How to simplify a ratio, step by step
The greatest common divisor method, with examples for decimals, three-part ratios and mixed units.
3 min read →The idea in one line
A percentage is "out of 100", so to convert a ratio you first need to know what the whole is. In a ratio, the whole is simply all the parts added together.
Ratio to percentage: two steps
- Add the parts to get the total.
- Divide each part by the total and multiply by 100.
Example 1: a two-part ratio
Blue and white paint are mixed in the ratio 3 : 2. What percentage of the mix is each colour?
The whole is 3 + 2 = 5 parts.
The whole is 3 + 2 = 5 parts.
Blue = 35 × 100% = 60%
White = 25 × 100% = 40%
Check: 60% + 40% = 100%. Always add your percentages at the end. If they do not total 100%, something slipped.
Example 2: three parts
A fertiliser is mixed in the ratio 1 : 2 : 7. The whole is 1 + 2 + 7 = 10 parts.
110 × 100% = 10%
210 × 100% = 20%
710 × 100% = 70%
Example 3: when the answer does not come out even
A concrete mix of cement, sand and gravel is 1 : 2 : 3. The whole is 6 parts, so the shares are not tidy numbers.
| Material | Part | Working | Percentage |
|---|---|---|---|
| Cement | 1 | 1 ÷ 6 × 100 | 16.67% |
| Sand | 2 | 2 ÷ 6 × 100 | 33.33% |
| Gravel | 3 | 3 ÷ 6 × 100 | 50% |
The rounded figures add up to 100%, but if you round to one decimal place you may see 99.9% or 100.1%. That is rounding, not a mistake.
Percentage to ratio
Going the other way is easier. A split of 25% and 75% is already a ratio of 25 : 75. Simplify it by dividing both by 25 and you get 1 : 3.
A school has 30% of pupils in Year 7 and 70% in other years. The ratio is 30 : 70, which simplifies to 3 : 7.
A common trap: "3 to 4" is not 75% of the whole
There are two different questions people mix up.
- Part of the whole. In a 3 : 4 ratio the first part is 3 ÷ 7 = 42.9% of the whole.
- One part compared with the other. The first part is 3 ÷ 4 = 75% as big as the second part.
Both are correct. They answer different questions, so read the wording carefully. "What share of the total?" means divide by the sum. "How big is A compared with B?" means divide by B.
Turn any ratio into percentages
Open the ratio to % calculatorEnter up to four parts and get each percentage with a small bar chart and the full working.
Frequently asked questions
How do I turn a ratio into a percentage?
Add all the parts to get the whole, divide each part by the whole and multiply by 100. For 3 : 2, blue is 3 ÷ 5 × 100 = 60% and white is 40%.
Do the percentages always add up to 100?
Exactly, yes. With rounding you may see 99.9% or 100.1%, which is only a rounding effect.
How do I convert a percentage split into a ratio?
Write the percentages as a ratio and simplify. 25% and 75% become 25 : 75, which simplifies to 1 : 3.