Ratio & Proportion Calculator
Calculate ratios between two or more values and find unknown values using proportions.
Ratios, proportions, and cross-multiplication
A proportion says two ratios are equal, and cross-multiplication solves it in one step. The difficulty is almost never the algebra - it is keeping the two sides consistent, and recognising when a relationship is not proportional at all.
Formula
If a / b = c / x, then x = (b x c) / a
Both ratios must be written in the same order and the same units, or the cross-multiplication produces a meaningless result.
Part-to-part and part-to-whole are different ratios
A concrete mix described as 1:2:3 is cement to sand to aggregate - a part-to-part ratio. The total is 6 parts, so cement is one sixth, or 16.7%, of the mix. Reading 1:2:3 as "one third cement" is a common and expensive error.
A ratio of 3:2 means the first quantity is 1.5 times the second, and the first is 60% of the total. Converting between the two forms is where most ratio problems actually go wrong.
The reliable habit: write down what the total number of parts is before doing anything else. For a ratio a:b:c, the total is a + b + c, and each share is its part over that total.
Direct and inverse proportion behave differently
In direct proportion, doubling one quantity doubles the other, and the ratio between them stays fixed. In inverse proportion, doubling one halves the other, and it is the product that stays fixed.
- Direct: ingredients in a recipe, distance at constant speed, cost at a fixed unit price, map distances against real distances.
- Inverse: workers against time to finish a job, speed against journey time, gear teeth against rotation speed, pressure against volume at constant temperature.
- Neither: fuel consumption against speed, which rises at both very low and very high speeds. Assuming proportionality where none exists is more damaging than getting the arithmetic wrong.
Scaling recipes, mixes, and drawings
Scale factors apply to every component or the ratio breaks. Scaling a recipe from 4 to 6 servings means multiplying every ingredient by 1.5, including the ones that feel like they should stay fixed.
Two things do not scale linearly in practice: cooking time, which depends on thickness and surface area rather than mass, and seasoning, which most cooks scale by roughly the square root of the factor.
For drawings, a 1:50 scale means 1 cm on paper is 50 cm in reality. Note that a 1:50 drawing enlarged to 1:25 doubles every length, quadruples every area, and this is why plan areas cannot be scaled by the linear factor.
Worked example
A concrete mix specifies 1:2:4 cement, sand, and aggregate by volume, and you need 0.9 m^3 of mixed concrete.
Total parts: 1 + 2 + 4 = 7. Dry materials shrink when mixed with water, so allow a factor of about 1.54: total dry volume needed is 0.9 x 1.54 = 1.386 m^3.
Cement: 1/7 x 1.386 = 0.198 m^3, which at 1,440 kg/m^3 is 285 kg, or about 11.4 bags of 25 kg. Sand: 2/7 x 1.386 = 0.396 m^3. Aggregate: 4/7 x 1.386 = 0.792 m^3.
The check that catches errors: the three volumes must sum back to 1.386, and cement must be one seventh of the total, not one third.
Reading a ratio as shares and percentages
| Ratio | Total parts | First share | As percentage |
|---|---|---|---|
| 1:1 | 2 | 1/2 | 50% |
| 1:2 | 3 | 1/3 | 33.3% |
| 2:3 | 5 | 2/5 | 40% |
| 3:2 | 5 | 3/5 | 60% |
| 1:2:3 | 6 | 1/6 | 16.7% |
| 1:2:4 | 7 | 1/7 | 14.3% |
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References
Last reviewed: 2026-08-07. This page is informational. For legal, medical, tax, or financial decisions, confirm the result with a qualified professional.