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.

Ratio Simplifier — Gera Tools

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.

Tips and example

This is handy for screen and image aspect ratios: enter 1920 and 1080 and it reduces to 16 : 9. A ratio with a zero term such as 0 : 5 simplifies to 0 : 1, while 0 : 0 is reported as undefined. The tool also shows the ratio as a single decimal value (2:3 becomes about 0.667) so you can compare proportions that do not reduce to tidy numbers.