Ratio Calculator
Simplify a two-part ratio and calculate an equivalent ratio from a known value using exact greatest-common-divisor arithmetic.
Simplify a ratio
How this tool works
A ratio compares two quantities in a fixed order. This calculator reduces positive whole-number ratios to their simplest equivalent form and shows the divisor used, making the result easy to verify instead of presenting an unexplained answer.
For whole numbers a and b, the simplified ratio is a ÷ gcd(a,b) to b ÷ gcd(a,b). The greatest common divisor is the largest positive integer that divides both inputs without a remainder.
How to use it
- Enter the first positive whole-number quantity.
- Enter the second positive whole-number quantity in the order it should be compared.
- Read the simplified ratio and greatest common divisor shown below the fields.
Worked examples
Simplifying a recipe ratio
- Input
- 12 parts flour to 8 parts sugar
- Output
- 3:2
The greatest common divisor of 12 and 8 is 4. Dividing both parts by 4 preserves their relationship and produces the simplest whole-number ratio, 3:2.
Scaling a classroom ratio
- Input
- 18 students to 6 tables
- Output
- 3:1
Both values divide evenly by 6, so the simplified relationship is three students for every table. This describes the ratio without changing its proportion.
Limitations
- This version accepts positive whole numbers and does not reduce decimal or negative inputs.
- A ratio describes relative quantities; it does not establish causation, probability, or percentage change.