Ratio Calculator
Enter the first ratio, a : b.
Use this ratio calculator for two-term proportions. Enter any three numbers in a:b = c:d and leave one slot blank; the tool solves the missing value. When a and b are nonzero whole numbers, it also shows the simplified a:b ratio.
How to use the ratio calculator
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1
Fill three values
Enter numbers for any three of a, b, c and d in the proportion a:b = c:d.
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2
Leave one value blank
The blank value is treated as the unknown. The calculator works when exactly one slot is empty.
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3
Read the result
The result card gives the missing value. If a and b are whole numbers, a second card shows a:b in lowest terms.
What this calculator solves
| Task | Example input | Result |
|---|---|---|
| Find d | 3:4 = 6:d | d = 8 |
| Find c | 3:4 = c:20 | c = 15 |
| Simplify a:b | a = 24, b = 36 | 2:3 |
Under the hood
- Proportion solving: a:b = c:d means a / b = c / d. The calculator cross-multiplies to get a × d = b × c, then rearranges that equation for the one blank value.
- Simplifying a:b: when a and b are nonzero whole numbers, the calculator divides both by their greatest common divisor. GCD(24, 36) = 12, so 24:36 becomes 2:3.
- Decimals: decimal values can be used for the missing-value solver. The simplified a:b card appears only when a and b are whole numbers.
Useful examples
- Recipes and mixtures: if 3 parts syrup match 8 parts water, enter 3:8 = 12:d to find the matching water amount.
- Maps: a map scale such as 1:50,000 is a ratio. If 1 cm on the map represents 50,000 cm on the ground, proportional reasoning converts map distance to real distance.
- Aspect ratios: 16:9 and 4:3 compare width to height. Enter the known width-height pair and one new value to find the matching dimension.
- Unit rates: if 8 items cost 12, enter 8:12 = 15:d to estimate the same unit price for 15 items.
What this tool does not do
This calculator does not split a target total into parts such as 120 in a 5:3 ratio, and it does not handle three-term ratios like 2:3:5. It is built for one missing value in a two-term proportion, plus optional simplification of the first integer ratio a:b.
Frequently Asked Questions
With one blank in a:b = c:d, the proportion has a single missing term to solve. With two blanks there are many possible answers, and with no blank there is nothing for the tool to calculate.
Yes. Decimal values work for solving the missing term in the proportion. The simplified a:b card appears only when a and b are nonzero whole numbers.
Simplification is shown only for the first ratio a:b, and only when both a and b are whole numbers other than zero. For example, 24 and 36 simplify to 2:3.
No. A target-total split such as dividing 120 into 5:3 parts is a different calculator mode and is not part of this tool. Use this page for equivalent proportions of the form a:b = c:d.
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