Guide · Ratios
Ratio and Proportion Calculator
Updated: June 2026
Ratios and proportions are two sides of the same coin: a ratio compares two quantities, and a proportion says two ratios are equal. Together they let you scale recipes, mix paint, share money fairly and read maps. This guide untangles the vocabulary, shows how to make and simplify equivalent ratios, and uses the rule of three to find any missing term.
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Ratio versus proportion
A ratio compares amounts: 3 parts blue to 4 parts yellow is written 3:4 or 3/4. A proportion is an equation between two ratios that are equal, like 3:4 = 9:12. The ratio is the relationship; the proportion is the claim that two such relationships match. Solving a proportion means finding a value that keeps both sides equal — which is precisely what the rule of three does.
Equivalent ratios
Two ratios are equivalent when one is a scaled copy of the other. Multiply or divide both parts by the same number and the relationship is unchanged:
This is exactly how a recipe scales. The proportion of ingredients stays the same even as the absolute amounts grow. To test whether two ratios are equivalent, cross-multiply: 2:5 and 6:15 are equivalent because 2 × 15 = 5 × 6 = 30.
Simplifying a ratio
To put a ratio in its simplest form, divide both parts by their greatest common divisor. 18:24 shares a factor of 6, so it simplifies to 3:4. A simplified ratio is the easiest version to compare and to read aloud, and it makes spotting equivalences much quicker.
Finding a missing term
Suppose a paint mix uses blue to yellow in the ratio 3:4, and you have 9 litres of blue. How much yellow keeps the same shade? Set up a proportion and cross-multiply:
3x = 36
x = 12 litres of yellow
Drop the three known numbers into the calculator, leave the unknown blank, and it returns 12 with the working shown. The same approach solves any missing term, whichever of the four positions it occupies.
Sharing in a given ratio
Ratios also split a total fairly. To share £60 between two people in the ratio 2:3, add the parts (2 + 3 = 5), divide the total by that (60 ÷ 5 = £12 per part), then multiply out: one person gets 2 × 12 = £24, the other 3 × 12 = £36. The two shares add back to £60, which is the natural check. This “parts” method appears constantly in budgeting, recipes and dividing winnings.
Where ratios and proportions show up
- Cooking — keeping flavour while scaling a recipe up or down.
- Mixing — paint, concrete, fertiliser and cocktails all rely on fixed ratios.
- Maps and models — scale is a ratio between drawing and reality.
- Finance — splitting costs, profits or rent between people.
- Aspect ratios — resizing images and video while keeping shape.
Frequently asked questions
What is the difference between a ratio and a proportion?
A ratio compares two quantities, like 3:4. A proportion states that two ratios are equal, like 3:4 = 9:12, and you solve it to find a missing term.
How do I find an equivalent ratio?
Multiply or divide both parts by the same number. 2:5 becomes 6:15 when both are multiplied by 3.
How do I find a missing term?
Write the ratios as a proportion and cross-multiply. For 3:4 = 9:x, solve 3x = 36, so x = 12.