Ratio Calculator

A ratio compares two quantities by division — "for every 8 of the first, there are 12 of the second". It is not a fraction of a whole but a relationship between parts, which is why ratios appear everywhere a proportion must be preserved: recipes, mixes, maps, odds and part-based percentages.

Simplifying a ratio

Ratios read best in lowest terms, and the calculator reduces by the Greatest Common Divisor (GCD) of the two numbers:

GCD(8, 12) = 4
8 ÷ 4 = 2
12 ÷ 4 = 3

So 8 : 12 simplifies to 2 : 3. The GCD appears in the output so you can see exactly what was divided out.

Converting ratio parts to percentages

Add the parts to get the total, then divide each part by that total:

Total = 8 + 12 = 20
First part = 8 ÷ 20 = 40%
Second part = 12 ÷ 20 = 60%

The two percentages always sum to 100%, turning a relationship into a share — handy when a mix written "2 : 3" needs to read as "40% of the batch is the first ingredient".

Part-to-part vs part-to-whole

A ratio such as 1 : 3 describes the relationship between two parts: one part of A for every three of B. But "part of the whole" phrasing reinterprets it: if A and B sit in a 1 : 3 ratio, then A is 1 ÷ (1 + 3) = 25% of the combined total. The step from ratio to percentage is exactly that conversion, and dropping the "+1" (treating 1 : 3 as "a third") is one of the most reliable ratio errors in everyday life.

Where ratios matter

• Cooking and mixing — recipes, cake batter, paint tints, concrete and mortar mixes.
• Maps and models — a scale of 1 : 50,000 means 1 unit on the map equals 50,000 of the same units on the ground (1 cm represents 50,000 cm = 500 m).
• Finance — debt-to-income, P/E ratios, profit-sharing splits between partners.
• Statistics and odds — comparing groups (3 girls to 5 boys is 3 : 5), betting odds, mix proportions.

Equivalent ratios — the many faces of one relation

8 : 12, 4 : 6, 2 : 3 and 20 : 30 all describe the same relationship, because doubling or halving both sides preserves the ratio. The simplified form (2 : 3) is the version used in every real-world scale-up — from a single serving to a catering batch — which is why simplification, not bare calculation, is usually the point of a ratio exercise.

Three-part and larger ratios

This tool handles two parts. For A : B : C, divide every number by the GCD of the whole set. For 6 : 9 : 15 the GCD is 3, giving 2 : 3 : 5 — the same method with one more term, and the standard way reading concrete mixes or profit splits among three partners.

Common mistakes

• Dividing only one side of the ratio — scaling 8 : 12 down to 2 : 12 loses the relationship completely.
• Treating a part-to-part ratio as a fraction of the whole without first adding the parts.
• Mixing units inside a ratio — "1 m : 30 cm" is invalid until both sit on the same unit (100 cm : 30 cm = 10 : 3).
• Reading "2 : 3" as the fraction 2/3 — the first part's share is 2 ÷ (2 + 3) = 2/5, not 2/3.
• Entering zero as a part; a ratio with one empty side is undefined and the math collapses.

For the shared-factor machinery behind simplification, see the HCF calculator, and for the percentage view of a part against a total, the percentage calculator.