Ratio Calculator
Simplify ratios, solve for missing values, scale ratios up or down, and convert between ratio formats — with step-by-step solutions.
Examples
18:24 → simplified 3:4 | 75%:25% | decimal 0.75
3:4 = x:20 → missing value x = 15
3:4 scaled by a factor of 5 → 15:20
Frequently Asked Questions
What is a ratio?
A ratio compares two or more quantities showing their relative sizes. A ratio of 3:4 means for every 3 of the first quantity there are 4 of the second. Ratios appear everywhere — cooking recipes (1 cup flour to 2 cups water), maps (1:50000 scale), financial analysis (price-to-earnings ratio), and mixing solutions (1 part bleach to 10 parts water). Understanding ratios is fundamental to proportional reasoning.
How do you simplify a ratio?
Divide both numbers by their greatest common divisor (GCD). For example 18:24 — the GCD of 18 and 24 is 6. Divide both by 6 to get 3:4. A simplified ratio uses the smallest whole numbers that maintain the same proportion. Always check if the simplified numbers share a common factor and continue dividing until they don't.
How do you solve a proportion with a missing value?
Use cross multiplication. If A/B = C/D then A times D equals B times C. Rearrange to solve for the unknown. For example in 3/4 = x/20 cross multiply to get 3 times 20 equals 4 times x. So 60 equals 4x and x equals 15. This method works for any proportion where three of the four values are known.
How are ratios used in cooking and recipes?
Recipes use ratios to scale serving sizes. If a recipe for 4 servings uses 2 cups of flour and you want 10 servings the ratio 4:10 helps you calculate 2 times (10/4) equals 5 cups of flour needed. Scaling recipes up or down maintains the correct proportions of ingredients. Professional bakers use baker's percentages which express all ingredients as a ratio relative to flour weight.
What is the difference between a ratio and a fraction?
A ratio compares two separate quantities (3:4 means 3 of one thing to 4 of another). A fraction represents a part of a whole (3/4 means 3 out of 4 parts total). Ratios can be written as fractions but they have different meanings. The ratio 3:4 means there are 7 total parts with 3 being the first kind. The fraction 3/4 means 3 out of 4 parts total which would be written as the ratio 3:1.