Equivalent Ratio Calculator
Enter a ratio a:b and a scale factor to get the equivalent ratio in lowest terms and scaled form, with a visual ratio bar and a table of common multiples.
- 1
Find GCD(a, b)
GCD(3, 4) = 1 - 2
Simplify to lowest terms
3 ÷ 1 : 4 ÷ 1 = 3 : 4Already in lowest terms — GCD is 1. - 3
Scale by k
3 × 3 : 4 × 3 = 9 : 12
How does this calculator work?
Equivalent ratios have the same value: a:b = (a×k):(b×k) for any positive integer k. Simplify by dividing both parts by GCD(a,b). Enter the ratio a:b and a scale factor k to get the equivalent ratio, its lowest-terms form, and a table of multiples from ×2 to ×6.
Formula
How this is calculated
Two ratios are equivalent when they represent the same relative size — the same proportion of one quantity to another. A ratio a:b is equivalent to (a×k):(b×k) for any non-zero integer k, because multiplying both parts by k is the same as multiplying by k/k = 1.
To simplify a ratio to its lowest terms, divide both parts by their greatest common divisor (GCD). The GCD is the largest integer that divides both a and b exactly. After division, the two parts share no common factor greater than 1 and the ratio cannot be simplified further. For example, 12:8 simplifies to 3:2 (GCD = 4), and 3:2 = 9:6 = 12:8 = 15:10 (all equivalent).
The ratio a:b can also be written as the fraction a/b, so ratio equivalence is the same concept as fraction equivalence. The calculator reduces the input to lowest terms, scales by the chosen factor, and generates a table of equivalents for quick reference. The ratio bar visually shows the relative proportion of the two parts.
Frequently asked questions
Simplify both ratios to lowest terms by dividing each by its GCD. If the simplified forms are identical, the ratios are equivalent. Alternatively, cross-multiply: a:b is equivalent to c:d if and only if a×d = b×c.
A ratio a:b compares two quantities; a fraction a/b expresses one quantity as a part of another. They are mathematically equivalent (a:b = a/b), so the same simplification rules apply. Ratios are often written with a colon to emphasise the comparison, while fractions are used in arithmetic.
This calculator works with positive integers. If you have a decimal ratio like 1.5:2, multiply both parts by the same power of 10 to clear decimals (e.g. 15:20), then simplify. The resulting integer ratio is equivalent to the original.
Also known as
TG we-Calculate Editorial Team. (2026). Equivalent Ratio Calculator [Online calculator]. TG we-Calculate. https://we-calculate.com/calculator/equivalent-ratio-calculator
TG we-Calculate Editorial Team. "Equivalent Ratio Calculator." TG we-Calculate. 2026. https://we-calculate.com/calculator/equivalent-ratio-calculator.
TG we-Calculate Editorial Team, "Equivalent Ratio Calculator," TG we-Calculate, 2026. [Online]. Available: https://we-calculate.com/calculator/equivalent-ratio-calculator
@misc{wecalculate_equivalent_ratio_calculator, title = {Equivalent Ratio Calculator}, author = {{TG we-Calculate Editorial Team}}, howpublished = {\url{https://we-calculate.com/calculator/equivalent-ratio-calculator}}, year = {2026}, note = {TG we-Calculate} }
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