Ratio Calculator
Simplify ratios, solve proportions and scale ratios up or down.
About Ratio Calculator
A ratio compares two quantities. Simplifying divides both parts by their greatest common divisor. To solve a proportion A:B = C:D for D, cross-multiply: D = (B × C) ÷ A.
Formulas
Simplified ratio
Simplified A:B = (A ÷ GCD) : (B ÷ GCD)
- A
- First part of the ratio
- B
- Second part of the ratio
- GCD(A,B)
- Greatest common divisor of A and B
Proportion — solve for D
A:B = C:D → D = (B × C) ÷ A
- A
- First known ratio term
- B
- Second known ratio term
- C
- New first term
- D
- Missing value to find
Worked example
With the default values below, Ratio Calculator returns Simplified Ratio (A:B) of 3 : 4. Change any input above and every figure here is recalculated in your browser.
Inputs used
- Aaccepts -1,000,000–1,000,000
- 3
- Baccepts -1,000,000–1,000,000
- 4
- C (for A:B = C:?)accepts -1,000,000–1,000,000
- 9
Results
- Simplified Ratio (A:B)
- 3 : 4
- Missing Value (D in A:B = C:D)
- 12.0000
- A ÷ B
- 0.7500
Step by step
- 1Find the GCD of A and B= 1
- 2Divide both parts by the GCD to simplify= 3 : 4GCD is 1 — the ratio is already in simplest form.
- 3Compute A ÷ B as a decimal= 0.7500
- 4Solve for D in A:B = C:D= 12.0000
Assumptions and limits
- The result is derived only from the 3 inputs listed above. Anything not among them is not part of the calculation.
- In particular, this calculator does not take inflation, tax, fees or charges or compounding frequency into account.
- Figures are rounded for display to 4 decimal places, so totals built from several rounded parts can differ slightly from the unrounded arithmetic.
How these calculators are built and tested is described on the Methodology page. If a figure looks wrong, please report it.
Frequently Asked Questions
How do I scale a recipe with ratios?
Set the known ratio as A:B, put your new amount as C, and the calculator solves for the matching quantity D that keeps the proportion identical.
What does a simplified ratio mean?
It expresses the same relationship using the smallest whole numbers. For example, 6:8 simplifies to 3:4.