About the Ratio Calculator
A ratio calculator simplifies a ratio to its lowest terms and scales it up or down by a factor. Ratios express relative quantity — two parts of this to three of that — and they appear anywhere a recipe, a mixture, a map, or a set of proportions has to hold as the absolute amounts change.
The formula
a : b → (a / g) : (b / g), where g = GCD(a, b)g is the greatest common divisor of the two terms. Dividing both by g yields the simplest equivalent ratio; multiplying both by the same factor scales it while preserving the relationship.
How to use this calculator
- 1Enter your Value A. The field starts at
4, which you can overwrite. - 2Enter your Value B. The field starts at
6, which you can overwrite. - 3Enter your Scale Factor. The field starts at
3, which you can overwrite. - 4Read the result straight away — it recalculates as you type, so there is no button to press. Use Share to copy a link that reopens the page with your exact numbers filled in.
Worked example
| Input | Value |
|---|---|
| Value A | 4 |
| Value B | 6 |
| Scale Factor | 3 |
Result
Ratio: 4 : 6
Simplified: 2 : 3
As Fraction: 0.666667
Scaled ×3: 12 : 18
Percentage A: 40.00%
Percentage B: 60.00%
Those are the values the page loads with, so you can reproduce this result yourself and then change one field at a time to see what drives the outcome.
Understanding your result
The defining property of a ratio is that multiplying or dividing both sides by the same number leaves it unchanged. 4:6, 2:3, and 40:60 all express the same relationship, which is what lets you scale a recipe from four servings to ten without changing how it tastes.
Ratios and fractions are related but not identical. The ratio 2:3 describes a total of five parts, of which two are the first quantity — as a fraction of the whole that is 2/5, not 2/3. Reading 2:3 as the fraction two thirds is the most common mistake, and it matters whenever you are dividing something into shares.
Things worth knowing
- Both terms must be in the same units before you form a ratio. Comparing centimetres to metres gives a meaningless result.
- A ratio of a to b corresponds to a fraction of a/(a + b) of the total, not a/b.
- To find a missing term in a proportion, cross-multiply: if 3:4 = x:20 then 4x = 60 and x = 15.
- Aspect ratios such as 16:9 work identically — they describe shape, so any resolution reducing to 16:9 has the same proportions.
- Three-part ratios follow the same rules; divide all terms by their common divisor.
Frequently asked questions
How do I simplify a ratio?+
Divide both terms by their greatest common divisor. For 18:24 the GCD is 6, so it simplifies to 3:4. The relationship is unchanged but the numbers are as small as possible.
What is the difference between a ratio and a fraction?+
A ratio compares two quantities to each other; a fraction compares a part to the whole. The ratio 2:3 means the whole has five parts, so the first quantity is 2/5 of the total.
How do I scale a recipe using ratios?+
Multiply every quantity by the same factor. Doubling a 2:3 flour-to-water ratio gives 4:6, which is the same mixture in twice the volume.
How do I find a missing value in a proportion?+
Cross-multiply and solve. For 3:4 = x:20, multiply 3 by 20 and divide by 4 to get x = 15. The two ratios then express the same relationship.