Math
Ratio Calculator
Enter two quantities to see the ratio reduced, split as percentages and expressed as 1 to n.
The formula
simplified = a ÷ gcd(a, b) : b ÷ gcd(a, b)
share of a = a ÷ (a + b) × 100
Worked example
A 16 : 24 mix
- gcd(16, 24) = 8
- 16 ÷ 8 = 2 and 24 ÷ 8 = 3, so 2 : 3
- 16 ÷ 40 = 40% and 24 ÷ 40 = 60%
Where this goes wrong
Mixing part-to-part with part-to-whole
A 2:3 ratio means five parts in total, so the first share is two fifths — 40%, not 50% and not 66%. Reading a ratio as if the second number were the total is the single commonest ratio error, and it shows up wherever mixes and splits are written down.
Questions
- What is the difference between a ratio and a fraction?
- A ratio compares two parts to each other; a fraction compares one part to the whole. A 2:3 mix means 2 parts in every 5, which is the fraction 2/5.
- How do I scale a ratio up?
- Multiply both sides by the same number. A 2:3 ratio needing 10 units of the first part becomes 10:15 — the relationship holds as long as both sides move together.
- Why express a ratio as 1 to n?
- It makes two ratios directly comparable. 16:24 and 21:31 are hard to rank by eye, but 1:1.5 against 1:1.48 settles it immediately.