Ratio Calculator
Simplify a ratio to lowest terms, solve A:B = C:D for a missing value, or scale a ratio by any factor (steps included).
Details
Your ratio
Simplified ratio
2 : 3
4 : 6 in its simplest form
This handles the three things people need from ratios: simplifying one down to its smallest whole numbers, finding a missing value when two ratios match, and scaling a ratio up or down.
It returns the answer with the working shown, including the number it divided by when simplifying.
What is a ratio?
A ratio compares two amounts. Writing 2 : 3 means that for every 2 of the first thing, there are 3 of the second.
It says nothing about the actual totals. A 2 : 3 mix could be 2 and 3, or 20 and 30, or 200 and 300. What stays fixed is the relationship between them, which is why a recipe scales up without changing how it tastes.
That is also why ratios can be simplified. 12 : 18 and 2 : 3 describe exactly the same mix, and the second is easier to hold in your head.
Six is the largest number that divides into both 12 and 18. Dividing both sides by it leaves the ratio unchanged, just written more simply.
What to enter
- What do you want to do?
- Simplify a ratio, find a missing value, or scale one up and down.
- A and B
- The two sides of your ratio. In 12 : 18, A is 12 and B is 18.
- C and D
- Only used when finding a missing value. Leave the unknown one blank and the calculator fills it in.
What this assumes
Both sides are measured in the same units. Comparing 2 metres to 3 centimetres as 2 : 3 is wrong; convert first.
How to calculate a ratio
Two jobs cover almost everything people need: making a ratio smaller, and filling in a missing number.
- A, B
- The ratio you know
- C, D
- The matching ratio, with one value missing
To simplify. Find the largest number that divides into both sides, then divide both by it. For 12 : 18 that number is 6, giving 2 : 3.
To find a missing value. Multiply diagonally across the equals sign, then divide by the number left over. This is called cross-multiplying.
To scale. Multiply both sides by the same number. Doubling 2 : 3 gives 4 : 6, which is still the same mix.
See a worked example: 2 parts squash to 3 parts water, using 8 parts squash
- Known ratio
- 2 : 3
- You have
- 8 parts squash
Write it out: 2 : 3 = 8 : ?
Cross-multiply: 3 × 8 = 24.
Divide by the number diagonally opposite the gap: 24 ÷ 2 = 12.
Sanity check: 8 is four times 2, so the other side should be four times 3. It is.
12 parts water
Frequently asked questions
A ratio usually compares one part to another part. A fraction compares a part to the whole.
In a 2 : 3 mix there are 5 parts in total, so the first ingredient is 2/5 of the mixture, not 2/3. Mixing these up is the single most common ratio mistake. The fraction calculator handles the part-of-the-whole version.
Add both sides to get the total, then work out what share each side is of that total.
For 2 : 3, the total is 5. So the first part is 2 ÷ 5 = 0.4, which is 40%, and the second is 60%. You can check any of these on the percentage calculator.
Yes. Concrete is often mixed 1 : 2 : 3 for cement, sand and gravel, which is what the concrete calculator assumes, and it works exactly the same way: for every 1 bucket of cement you use 2 of sand and 3 of gravel.
Simplifying works the same too, by dividing every part by the same number.
No, and the order matters a great deal. 2 : 3 squash to water is a weaker drink than 3 : 2.
Always note which thing is named first. Most real mistakes with ratios are order mistakes rather than arithmetic ones.
Problems people actually run into
Treating the first number as a share of the total
Someone told to split £100 in the ratio 2 : 3 often hands over £20 and £30, or gives two-thirds to the first person. Neither is right.
Add the parts first: 2 + 3 = 5. Then one share is £100 ÷ 5 = £20, so the split is £40 and £60. Counting the total number of parts before dividing anything fixes almost every ratio error.
Results are estimates for general information only and are not professional financial, medical, or legal advice. Read our full disclaimer.
Last updated: August 29, 2026