Ratio Calculator

The ratio 10:15 reduces to 2:3.

How it works

• Read the terms for the selected mode.
• Scaled any decimal terms to integers, then reduced by the greatest common divisor or applied the proportion.
• Rounded to the documented precision (12 significant digits for simplification, the selected decimals for a split).

10:15 = 2:3 (gcd 5)

• The two terms cannot both be zero; a denominator of zero is rejected with a field message.

Methodology

1. Scale decimal terms to integers by the largest number of decimal places present.
2. Simplify by dividing both terms by their greatest common divisor.
3. Solve a proportion with cross-multiplication: x = b·c/a.
4. Split a total by the ratio shares: partA = total·a/(a+b), partB = total − partA.

Usage

1. Choose the ratio operation: simplify, scale, solve or split.
2. Enter the two ratio terms and, for scale/solve/split, the factor, the third term or the total.
3. Read the resulting ratio, the missing term or the two shares.

Examples

These are examples, not current values: they use fixed inputs, while the interactive tool computes live results in your browser.

Simplify

{
  "mode": "simplify",
  "a": 10,
  "b": 15
}

Scale

{
  "mode": "scale",
  "a": 2,
  "b": 3,
  "factor": 4
}

Solve

{
  "mode": "solve",
  "a": 2,
  "b": 3,
  "c": 4
}

Split

{
  "mode": "split",
  "a": 1,
  "b": 3,
  "total": 100
}

Limitations

Ratios versus percentages

A ratio compares parts directly (2:3), while a percentage expresses a part of a whole out of 100. Simplifying a ratio keeps the proportion and makes the smallest integer terms visible.