Ratio Calculator
Simplify a ratio to its lowest terms and find its decimal equivalent.
About the Ratio Calculator
A ratio compares two quantities directly, and simplifying it to the smallest whole numbers that preserve the same relationship makes it far easier to read and communicate — this calculator does exactly that, plus gives the decimal equivalent for quick reference.
How It Works
The calculator finds the greatest common divisor of the two numbers you enter, then divides both numbers by that divisor to reduce the ratio to its simplest whole-number form. It also divides A by B directly to give the decimal equivalent.
Simplified Ratio = A/GCD(A,B) : B/GCD(A,B). Decimal Equivalent = A / B.
Worked example
Scenario: Simplifying the ratio 12 : 18.
- Greatest common factor of 12 and 18: 6.
- Divide both sides: 12 ÷ 6 = 2 and 18 ÷ 6 = 3.
- Simplified ratio: 2 : 3, equivalent to 1 : 1.5.
Result: 12 : 18 simplifies to 2 : 3.
How to read and simplify a ratio
A ratio compares quantities in the same order they are entered. The ratio 12:18 simplifies to 2:3 because both terms can be divided by 6. The order matters: 2:3 and 3:2 describe different comparisons. Ratios can also be expressed as fractions or decimal rates when that form is more useful.
Tips and common mistakes
- Decimals are converted first: 1.5 : 2.5 becomes 15 : 25, which simplifies to 3 : 5.
- The '1 : x' form is handy for scales and mixing ratios.
- To scale a ratio to a target amount, use the Proportion Calculator.
Assumptions & Limitations
- Assumes both values are positive whole numbers or can be reasonably treated as such for ratio simplification.
- Works the same regardless of which quantity is entered first, as long as the order is kept consistent with what each number represents.
- For proportional scaling problems (finding an unknown given three known ratio terms), use the Proportion Calculator instead.