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Math tool

Ratio Calculator

Reduce two ratio parts to their simplest exact form and see the corresponding decimal relationship.

Free · Private · Runs in your browser

Exact ratio arithmetic

Enter two ratio parts

Reduce a signed whole-number ratio to its simplest equivalent form. Values and results stay in your browser.

Ratio values

Each entry must be a whole number from −1,000,000 through 1,000,000. The second part cannot be zero.

Your reduced ratio will appear here after you submit valid values.

Formula and calculation method

A ratio compares two quantities. For input parts a andb, the calculator finds their greatest common divisor and divides both parts by it. For example, 18:24 becomes 3:4 because both parts divide evenly by 6.

The reduced ratio is exact. The decimal relationship is a convenience display calculated as a ÷ bafter reduction and rounded to ten decimal places.

Conventions and boundaries

  • Inputs: two signed whole-number ratio parts, each between −1,000,000 and 1,000,000.
  • Signs: a negative second part is normalized into the first part so the displayed second part is positive.
  • Zero: 0:x becomes 0:1 when x is nonzero. 0:0 and any zero second part are rejected.
  • Precision: the ratio is exact integer arithmetic; the decimal is rounded only at the display boundary.

Limitations

This tool accepts integer parts only. It does not parse decimal, unit-bearing, algebraic, or expression inputs, and it does not decide whether two quantities are meaningfully comparable. Use the Percentage Calculator for percentage relationships or the Fraction Calculator for exact fraction operations.

Worked examples

  • 18:24 reduces to 3:4.
  • 6:−9 normalizes and reduces to −2:3.
  • 0:7 reduces to 0:1.

Version and verification

Calculation version 1.0.0; formulas and deterministic fixtures last verified 2026-08-19. Automated tests cover reduction, signs, zero behavior, bounds, equivalence, and invalid inputs.