Answer first
What this calculator tells you
Solve a proportion a ÷ b = c ÷ x for the unknown value. Scale a measurement, a map distance or a mixing ratio by cross-multiplying. Formula: a ÷ b = c ÷ x, so x = b × c ÷ a. At the worked-example inputs, the unknown value (x) is 20. Holding every other input steady, moving a from 1 to 5 moves the result from 12 to 60.
Transparent method
The formula
Scale a measurement, a map distance or a mixing ratio by cross-multiplying.
Worked example
Example inputs
How to interpret the result
A proportion says two ratios are equal, and cross-multiplying finds the missing part. If 3 parts of concentrate go with 4 of water, then 15 parts of concentrate go with 20 of water. The same step scales a map distance, a recipe, a photo enlargement or a dose. It works because both ratios describe the same relationship at different sizes.
At the worked-example inputs the unknown value (x) is 20. It rises with b and c and falls as a increases.
These are exact mathematical formulas; results are limited only by floating-point precision, not by real-world estimation. Confirm the convention (rounding rule, sign, base) your assignment or application expects.
Before you rely on it
What to check
Line up the units before you multiply. The top numbers must describe the same thing, and so must the bottom numbers.
The common error
Where people go wrong with proportion calculator
Putting one ratio upside down. Writing 3 over 4 equals x over 15 solves a different problem and returns 11.25 instead of 20.
Sensitivity evidence
How a changes the unknown value (x)
Holding every other input at the worked-example value, moving a from 1 to 5 moves the unknown value (x) from 12 to 60: a spread of 48, or 240% of the worked-example result.
| a | Unknown value (x) | First ratio as a decimal |
|---|---|---|
| 1 | 60 | 0.25 |
| 2 | 30 | 0.5 |
| 3worked example | 20 | 0.75 |
| 4 | 15 | 1 |
| 5 | 12 | 1.3 |
Every input, tested
Which input moves the unknown value (x) most
Of the 3 inputs, a moves the unknown value (x) most (15 across the range tested) and c moves it least (4).
| Input | Tested from | To | Unknown value (x) at each end | Swing |
|---|---|---|---|---|
| a | 2 | 4 | 30 to 15 | 15 (75%) |
| b | 3 | 5 | 15 to 25 | 10 (50%) |
| c | 14 | 17 | 18.7 to 22.7 | 4 (20%) |
Two variables at once
Unknown value (x) by a and b
Across the grid the unknown value (x) runs from 6 to 90. Moving a from 1 to 5 shifts it by 48 at the middle column, and moving b from 2 to 6 shifts it by 20 at the middle row, so a is the bigger lever here.
| a \ b | 2 | 4 | 6 |
|---|---|---|---|
| 1 | 30 | 60 | 90 |
| 2 | 15 | 30 | 45 |
| 3 | 10 | 20 | 30 |
| 4 | 7.5 | 15 | 22.5 |
| 5 | 6 | 12 | 18 |
The highlighted cell is the worked example: 20.
Step by step
The worked example, input by input
| Input | Value used | What it means |
|---|---|---|
| a | 3 | The known top number of the first ratio. |
| b | 4 | The known bottom number of the first ratio. |
| c | 15 | The known top number of the second ratio. |
| Unknown value (x) | 20 | |
| First ratio as a decimal | 0.75 | |
Inputs, definitions and assumptions
a
The known top number of the first ratio. The prefilled worked-example value is 3.
b
The known bottom number of the first ratio. The prefilled worked-example value is 4.
c
The known top number of the second ratio. The prefilled worked-example value is 15.
How to use this calculator
- 1Verify the inputs. Gather a, b and c from your own documents; the prefilled values are examples.
- 2Save a baseline. The worked example puts the unknown value (x) at 20. Store your own version of it as Scenario A.
- 3Test one change. Start with a, the input with the biggest effect here: moving a from 2 to 4 takes the unknown value (x) from 30 to 15, a swing of 75% of the worked-example figure.
- 4Check the extremes. At half the example a (1.5) the unknown value (x) is 40; at double (6) it is 10.
People also ask
Frequently asked questions
How do you calculate proportion?
a ÷ b = c ÷ x, so x = b × c ÷ a. At the worked-example inputs the unknown value (x) is 20.
What does the proportion result mean?
Scale a measurement, a map distance or a mixing ratio by cross-multiplying. At the worked-example inputs the unknown value (x) is 20. It rises with b and c and falls as a increases.
How much does a change the unknown value (x)?
Holding every other input at the worked-example value, moving a from 1 to 5 moves the unknown value (x) from 12 to 60, a spread of 48.
What are the limits of this proportion calculator?
These are exact mathematical formulas; results are limited only by floating-point precision, not by real-world estimation. Confirm the convention (rounding rule, sign, base) your assignment or application expects. The tables on this page test a only from 1 to 5; a value outside that range is not tabulated here.
Which input moves the unknown value (x) most in the proportion calculator?
Ranked by how far each moves the unknown value (x) across the range tested: a (15, 75%), b (10, 50%) and c (4, 20%).
If I double a in the proportion calculator, does the unknown value (x) double?
Doubling it from 3 to 6 takes the unknown value (x) from 20 to 10, which is 0.50 times the worked-example figure. So it falls instead of rising. Halving it to 1.5 gives 40.
How much does b matter in the proportion calculator?
The worked example uses 4. With the other inputs left at the worked example, moving b from 3 to 5 takes the unknown value (x) from 15 to 25, a swing of 50% of the worked-example figure.
How much does c matter in the proportion calculator?
The worked example uses 15. Holding every other input at its worked-example value, moving c from 14 to 17 takes the unknown value (x) from 18.7 to 22.7, a swing of 20% of the worked-example figure.
Which inputs change the first ratio as a decimal in the proportion calculator?
At the worked-example inputs it is 0.75. A takes it from 0.5 to 1 and b takes it from 1 to 0.6.
Why can't you divide by zero?
Division asks how many times the divisor fits into a number. Zero times any number never gives a non-zero result, so no answer works. The calculators show a dash instead of inventing one.
Sources and evidence
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