Ratio Calculator
Enter a ratio to simplify it, scale it, or solve A:B = C:D for the unknown term — all calculated instantly in your browser.
How to use Ratio Calculator
The ratio calculator provides three modes in one tool: simplify a ratio to its lowest terms using the greatest common divisor; scale a ratio by any multiplier; and solve A:B = C:D for any missing term by cross-multiplication. Results are shown instantly with the simplified or scaled ratio or the solved unknown value. Useful for recipes, mixing solutions, map scales, aspect ratios, financial comparisons, and unit conversions.
- Select the mode: Simplify, Scale, or Solve A:B = C:?
- In Simplify mode, enter the two ratio values A and B.
- In Scale mode, enter A, B, and the multiplier to produce a scaled version of the ratio.
- In Solve mode, enter three of the four values (A, B, C, D) and leave the unknown blank.
Your data never leaves your device — 100% private processing.
How ratio simplification works
A ratio A:B is simplified by dividing both terms by their greatest common divisor (GCD). The GCD is computed using the Euclidean algorithm: repeatedly replace the larger number with the remainder of dividing the larger by the smaller until the remainder is zero. For example, GCD(12, 8): 12 mod 8 = 4, 8 mod 4 = 0 → GCD = 4. So 12:8 = (12÷4):(8÷4) = 3:2. A simplified ratio has no common factors other than 1.
| Original ratio | GCD | Simplified |
|---|---|---|
| 10:15 | 5 | 2:3 |
| 12:8 | 4 | 3:2 |
| 100:25 | 25 | 4:1 |
| 7:3 | 1 | 7:3 (already simplified) |
| 360:240 | 120 | 3:2 |
Solving for missing ratio terms
When A:B = C:D, the cross-multiplication rule states A×D = B×C (the product of the means equals the product of the extremes). Given any three values, the fourth is solved by rearranging: D = (B×C)/A; C = (A×D)/B; B = (A×D)/C; A = (B×C)/D. This is used in scaling recipes (if 2 cups flour to 3 cups water makes 1 loaf, how much water for 5 cups flour?), currency conversion, and map scale calculations.
Glossary
- Ratio
- A comparison of two quantities expressed as A:B or A/B, indicating how many times one contains the other.
- Greatest Common Divisor (GCD)
- The largest positive integer that divides both numbers without a remainder; used to simplify ratios.
- Cross-multiplication
- Multiplying the numerator of one fraction by the denominator of the other to solve proportions: if A/B = C/D then A×D = B×C.
- Aspect ratio
- The ratio of width to height of an image or screen, e.g. 16:9 for widescreen HD displays.
Related reading
Frequently Asked Questions
Get weekly tool tips & updates
New tools, power-user tips, and productivity hacks — delivered free every Friday.
No spam, ever. Unsubscribe with one click.
Why use Ratio Calculator?
- Step-by-step explanations alongside every calculation
- Printable or shareable result summaries
- Works entirely offline in your browser
- Built-in input validation prevents common mistakes
Common use cases
- Calculate loan repayments before applying
- Check compound interest on savings accounts
- Estimate tax owed before filing
- Work out break-even point for a new business
- Plan retirement savings contributions
Related Calculators
Proportion Calculator
Solve proportions for an unknown value. Enter three terms of A/B = C/D and get the fourth, with cross-multiplication shown. Free and private.
Percentage Calculator
Calculate percentages instantly. Find what X% of a number is, what percentage X is of Y, or calculate percentage change.
Fraction Calculator
Calculate fractions online. Add, subtract, multiply, and divide fractions and mixed numbers with step-by-step solutions. Free fraction calculator for students.
BMI Calculator
Calculate your Body Mass Index (BMI) instantly. Supports metric (kg/cm) and imperial (lbs/ft+in) units. Free online BMI calculator.
Age Calculator
Calculate your exact age in years, months, and days. Find your next birthday countdown and day of birth. Free online age calculator.
Scientific Calculator
Free online scientific calculator with trigonometric functions, logarithms, powers, and constants. Supports keyboard input and calculation history.
Explore all Calculators.