Ratio Calculator
Three common ratio tasks in one place: reduce a ratio to its simplest whole numbers, find the missing term of a proportion, or share a total between two or three parts in a given ratio. Decimals are accepted and results are exact.
Optional
Result
Enter at least two numbers to simplify their ratio.
The calculation runs in this browser tab. Nothing you enter is uploaded, saved or logged.
What is a ratio?
A ratio compares quantities of the same kind. A recipe that uses 2 cups of flour for 3 cups of water has a flour-to-water ratio of 2 : 3, read “2 to 3”. Only the relationship matters: 4 : 6 and 20 : 30 describe the same ratio, which is why ratios are simplified to the smallest whole numbers.
Two equal ratios form a proportion, such as 2 : 3 = 10 : 15. If three of the four numbers are known, the fourth follows from the cross product: A × x = B × C. Ratios are also used to share a total: splitting 100 in the ratio 2 : 3 gives 40 and 60, because the ratio has 5 parts and each part is worth 20.
How to use the Ratio Calculator
- Choose what you want to do: simplify a ratio, find the missing value, or split a total.
- Enter the numbers in the fields shown for that task. The third part is optional when simplifying or splitting.
- Read the result and the details, which show the equation, the scale factor or each share.
- Use Copy result to copy the answer, or Reset to start again.
Formula
- Simplify
- divide every part by their greatest common divisor (decimals are first scaled to whole numbers)
- Missing value in A : B = C : x
- x = B × C ÷ A
- Share of a total T in ratio a : b : c
- share of a = T × a ÷ (a + b + c)
To simplify 1.5 : 2.5, multiply both by 10 to get 15 : 25, then divide by their GCD, 5, giving 3 : 5.
The scale factor of a proportion is C ÷ A: how many times the first ratio was enlarged to get the second.
Worked example
Simplifying the ratio 12 : 18 : 30. These are the results the calculator gives:
| Question | Result |
|---|---|
| Input: What do you want to do? | Simplify a ratio (A : B : C) |
| Input: A | 12 |
| Input: B | 18 |
| Input: C (optional) | 30 |
| Simplified ratio | 2 : 3 : 5 |
| Original | 12 : 18 : 30 |
| A ÷ B | ≈ 0.666667 |
| Share of the whole | A 20.00% · B 30.00% · C 50.00% |
Assumptions and limits
- The parts of a ratio must be zero or positive, and not all zero. In the missing-value task, the first number A cannot be 0.
- Ratios of two or three parts are supported. For longer ratios, split them into pairs.
- Shares that do not divide evenly are rounded to 6 decimals for display and flagged; round them yourself to the unit that suits your use (cents, grams…), keeping the total correct.
- Ratios compare quantities in the same unit. Convert first if one part is in minutes and another in hours.
Frequently asked questions
How do I simplify a ratio?
Divide every part by their greatest common divisor. For 12 : 18 the GCD is 6, so the ratio simplifies to 2 : 3. If the parts are decimals, multiply them all by a power of ten first to make whole numbers.
How do I find a missing value in a proportion?
Use the cross product. In A : B = C : x, multiply B by C and divide by A. For 2 : 3 = 10 : x, x = 3 × 10 ÷ 2 = 15.
How do I split an amount in a given ratio?
Add the parts of the ratio, divide the total by that sum to get the value of one part, then multiply by each part. For 100 in the ratio 2 : 3 : 5, there are 10 parts of 10 each, giving 20, 30 and 50.
What is the difference between a ratio and a fraction?
A ratio compares parts to each other (2 : 3 means 2 parts to 3 parts), while a fraction compares a part to the whole. A 2 : 3 ratio corresponds to the fractions 2/5 and 3/5 of the total.
Can a ratio contain decimals or zero?
Decimals yes, they are scaled to whole numbers, so 0.5 : 0.75 becomes 2 : 3. A zero part is allowed as long as another part is not zero, and it stays zero (0 : 5 simplifies to 0 : 1).
Why do some shares show ≈?
When the total does not divide exactly in the ratio, a share has more decimals than the six displayed. The ≈ marks them as rounded.