About this calculator
A ratio compares quantities: a concrete mix of 1 : 2 : 4 (cement : sand : aggregate), a gear ratio, or a 2-stroke fuel mix of 50 : 1. This calculator simplifies a ratio of two or three terms (decimals are allowed), solves a proportion A : B = C : x for the missing value, and divides a total into parts in a given ratio.
For screen and image sizes, the Aspect Ratio calculator in Computer & IT also finds the nearest standard ratio.
Formula
Simplify a ratio
A : B : C = (A÷g) : (B÷g) : (C÷g)
g is the greatest common divisor of the terms after any decimals are removed by multiplying every term by the same power of 10. The unit ratio divides every term by A.
Solve A : B = C : x
A : B = C : x ⇒ x = B × C ÷ A
This is cross-multiplication: A × x = B × C.
Divide a total
Parti = T × termi ÷ (A + B + C)
Worked example
- Simplify 12 : 16 : 20 — the greatest common divisor is 4, so the ratio is 3 : 4 : 5; unit ratio 1 : 1.333 : 1.667.
- Solve 12 : 16 = 30 : x — x = 16 × 30 ÷ 12 = 40.
- Divide 960 in the ratio 12 : 16 : 20 — total parts 48, one part = 20, so 240, 320 and 400.
Assumptions and limitations
- All terms must be greater than zero.
- Decimals are simplified exactly if they have at most 9 decimal places (for example 1.5 : 2.25 = 2 : 3).
- Results are shown to 10 significant figures.
References
- Standard arithmetic of ratios and proportions (cross-multiplication).