Everyday mathematics

Ratio Calculator

Reduce an integer ratio and scale both original terms by the same factor. The reduced ratio expresses relative size; scaled terms retain the chosen numerical scale.

Explicit formulas and worked examples
Check your inputs, then calculate
Data is calculated in this browser only

Check the stated input format, calculation convention and limits before using the result.

Check the example inputs, then calculate. Your values stay in this browser.

The ratio 0:0 is undefined; other zero or negative terms are preserved.

Calculation notes

Understand the Ratio Calculator

Ratio Calculator validates first integer, second integer, scale factor before applying the displayed equation. The ratio 0:0 is undefined; other zero or negative terms are preserved.

Formula and logic

What is the formula for the Ratio Calculator?

Ratio Calculator: reduced ratio = (a/gcd(a,b)) : (b/gcd(a,b)); scaled = original × scale. Input definitions: a = First integer; b = Second integer; scale = Scale factor. Use the selected convention throughout the calculation.

Worked example

How can I reproduce the Ratio Calculator example?

Ratio Calculator baseline input: First integer: 12; Second integer: 18; Scale factor: 1. Output: Simplified ratio = 2:3; Scaled first term = 12; Scaled second term = 18. Substitute these values into the displayed equation to reproduce the result.

How to read the result

How should I interpret the Ratio Calculator result?

Read simplified ratio with its stated unit and convention. The default example and the independent worked scenario use different inputs, so compare the assumptions before comparing the numbers.
Change one input at a time and use the equation to explain the result; do not mix unit, grade-scale, time-zone or rounding conventions across comparisons.

Limits and assumptions

What limits apply to the Ratio Calculator?

The ratio 0:0 is undefined; other zero or negative terms are preserved.
Decimal ratios must first be converted to equivalent integers.

Content and calculation reviewed: 2026-10-11

Understand the calculation

How to use it and the math behind it

Read the complete explanation

Four steps to check your inputs and results

Reduce an integer ratio and scale both original terms by the same factor. The reduced ratio expresses relative size; scaled terms retain the chosen numerical scale.
Enter First integer, Second integer, Scale factor in the stated format. Baseline values are for reproduction.
Check the output unit and convention: Read simplified ratio with its stated unit and convention. The default example and the independent worked scenario use different inputs, so compare the assumptions before comparing the numbers.
Change one input and compare the result. The ratio 0:0 is undefined; other zero or negative terms are preserved. Decimal ratios must first be converted to equivalent integers.