How does ratio simplification work?

Both terms of the ratio are divided by their greatest common divisor (GCD), the largest number that divides both exactly. For 24:36 the GCD is 12, so dividing gives 2:3, which is the same proportion in its simplest whole-number form.

Can I simplify a ratio with decimals?

Yes. Decimal terms are first scaled to whole numbers by removing the decimal point, then reduced by their GCD. For example 1.5:4.5 becomes 15:45 and then 1:3, which is the simplest exact form.

What is the greatest common divisor?

The greatest common divisor of two integers is the largest integer that divides both with no remainder. The tool finds it with the Euclidean algorithm, which repeatedly replaces the larger number with the remainder of dividing it by the smaller.

What happens if one term is zero?

A ratio like 0:5 simplifies to 0:1 because zero shares all of the other number as a common factor. If both terms are zero the ratio is undefined and the tool reports an error rather than dividing by zero.

Is this useful for aspect ratios?

Yes. Entering a width and height such as 1920 and 1080 reduces to 16:9, the standard widescreen aspect ratio. Any pixel dimensions can be reduced the same way to identify their underlying aspect ratio.

What is the Ratio Simplifier?

Simplify any ratio to its lowest terms by dividing both sides by their greatest common divisor. Handles whole numbers and decimals, scaling fractional terms to integers first. Shows the reduced ratio and its decimal value. Runs in your browser. It runs free in your browser on Gera Tools, with nothing uploaded.

Ratio Simplifier — Gera Tools

Name: Ratio Simplifier
Creator: Gera Tools
License: https://creativecommons.org/licenses/by/4.0/

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A ratio compares two quantities, and the same comparison can be written many ways — 24:36, 8:12, and 2:3 all describe the same proportion. This tool reduces any ratio to its simplest whole-number form so it is easy to read, compare, and communicate.

How it works

Simplifying a ratio means dividing both terms by their greatest common divisor (GCD). The tool finds the GCD with the Euclidean algorithm, which repeatedly replaces the pair (a, b) with (b, a mod b) until the remainder is zero:

24 : 36
  gcd(24, 36) = 12
  24 / 12 = 2
  36 / 12 = 3
  simplified -> 2 : 3

When you enter decimals, the tool first scales both terms up to whole numbers by clearing the decimal points, then reduces. So 1.5 : 4.5 is scaled to 15 : 45 and reduced to 1 : 3. All arithmetic uses exact integer math, so there is no rounding error.

Worked examples

Aspect ratio from pixel dimensions: Enter 1920 and 1080 and the result is 16:9 — the standard widescreen aspect ratio used by almost all modern displays, video platforms, and presentation software. The same logic works for any resolution: 2560:1440 reduces to 16:9, while 2560:1600 reduces to 8:5.

Mixing ratios in recipes: A concrete mix of cement, sand, and gravel in the proportions 2 : 6 : 4 can be simplified by applying the GCD of all three terms (here, 2) to get 1 : 3 : 2. Smaller numbers are easier to measure when scaling a batch.

Gear ratios in engineering: A gearbox with a 48-tooth driven gear and a 16-tooth driving gear has a ratio of 48:16, which simplifies to 3:1. This tells you immediately that for every turn of the driving gear, the output turns three times slower.

When the ratio has decimals

Decimal inputs arise in unit conversions, density comparisons, and survey measurements. Entering 7.5 : 10 scales up to 75 : 100, which reduces to 3 : 4. The scaling step always finds the smallest power of ten that clears all decimal places, so there is no accumulated rounding.

Reading the decimal representation

The tool also displays the ratio as a single number (its value as a fraction). 2:3 is approximately 0.667, and 16:9 is approximately 1.778. This is useful for programmatic comparisons — when you need to check whether two images have the same proportions without simplifying both — and for spotting which of two ratios represents the larger or smaller proportion at a glance.

Edge cases

A ratio like 0:5 simplifies to 0:1 because zero shares all of any number as a common divisor. If both terms are zero, the ratio is mathematically undefined and the tool returns an error rather than attempting a division by zero. Negative inputs are not meaningful for most ratio contexts, so enter absolute values.