Result
Ratio Calculator: Simplify Positive Whole Numbers
Reduce two positive whole numbers to their simplest equivalent ratio. The order of the two quantities stays the same.
Formula: Simplified ratio = (a ÷ gcd(a,b)) : (b ÷ gcd(a,b)).
Worked example: For 48 : 18, the greatest common divisor is 6. Divide both terms by 6 to obtain 8 : 3.
Use positive whole numbers no larger than 9,007,199,254,740,991. Zero, negative values and decimals are outside this tool’s input rules.
Method, examples and limits
Keep the same units
Before simplifying measurements, put both quantities in the same unit. For 2 metres to 50 centimetres, use 200 : 50, which simplifies to 4 : 1. Entering 2 : 50 directly describes a different comparison. Counts such as red and blue counters do not need a length conversion.
Distinguish a part from the whole
If red to blue is 8 : 3, there are 11 total parts. Red is 8/11 of the combined group, not 8/3 of the group. A ratio compares the two named quantities; a fraction of the total uses their sum as the denominator.
Scale both terms together
The ratios 8 : 3, 16 : 6 and 48 : 18 are equivalent because both terms are multiplied by the same positive factor. Adding the same number to each term generally changes the ratio. For a decimal ratio such as 2.5 : 1.5, multiply both terms by 10 and enter 25 : 15.
Interpret a simplified result
A result of 8 : 3 describes relative amounts, not a required batch size. A recipe can use 80 g and 30 g or another matching scale. The calculator simplifies two inputs; it does not solve a missing fourth value or decide whether a recipe is suitable for a particular use.
Reference (English): Wolfram MathWorld: Euclidean Algorithm
Maintained by: Muhammad Bhutto · 2026-10-21 · Methodology · Report an error