Question 1

How does simplifying a ratio work?

Accepted Answer

Both sides are divided by their greatest common divisor (GCD). For 12:8, GCD(12, 8) = 4, so 12÷4 = 3 and 8÷4 = 2 — giving 3:2. The simplified ratio expresses the same relationship using the smallest possible whole numbers. The calculator also shows the GCD (factor) used.

Question 2

How does the proportion solver work?

Accepted Answer

If A:B = C:D, then A × D = B × C (cross-multiplication). To find D when you know A, B, and C: D = (B × C) ÷ A. To find C when you know A, B, and D: C = (A × D) ÷ B. Enter any three values and pick which unknown you want solved.

Question 3

Can I enter decimal ratio values?

Accepted Answer

Yes — the calculator accepts any finite numbers. For simplification, the GCD is computed on the rounded versions of your inputs, so 8.5:3.5 may not simplify as cleanly as integer inputs would. Scale and proportion modes return exact decimal results.

Question 4

How do I check if two ratios are equivalent?

Accepted Answer

Simplify both and compare the results. If 12:8 and 9:6 both simplify to 3:2, they are equivalent. Alternatively, cross-multiply: A:B = C:D is true if A × D = B × C.

Question 5

What if one side of my ratio is zero?

Accepted Answer

A zero denominator (B = 0) is always an error — you cannot divide by zero. A zero numerator (A = 0) is accepted in simplify mode and always returns 0:1. In proportion mode, A = 0 or B = 0 causes a division-by-zero error.

Mode	What it solves	Formula
Simplify	Reduce A:B to lowest terms	A÷GCD : B÷GCD
Scale	Multiply both sides by N	A×N : B×N
Proportion	Find missing value in A:B = C:D	D = B×C÷A

Ratio Calculator

Three ways to work with ratios

Examples — One Per Mode

Frequently Asked Questions

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