What this calculator does
A proportion states that two ratios are equal, and solving one means finding the missing term. It is the arithmetic behind scaling recipes, reading maps, mixing materials and converting between any two units that are related linearly.
The calculator also simplifies the ratio to lowest terms and expresses it as a share of the whole. That last figure is often the one people actually want: a 3 : 4 ratio means the first part is 43% of the total, not 75% of it, and the distinction catches people out.
The formula
Cross-multiplication converts the proportion a/b = c/d into ad = bc, which rearranges to give whichever term is missing. Simplification divides both sides of the ratio by their greatest common divisor.
| Term | Meaning |
|---|---|
| Proportion | A statement that two ratios are equal. |
| Cross-multiply | a/b = c/d becomes ad = bc. |
| Simplified ratio | Both terms divided by their greatest common divisor. |
| Share of the whole | a ÷ (a + b), as a percentage. |
The inputs explained
| Field | What to enter |
|---|---|
| A | First term of the known ratio. |
| B | Second term of the known ratio. |
| C | First term of the second ratio: the one whose partner you want. |
When to use it
Scaling a mixture
Concrete at 1 : 3, paint tinting, fertiliser dilution. Enter the specified ratio and the quantity you have of one component to find how much of the other you need.
Reading a map or a drawing
A 1 : 25,000 scale means one unit on the map is 25,000 in reality. Enter the measured distance to convert it.
Splitting something proportionally
Dividing profit, rent or costs in an agreed ratio. The share-of-the-whole figure converts the ratio into percentages directly.
Converting between units
Any linear conversion is a proportion. Enter a known equivalence as a : b and your quantity as c to get the answer.
Worked examples
Every figure in the tables below is produced by this page’s own calculator at build time, so the numbers and the tool always agree. Select any row to load that scenario.
Solving 3 : 4 = c : d
A fixed 3 : 4 ratio scaled up to various first terms.
| C | D | Proportion | As a decimal |
|---|---|---|---|
| 6 | 8.000 | 3.000 : 4.000 = 6.000 : 8.000 | 0.7500 |
| 9 | 12.000 | 3.000 : 4.000 = 9.000 : 12.000 | 0.7500 |
| 12 | 16.000 | 3.000 : 4.000 = 12.000 : 16.000 | 0.7500 |
| 15 | 20.000 | 3.000 : 4.000 = 15.000 : 20.000 | 0.7500 |
| 30 | 40.000 | 3.000 : 4.000 = 30.000 : 40.000 | 0.7500 |
| 75 | 100.000 | 3.000 : 4.000 = 75.000 : 100.000 | 0.7500 |
How the ratio itself changes the share
Holding B at 4 and changing A shows how the share of the whole moves.
| A | Simplified ratio | As a decimal | A as a share of the whole |
|---|---|---|---|
| 1 : 4 | 1 : 4 | 0.2500 | 20.0% |
| 2 : 4 | 1 : 2 | 0.5000 | 33.3% |
| 3 : 4 | 3 : 4 | 0.7500 | 42.9% |
| 4 : 4 | 1 : 1 | 1.000 | 50.0% |
| 6 : 4 | 3 : 2 | 1.500 | 60.0% |
| 12 : 4 | 3 : 1 | 3.000 | 75.0% |
Questions
How do I solve a proportion?
Cross-multiply. From a/b = c/d you get ad = bc, then divide to isolate whichever term is unknown. This calculator solves for D.
What is the difference between a ratio and a fraction?
A ratio compares two parts to each other; a fraction compares a part to the whole. A 3 : 4 ratio corresponds to the fraction 3/7 of the total, not 3/4.
How do I simplify a ratio?
Divide both terms by their greatest common divisor. 18 : 24 has a GCD of 6, giving 3 : 4.
Can ratios have decimals?
Yes, though whole numbers are conventional. Multiply both terms by the same power of ten to clear the decimals: 1.5 : 2 becomes 3 : 4.
What about ratios with three parts?
The same logic extends: for a : b : c, scale all three terms by the same factor. This calculator handles two-term proportions; for three parts, work out the scale factor from one known pair and apply it across.
For simplification, see GCD and LCM. For percentage shares, use the percentage calculator.