How to use this calculator
A ratio describes relative quantities in a fixed order. The simplified terms express the same relationship using the smallest integers. Decimal terms are first scaled by a common power of ten. To solve a proportion, the two fractions must describe the same relationship and use consistent units.
Recipes, mixing and map scales
Simplify a recipe ratio
A recipe uses 300 g of flour and 450 g of water. Enter 300 and 450 in ratio mode to obtain 2 : 3. Order matters: this states flour to water, not water to flour. Both terms use the same mass unit.
Scale the number of portions
If 200 g serves 4 portions, how much serves 6? In proportion mode enter A = 200, B = 4 and D = 6. The equation is 200 / 4 = x / 6, so x = 300 g. This assumes the ingredient scales directly with the portion count.
Read a map scale
If 3 cm on a map represents 150 m, 8 cm represents 400 m. Enter A = 150, B = 3 and D = 8. Keep B and D in centimetres; x has the same unit as A, metres. For a dimensionless map ratio, first convert 150 m to 15,000 cm: the scale is 3 : 15,000 = 1 : 5,000.
Part-to-part is not part-to-total
A 2 : 3 mixture has five parts in total. The first ingredient is 2/5, or 40% of the mixture, not 2/3. Use the percentage calculator with part 2 and whole 5 to check it. The ratio tool handles two terms; it does not solve three-ingredient mixtures or account for chemical concentration.
The formula
Worked examples
Simplify 12 : 18
The greatest common divisor is 6, so 12 : 18 = 2 : 3.
Simplify 1.5 : 2.5
Multiply both terms by 10: 15 : 25. Divide by 5 to get 3 : 5.
Solve 3 / 4 = x / 20
x = 3 × 20 / 4 = 15.
Special cases & input limits
Simplification accepts nonnegative terms, including a single zero: 0 : 5 becomes 0 : 1. The ratio 0 : 0 is rejected. Proportions accept signed inputs but require nonzero denominators B and D. All four positions have fixed labels, with x as the missing numerator.
Inputs support a decimal point and scientific notation, up to 30 significant digits and a magnitude of 10⁻²⁰ to 10³⁰, or zero. Select 0–12 display decimal places. Very small or large answers use scientific notation so a nonzero result is not displayed as zero.
A common mistake
Do not compare unlike units without converting them. The ratio 1 metre to 50 centimetres is 100 : 50 = 2 : 1, not 1 : 50.
Content updated · Calculation methodology