Ratio Calculator
Keeping Proportions Honest
A ratio compresses a relationship between two quantities into its simplest form, and a proportion assumes that relationship holds even when one of the four numbers involved is unknown. Both show up constantly outside the classroom — scaling a recipe, mixing a solution, or converting a map scale to real distance all rely on exactly this kind of reasoning. This calculator handles both directions: reducing a ratio to lowest terms, or solving for a missing value in an A:B = C:D proportion.
The Formulas
Proportion: A/B = C/D → solve for whichever value is unknown
A = (B×C)/D, B = (A×D)/C, C = (A×D)/B, D = (B×C)/A
Where Ratios and Proportions Matter
- Cooking and scaling recipes — keeping ingredient ratios constant when doubling or halving a batch.
- Mixing solutions — concrete, paint, fertilizer, and cleaning solutions are all specified by ratio.
- Maps and scale models — converting a scale ratio (like 1:50,000) into real-world distance.
- Financial ratios — debt-to-income, price-to-earnings, and similar comparisons reduce the same way.
| Original Ratio | Simplified |
|---|---|
| 8:12 | 2:3 |
| 4.5:9 | 1:2 |
Example proportion: if 2:3 = C:12, then C = (2×12)/3 = 8.
How to Use This Calculator
- Choose a mode: Simplify a Ratio or Find a Missing Value (Proportion).
- For simplifying, enter Value A and Value B.
- For a proportion, choose which of A, B, C, or D is unknown, then fill in the other three fields.
- Select Calculate to see the simplified ratio or the solved missing value.
Related Calculations
Working with fractions instead of ratios? The Fraction Calculator handles addition, subtraction, multiplication, and division directly, and the Percentage Calculator covers proportional comparisons expressed as percentages.