Ratio Calculator
Simplify a ratio, scale it, and solve for a missing term.
What the Ratio Calculator does
A ratio compares two quantities. Leave C and D blank to simplify A : B. Fill in three of the four boxes and the calculator solves the proportion for the missing term by cross-multiplication.
Formula
A : B = C : D → A × D = B × CSimplify by dividing both terms by their GCD
Inputs explained
| Input | Unit | Required | Notes |
|---|---|---|---|
| A | number | Yes | — |
| B | number | Yes | — |
| C | number | Optional | Leave C and D blank to just simplify A : B. |
| D | number | Optional | Leave one of C or D blank to solve for it. |
How to use it
- Enter A and B.
- Optionally add C and D.
- Select Calculate.
Worked example
A map scale is 3 cm : 45 km. How many km does 7 cm represent?
- A
- 3
- B
- 45
- C
- 7
- D
- (blank)
D = (45 × 7) ÷ 3 = 105 km.
Reading the result
- A ratio and a fraction use the same numbers to answer different questions — 3:4 compares two separate quantities to each other, while 3/4 expresses one quantity as a share of a whole that includes it. Solving "A is to B as C is to what" assumes the same underlying relationship holds, not that the numbers are interchangeable with a fraction.
Common mistakes
- Treating a ratio like 3:4 as equivalent to the fraction 3/4 in every context. In a mixing or scaling problem, the distinction between "part to part" and "part to whole" changes which calculation actually applies.
Frequently asked questions
How do I simplify a ratio with decimals?
Multiply both sides by 10 until both terms are whole numbers, then divide by their greatest common divisor.
What is the difference between a ratio and a fraction?
A ratio compares parts to parts (2 : 3 means 2 for every 3). A fraction compares a part to the whole (2/5 of the total).