Ratio Calculator
Reduce a ratio to its simplest form, find the missing term in a proportion, or divide a total between shares.
How it works
A ratio compares quantities of the same kind, and dividing every term by their greatest common divisor gives the simplest equivalent form. 12:18 and 2:3 describe the same relationship.
Splitting a total works by adding the ratio terms to get the number of parts, then giving each share its own number of parts. For 3:2 over 500, there are 5 parts of 100, so the shares are 300 and 200.
A ratio is not a fraction of the whole. In 3:2, the first share is three fifths of the total, not three halves — mixing those up is the usual source of an answer that looks nearly right.
The formula
Simplify
divide every term by their gcd
Proportion
a : b = c : d → a × d = b × c
Split a total
share = total × (term ÷ sum of terms)
Worked examples
| Scenario | Working | Result |
|---|---|---|
| Simplify 12:18 | gcd is 6 | 2:3 |
| Split 500 in 3:2 | 5 parts of 100 | 300 and 200 |
| Solve 3:4 = 9:? | 3 × ? = 4 × 9 | 12 |
When you'd use it
- Splitting a bill, a profit or a workload fairly
- Scaling a recipe or a mixture
- Converting a ratio into percentages
- Checking two ratios are equivalent
Common questions
Is 3:2 the same as 3/2?
Not as a share of the whole. In a 3:2 split there are five parts, so the first share is 3/5 of the total. The fraction 3/2 compares the first part to the second, which is a different question.
How do I turn a ratio into percentages?
Divide each term by the sum of all terms, then multiply by 100. For 3:2 that is 60% and 40%.
Can a ratio have more than two terms?
Yes. 2:3:5 splits a total into ten parts. Simplifying still works the same way — divide every term by the greatest common divisor of all of them.