Ratio Calculator
A ratio states how two quantities compare: two parts colour to three parts water, 40 kilometres per litre, two ingredients in a mix. Reducing one is the opening move of nearly every proportion problem, and this page does three jobs at once — it cuts your pair to smallest terms, converts the first value into a share of the whole, and works out what a single part is worth.
Enter values
Results
- Simplified ratio
- 2 : 3
- A as a share of A + B
- 40%
- What one part is worth
- 100
How is the Ratio calculated?
Enter quantity A and quantity B — counts, amounts, scores, anything sharing a unit. The calculator scales both to whole numbers when decimals appear, divides them by their greatest common divisor, and prints the simplified ratio. It then adds the pair to show A as a percentage of A + B, and finally spreads that total across the simplified parts to give the unitary value: what one part equals. Both fields at 0 return dashes.
Formula
Simplified ratio: divide A and B by gcd(A, B), so 200 : 300 becomes 2 : 3. Share of A = A ÷ (A + B) × 100. Unitary value = (A + B) ÷ (a + b), where a : b is the simplified pair. gcd is the largest number dividing both values, the share needs a non-zero total, and 0 : 0 is not a ratio at all.
Example
A painter mixes 200 ml of colour with 300 ml of water. The ratio cuts to 2 : 3 after dividing both sides by 100, colour holds 200 ÷ 500 × 100 = 40% of the mixture, and one part is worth 500 ÷ 5 = 100 ml — so four parts would take 400 ml. Swap the inputs to 300 and 200 and the ratio flips to 3 : 2 with a 60% share, while one part keeps its 100 ml value.
Things to remember
A ratio answers how much of each; a percentage answers how much of the whole — two views of one fact, and the share row hands you both. Keep the unitary method close whenever something must be divided in the same proportion: splitting a bill, scaling a recipe or spreading marks across sections of equal weight.
Frequently Asked Questions
How do you simplify a ratio step by step?
Write both terms as whole numbers if decimals appear, find the greatest common divisor of the pair, then divide both terms by it. For 45 and 30 that GCD is 15, giving 3 : 2. The proportion itself never changes — only the units you count it in.
What is the unitary method in maths?
It values one part of a ratio first, then scales up from there. If 2 : 3 shares 500 ml, one part is 100 ml, so seven parts would need 700 ml. Any quantity can then be split in the same proportion without redoing the whole calculation from scratch.
What is the difference between a ratio and a percent?
A ratio compares the two quantities to each other, while a percentage measures one of them against their total. 200 to 300 is a 2 : 3 ratio and, at the same time, 40% of everything — the calculator prints both readings from a single pair of inputs.
What happens if one of the ratio numbers is 0?
A pair like 300 : 0 simplifies to 1 : 0: the second quantity contributes nothing, so the first holds 100% of the total and one part equals the whole amount. Only 0 : 0 breaks the idea entirely, and the calculator shows dashes for that case.
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