Ratio Calculator

Simplify any ratio to its lowest terms, or solve for a missing value in a proportion of the form A : B = C : D. The calculator also shows the ratio as a fraction, a decimal and a percentage, so you can move between representations in one step.

Choose a mode

Both terms must be positive integers or decimals. The result is scaled to the smallest whole-number ratio whenever possible.

Choose a mode, enter values, and press Calculate.

What a ratio is

A ratio compares two or more quantities of the same kind. Writing 3 : 5 means "for every 3 of the first thing, there are 5 of the second". Ratios appear everywhere: recipes (flour to sugar), maps (1 cm on the map to 1 km in reality), scale drawings, gear ratios, odds in gambling and proportions in chemistry.

A two-term ratio can also be written as a fraction (3/5), a decimal (0.6) or a percentage (60%). All four representations carry the same information — the calculator shows them together so you can pick the form that fits your context.

Formulas used by this calculator

1. Simplifying a ratio

simplified ratio = (a ÷ g) : (b ÷ g) where g = gcd(a, b)

Divide both terms by their greatest common divisor. For example, 12 : 18 → gcd(12, 18) = 6 → 2 : 3.

If the two terms are not whole numbers, the calculator first converts to integers by multiplying by a power of 10, then simplifies. This lets you simplify ratios like 1.5 : 2.5 → 3 : 5.

2. Solving A : B = C : D

A × D = B × C (cross-multiplication)

Given three of the four values, isolate the unknown:

  • Missing A: A = (B × C) / D
  • Missing B: B = (A × D) / C
  • Missing C: C = (A × D) / B
  • Missing D: D = (B × C) / A

Worked examples

Example 1 — Simplify a ratio

Ratio: 24 : 36

gcd(24, 36) = 12. Divide both sides: 24/12 : 36/12 → 2 : 3.

Simplified: 2 : 3

Example 2 — Simplify a ratio with decimals

Ratio: 1.5 : 2.5

Multiply both sides by 10 to clear decimals: 15 : 25. gcd(15, 25) = 5. Divide: 3 : 5.

Simplified: 3 : 5

Example 3 — Solve for a missing term

Find x in 3 : 5 = 9 : x.

Cross-multiply: 3 × x = 5 × 9 = 45. Divide: x = 45 / 3 = 15.

x = 15

Example 4 — Real-world: recipe scaling

A recipe uses flour and sugar in the ratio 4 : 1. You have 600 g of flour. How much sugar do you need?

Set up the proportion: 4 : 1 = 600 : x. Cross-multiply: 4 × x = 1 × 600 = 600. Divide: x = 150.

Sugar = 150 g

Ratio, fraction, decimal and percentage

For a two-term ratio a : b, the four representations are related by simple arithmetic:

FormValue for 3 : 5Formula
Ratio 3 : 5 —
Fraction 3/5 a / b
Decimal 0.6 a ÷ b
Percentage 60% (a ÷ b) × 100
Ratio as part : total 3 : 8 a : (a + b)

The last form — part : total — is useful for probability and for questions like "what fraction of the mixture is flour?".

Common mistakes

  • Confusing ratios with fractions. A fraction is part of a whole; a ratio compares two quantities. 3 : 5 means "3 of A for every 5 of B", not "3 out of 5".
  • Reversing the order of terms. 3 : 5 and 5 : 3 describe different situations. Always state which quantity comes first.
  • Adding the same amount to both terms. A ratio is not preserved when you add. It is preserved when you multiply or divide both terms by the same non-zero number.
  • Misreading "part : part" versus "part : whole". If a bag has 3 red and 5 blue marbles, the ratio of red to blue is 3 : 5, but red as a fraction of the total is 3/8.

Proportion Calculator

Solve a : b = c : d for the missing term.

Fraction Calculator

Add, subtract, multiply and divide fractions.

Greatest Common Factor Calculator

The divisor used to simplify ratios.

Percentage Calculator

Convert ratios to percentages and back.

Frequently asked questions

Divide both terms by their greatest common divisor. For example, 12 : 18 has gcd 6, so it simplifies to 2 : 3.

Use cross-multiplication: A × D = B × C. Enter any three values and leave the fourth empty — the calculator will solve for it.

Yes. Ratios can have three or more terms, such as 2 : 3 : 5. This calculator handles two-term ratios; for three-term ratios you can simplify pairwise or use the GCF calculator to find the common divisor for all terms.

A ratio compares two or more quantities of the same kind and can have more than two terms. A fraction is a single number representing a part of a whole. A two-term ratio a : b can be written as the fraction a/b, which is why the two are often confused.

Ratios usually describe quantities of things, which are non-negative. However, the arithmetic of ratios — especially the cross-multiplication form — works with negative values too if your problem requires it.