Ratio Calculator
Show the math
What Your Result Means
- Solved Value: The missing term computed by cross-multiplication. If you entered A, B, and C, the calculator finds D such that A/B = C/D.
- Simplified A:B: The ratio of A to B reduced to its simplest whole-number form using the greatest common divisor. For example, 6:9 simplifies to 2:3.
- Proportion: The complete A:B = C:D statement with all four values filled in. You can verify by confirming A × D = B × C (the cross products are equal).
How This Calculator Works
You fill in any three of the four fields (A, B, C, D) and leave one blank. The calculator uses cross-multiplication — A × D = B × C — to solve for the missing value. It also computes the GCD of A and B to produce a simplified ratio. If fewer than three values are provided, no solution is shown. Non-integer inputs are displayed as decimal ratios rather than simplified whole numbers.
Quick Questions
What is cross-multiplication?
If A/B = C/D, then A × D = B × C. This is the fundamental property of proportions. Rearranging this equation lets you solve for whichever value is missing.
Can I use decimals or fractions?
Yes, the calculator accepts decimal inputs. Fraction inputs need to be converted to decimals first (e.g., enter 0.5 instead of 1/2). The simplified ratio output works best with whole-number inputs.
What if I leave more than one field blank?
The calculator needs at least three values to solve for the fourth. With two or more blanks, there are infinite solutions, so no result is displayed.
When would I use a ratio calculator?
Common uses include scaling recipes, converting map distances to real distances, calculating ingredient proportions, resizing images, mixing paint colors, and solving proportion word problems in math class.
Sources
- Khan Academy — Ratios, Rates, and Proportions (cross-multiplication and ratio fundamentals)
- Wikipedia — Ratio (mathematical definition and properties)
Method & review
Estimate only. Results reflect your inputs and standard formulas. Double-check important decisions independently.