of the dry volume. To make 8 buckets of dry mix you need 8 × 1/4 = 2 buckets of cement and 6 of sand.
To split an amount in a ratio, divide it by the total number of parts and multiply by each part. To share $250 in the ratio 2 : 3: one part is $250 ÷ 5 = $50, so the shares are $100 and $150.
Common ratios
| Context | Ratio | Meaning |
|---|---|---|
| Widescreen TV / video | 16 : 9 | width is 1.78 × height |
| Traditional photo | 3 : 2 | width is 1.5 × height |
| Roof pitch | 6 : 12 | 6 in of rise per 12 in of run (see the roof pitch calculator) |
| Map scale | 1 : 24,000 | 1 unit on the map = 24,000 on the ground |
Caveats and assumptions
- Both terms must be positive. Ratios of three or more terms aren’t supported here; simplify them by dividing every term by their common GCD.
- Decimal terms are handled up to six decimal places.
- Scaled values are rounded to four decimal places.
- Always confirm whether a mix ratio is by volume or by weight; the two give different amounts.
Frequently asked questions
How do I simplify a ratio?
Divide both terms by their greatest common divisor. For 12 : 18 the GCD is 6, so it simplifies to 2 : 3.
How do I solve a proportion?
Cross-multiply. For 2 : 3 = 10 : x, 2x = 30, so x = 15.
How do I convert a ratio to a percentage?
Add the parts to get the total, then divide each part by the total and multiply by 100. For 2 : 3, the shares are 40% and 60%.
What is a 1 : n ratio?
The ratio scaled so the first term is 1. 2 : 3 becomes 1 : 1.5, which makes ratios easy to compare.
Is a ratio the same as a fraction?
They are closely related. The ratio 2 : 3 can be written as the fraction 2/3 when it compares the two parts, but the first part is 2/5 of the whole.
Sources
- OpenStax Prealgebra 2e — 5.6 Ratios and Rate — ratio definition and simplification
- OpenStax Prealgebra 2e — 6.5 Solve Proportions and their Applications — cross-multiplication
- OpenStax Prealgebra 2e — 4.1 Visualize Fractions — equivalent fractions
This calculator gives estimates for planning and education. Check measurements, local codes, supplier specs and your school's official policy before relying on a result. See our disclaimer and how we build and check calculators.