Ratio Calculator
Simplify ratios, scale to find missing values, and share amounts in a given ratio — full step-by-step working for 2-part and 3-part ratios.
Ratio calculator
Find the Highest Common Factor (HCF), then divide each part
Step by step calculations
Choose a mode, enter your values and press Calculate to see the step by step formula and working.
Ratio Calculator Explained
Core concepts, classroom applications, and plain-English explanations for all audiences.
When would you actually use this?
Ratios are everywhere in the kitchen. A classic orange squash says "dilute 1 part squash to 4 parts water" — that's a 1:4 ratio. If you want to make 750 ml of drink, you need 150 ml of squash and 600 ml of water. Same maths, different numbers: ratios scale up and down whilst keeping the relationship fixed.
Worked example
"A recipe for 4 people uses flour and butter in the ratio 3:2. You want to scale it up for 10 people. How much of each do you need if the original uses 150 g flour?"
Scale factor: 10 ÷ 4 = 2.5
Flour: 150 × 2.5 = 375 g
Butter: 100 × 2.5 = 250 g
Original butter: 150 × (2/3) = 100 g. The ratio stays 3:2 throughout.
Maps and scale
An OS Landranger map has a scale of 1:50,000. This is a ratio — 1 cm on the map represents 50,000 cm (500 m) in real life. If two towns are 6 cm apart on the map, the real distance is 6 × 500 m = 3 km. Every map uses ratios to compress reality to a manageable size.
Mistake to avoid
Confusing the ratio parts with the total. In a 3:2 ratio, there are 5 parts total — not 3 and 2 separately. When sharing £200 in ratio 3:2, each part is £200 ÷ 5 = £40, giving £120 and £80 (not £60 and £40).
Ratios in everyday life
Cooking
A recipe might call for flour and sugar in a ratio of 3:2, meaning for every 3 cups of flour, you use 2 cups of sugar.
Mixing Paint
To get a specific shade, you might mix blue and yellow paint in a ratio of 1:4, meaning one part blue to four parts yellow.
Maps and Models
A map scale of 1:100,000 means that 1 unit on the map represents 100,000 units in real life.
Diluting Liquids
A cleaning concentrate might be diluted with water in a ratio of 1:10, meaning one part concentrate to ten parts water.
What is a Ratio?
A ratio is a way to compare two or more quantities. It tells you how much of one thing there is in relation to another. For example, if you have 2 red apples and 3 green apples, the ratio of red to green apples is 2:3.
Ratios are often used to show proportions, scale, or how ingredients are mixed. The order of the numbers in a ratio is important, as it reflects the order of the items being compared. Ratios can be simplified, just like fractions, by dividing all parts by their highest common factor.
Common mistakes to avoid
- Simplifying 12:18 to 6:9:The ratio has been divided by 2, but 6 and 9 still have a common factor (3). It's not fully simplified. Divide by the HCF (6) to get 2:3.
- Sharing £50 in the ratio 2:3 by doing 50/2 and 50/3:You need to find the total number of parts first, not divide by individual parts. Add the ratio parts (2+3=5), then divide the amount by the total parts (50/5=10). Multiply 10 by each ratio part (2x10=20, 3x10=30).
- Writing the ratio of boys to girls as 3:2 when there are 2 boys and 3 girls:The order of the numbers in a ratio must match the order of the items being compared. The ratio of boys to girls is 2:3.