Work with ratios two ways. This free ratio calculator simplifies a ratio to lowest terms, or solves a proportion (A:B = C:D) for the missing value — decimals supported.
Enter a ratio like 10 : 15 and it reduces to lowest terms by dividing both sides by their greatest common divisor. Decimals are supported.
Enter three of the four values in A : B = C : D and leave the unknown blank. The calculator solves for the missing one (cross-multiplication).
A ratio compares two quantities. Simplifying keeps the same proportion with the smallest whole numbers; solving a proportion finds an unknown that keeps two ratios equal.
How the Ratio Calculator Works
This calculator handles ratios two different ways: reducing a single ratio to its lowest terms, or solving for a missing value in a proportion where two ratios are set equal. Switch between “Simplify ratio” and “Solve proportion” mode depending on which problem you have.
Formula: To simplify A : B, any decimal terms are first scaled up by a power of 10 until both become whole numbers, then both are divided by their greatest common factor (GCF) to get the reduced ratio. To solve a proportion A : B = C : D where exactly one term is left blank, the calculator cross-multiplies to isolate it: if A is missing, A = (B × C) ÷ D; if B is missing, B = (A × D) ÷ C; if C is missing, C = (A × D) ÷ B; if D is missing, D = (B × C) ÷ A.
- A — first term of the ratio (Simplify mode) or first term of the proportion (Solve mode)
- B — second term of the ratio or proportion
- C — third term, used only in Solve Proportion mode
- D — fourth term, used only in Solve Proportion mode; leave whichever of A, B, C, or D is unknown blank
Example Scenarios
| A | B | C | D | Result |
|---|---|---|---|---|
| 10 | 15 | — | — | Simplifies to 2 : 3 |
| 8 | 20 | — | — | Simplifies to 2 : 5 |
| 2.5 | 5 | — | — | Simplifies to 1 : 2 |
| 4 | 6 | ? | 15 | C = 10 |
| 3 | ? | 9 | 12 | B = 4 |
| ? | 8 | 5 | 20 | A = 2 |
Ratio Calculator FAQ
What’s the difference between simplifying a ratio and solving a proportion?
Simplifying takes one ratio, like 10:15, and reduces it to the smallest whole numbers that keep the same relationship (2:3). Solving a proportion takes two ratios set equal to each other, like 4:6 = ?:15, and finds the one missing term that keeps both sides equivalent.Can I simplify a ratio that has decimal numbers, like 2.5:5?
Yes. The calculator scales both terms up by a power of 10 until they’re whole numbers, reduces them by their greatest common factor, then presents the simplified whole-number ratio — so 2.5:5 becomes 25:50 internally, then reduces to 1:2.How does the calculator find the missing value in a proportion?
It uses cross-multiplication. In A:B = C:D, if one term is unknown, multiplying the two terms diagonally across from it and dividing by the remaining known term isolates the missing value — the same technique taught for solving proportions by hand.Why does 10:15 simplify to 2:3?
10 and 15 share a greatest common factor of 5. Dividing both terms by 5 gives 2 and 3, which is the smallest whole-number pair that preserves the same relationship — 2:3 and 10:15 both represent the same underlying comparison.Can I use the ratio calculator for recipe scaling or map scales?
Yes — Solve Proportion mode is well suited to this. Enter your known ratio (like a map’s scale or a recipe’s original quantities) as A:B, then enter your target value as C or D, leaving the other blank to find the matching amount.What happens if I enter zero as one of the terms?
A zero denominator (B or D) makes the ratio or proportion undefined, since you can’t divide by zero. The calculator will show an error rather than a result in that case, so double-check your inputs if you see one.Related Calculators
If your ratio problem starts life as a fraction, the fraction simplifier reduces it the same way this tool reduces ratios. For percentage-based comparisons instead of ratios, the percentage calculator and the aggregate percentage calculator cover related classroom and workplace scenarios.