Ratio Calculator
Ratios turn up in recipes, maps, mixing paint, splitting bills and scaling drawings — and all of it is the same arithmetic.
Simplifying and splitting
A ratio compares quantities of the same kind. Simplifying works exactly as it does with fractions: divide both sides by their greatest common divisor. 16 : 24 has a GCD of 8, so it becomes 2 : 3.
To split a total in a given ratio, work out the value of one part:
Splitting £200 in the ratio 2 : 3 means five parts of £40, giving £80 and £120. The check is always that the shares sum back to the total.
Solving proportions
A proportion states that two ratios are equal, and cross-multiplication solves it:
This is the single most useful piece of arithmetic in everyday life. Scaling a recipe from four people to seven, converting a map distance to real distance, working out how much paint a larger wall needs, adjusting a drawing to a new size — all the same operation.
Worked example: a recipe for 4 uses 300 g of flour. For 7 people, 4 : 300 = 7 : d, so d = (300 × 7) ÷ 4 = 525 g.
Different ways ratios are written
| Form | Example | Where you see it |
|---|---|---|
| Part to part | 2 : 3 | Mixing, recipes, splitting |
| Part to whole | 2/5 | Fractions, probability |
| 1 : n form | 1 : 1.5 | Scale drawings, gear ratios |
| Percentage | 40 % : 60 % | Reporting and comparison |
| Three-part | 2 : 3 : 5 | Recipes, cost allocation |
The distinction that causes most errors is part-to-part versus part-to-whole. A ratio of 2 : 3 means two out of five, not two out of three. Concrete mixed “1 : 5 cement to ballast” is one part in six, not one part in five.
Map scales use the 1 : n form, where 1 : 25,000 means one centimetre on the map is 25,000 cm — 250 metres — on the ground.
Frequently asked questions
What is the difference between a ratio and a fraction?
A fraction compares a part to the whole. A ratio usually compares parts to each other. The ratio 2 : 3 corresponds to the fractions 2/5 and 3/5 of the total. Misreading 2 : 3 as 2/3 is easily the most common ratio error.
How do I split in a three-part ratio?
Identically — add all three parts to get the number of shares, divide the total by that, then multiply. Splitting £600 in the ratio 1 : 2 : 3 gives six shares of £100, so £100, £200 and £300.
What does a 1:5 dilution mean?
Ambiguously, one of two things, which is why it causes accidents. In most scientific usage it means one part concentrate to five parts diluent — six parts in total. Some product labels mean one part made up to five parts. Check the instructions rather than assuming.