Ratio Calculator
Enter three values of a proportion A : B = C : D and this calculator solves the missing fourth, using cross multiplication. It also reduces the ratio A : B to its simplest form. This is the classic rule of three, the single most used piece of everyday math.
Fill in A, B, and C to solve A : B = C : D for the missing D.
- Missing value D
- 437.5
- Ratio 4 : 250 simplified
- 2 : 125
The same calculation scales a recipe from 4 servings to 7, converts a map distance to real distance, adjusts a paint or concrete mixture, or answers questions like: if 3 workers finish in 12 days, what changes with 5 workers? (Careful with that last type: quantities that work inversely, like workers and days, need the ratio flipped.)
How it's calculated
A : B = C : D → D = (B × C) ÷ A
Cross multiplication: in a true proportion, A × D = B × C. Knowing any three values gives the fourth. Simplifying a ratio divides both sides by their greatest common divisor, so 18:24 reduces to 3:4.
Worked example
A recipe uses 250 g of flour for 4 servings. For 7 servings: 4 : 250 = 7 : D, so D = (250 × 7) ÷ 4 = 437.5 g. And the ratio 18 : 24 simplifies to 3 : 4, since the GCD of 18 and 24 is 6.
Frequently asked questions
›What is the rule of three?
The traditional name for solving a proportion with three known values. Direct rule of three applies when quantities grow together (more servings, more flour). Inverse rule of three applies when one grows as the other shrinks (more workers, fewer days), and requires flipping one ratio.
›How do I simplify a ratio with decimals?
Multiply both sides by a power of ten until both are whole numbers, then divide by their GCD. For example, 2.5 : 1.5 becomes 25 : 15, which simplifies to 5 : 3.
›How are ratios different from fractions?
A ratio compares two quantities (3 : 4), while a fraction expresses a part of a whole (3/7 of the total if the ratio is 3 : 4). Converting between them trips people up: a 3 : 4 ratio means the first part is 3/7 of the total, not 3/4.
›What are common real uses of proportions?
Recipe scaling, currency estimation, map reading, medication dosing by weight, mixing fuel or fertilizer, unit pricing at the supermarket, and converting between screen resolutions or photo sizes.
Related tools
Fraction to Decimal Converter
Convert any fraction to a decimal and percentage, and see the fraction in lowest terms. Works with improper fractions too.
Percentage Calculator
Calculate percentages three ways: what is X% of Y, what percent X is of Y, and the percentage change between two numbers.
Average Calculator
Calculate the mean, median, sum, and count of any list of numbers. Paste or type values separated by commas, spaces, or new lines.