Free online proportion calculator
A proportion states that two ratios are equal. Enter three values in A/B = C/D and this calculator finds the fourth using cross-multiplication.
Solve A/B = C/D — enter three values and select which one to solve for.
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How to use
- Enter three of the four values: A, B, C, and D.
- Select which variable to solve for.
- Click Solve Proportion.
- See the result and a verification check.
Formula
A/B = C/D — cross multiply: A × D = B × C
| Solve for | Formula |
|---|---|
| A | A = B × C / D |
| B | B = A × D / C |
| C | C = A × D / B |
| D | D = B × C / A |
Worked example
Recipe scaling: A recipe calls for 3 cups flour for 4 servings. How much for 10 servings?
- A = 3 (cups), B = 4 (servings), D = 10, solve for C
- C = A × D / B = 3 × 10 / 4 = 7.5 cups
Unit rate: If a car travels 60 miles in 2 hours, how far in 5 hours?
- A = 60, B = 2, D = 5, solve for C
- C = 60 × 5 / 2 = 150 miles
References
- Proportionality (mathematics)Wikipedia · en.wikipedia.org
- Directly ProportionalWolfram MathWorld · mathworld.wolfram.com
Frequently asked
How do you solve a proportion?
Cross-multiply and divide. For A/B = C/D, rearrange to find the missing variable: A = B×C/D, B = A×D/C, C = A×D/B, D = B×C/A.
What is cross-multiplication?
Cross-multiplication means A×D = B×C. This is true for any valid proportion. To find D, divide both sides by A.
What is a proportion used for?
Proportions appear everywhere — scaling recipes, converting units, calculating percentages, map scales, similar triangles, and speed/distance/time problems.
What is the difference between ratio and proportion?
A ratio compares two quantities (3:4). A proportion is a statement that two ratios are equal (3/4 = 6/8). This calculator solves proportion equations.
Can a proportion have zero values?
The denominator (B or D) cannot be zero. Numerators and other variables can theoretically be zero, but most practical applications use positive values.
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