Ratio Calculator

Simplify integer or decimal ratios (A:B) to lowest terms, solve unknown X in proportions (A:B = C:X), and calculate unit ratios and percentage shares.

Category: Math

How to Use Ratio Calculator

  1. Select 'Simplify Ratio (A : B)' to reduce two terms to lowest integer form, or 'Solve Proportion (A : B = C : X)' to find a missing fourth proportional value.
  2. Enter numeric values for Value A and Value B (plus Value C when solving a proportion).
  3. Click Calculate to view the simplified ratio, GCD scaling factor, unit ratios (1:n and n:1), percentage split, or cross-multiplied X solution.

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Frequently Asked Questions

How do I simplify a ratio A : B to its lowest integer terms?

Select 'Simplify Ratio (A : B)' mode and enter values A and B. If A or B contains decimals (such as 1.5 : 2.5), the calculator first scales both terms by powers of 10 to form integers (15 : 25) and then divides both by their Greatest Common Divisor (GCD = 5) to output 3 : 5.

How do I solve for X in the proportion A : B = C : X?

Select 'Solve Proportion (A : B = C : X)' mode and enter A, B, and C. Since A / B = C / X, cross-multiplication yields A × X = B × C, so X = (B × C) ÷ A. For example, if 16 : 9 = 1920 : X, then X = (9 × 1920) ÷ 16 = 1080.

What are unit ratios (1 : n and n : 1)?

A unit ratio expresses the comparison with one of the terms normalized to 1. The 1 : n form divides both sides by A (yielding 1 : B/A), while the n : 1 form divides both sides by B (yielding A/B : 1). Unit ratios are widely used in map scales, photography aspect ratios, and financial debt-to-equity ratios.

How does the calculator convert a ratio into percentage shares?

When simplifying positive ratio terms A : B, the total number of parts is A + B. Share A accounts for (A ÷ (A + B)) × 100% of the whole, and Share B accounts for (B ÷ (A + B)) × 100%. For example, a 3 : 2 ratio represents a 60% : 40% split.

Can Value A be zero when solving a proportion A : B = C : X?

No. Because solving A : B = C : X requires dividing (B × C) by A, setting A = 0 causes division by zero and leaves X undefined unless B × C is also zero (which is indeterminate).