How to use Proportion Calculator
The proportion calculator solves any proportion of the form A/B = C/D for a single missing value using cross-multiplication. Enter three of the four terms — A, B, C, or D — leave the unknown blank, and the tool computes the answer and shows every cross-multiplication step. Proportions are the foundation of scaling, unit conversion, map reading, recipe adjustment, and countless word problems in maths, science, and everyday life.
- Enter three of the four values A, B, C, D in the proportion A/B = C/D.
- Leave exactly one field blank — that is the unknown to be solved.
- Click Solve to compute the missing value.
- Read the step-by-step cross-multiplication working below the result.
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Cross-multiplication explained
A proportion states that two ratios are equal: A/B = C/D. Cross-multiplication exploits the fact that equivalent fractions share the same cross-products: A×D = B×C. Rearranging gives four solving formulas: A = (B×C)/D; B = (A×D)/C; C = (A×D)/B; D = (B×C)/A. For example, to find D given A=3, B=4, C=9: D = (4×9)/3 = 36/3 = 12. Always verify the answer by substituting back: 3/4 = 9/12 ✓ (both simplify to 3/4).
| A | B | C | D | Worked solution |
|---|---|---|---|---|
| 1 | 2 | 3 | ? | D = (2×3)/1 = 6 |
| 5 | ? | 20 | 8 | B = (5×8)/20 = 2 |
| ? | 4 | 6 | 8 | A = (4×6)/8 = 3 |
| 3 | 7 | ? | 21 | C = (3×21)/7 = 9 |
Real-world proportion applications
Proportions appear throughout everyday life. In cooking: scaling a recipe from 4 servings to 6 means each ingredient is multiplied by 6/4 = 1.5. In map reading: a 1:50,000 scale map means 1 cm represents 500 m, so 3.5 cm on the map is 3.5 × 500 = 1,750 m in reality. In unit conversion: 1 inch = 2.54 cm, so 7 inches = (7 × 2.54)/1 = 17.78 cm. In dosage calculation: if 400 mg is recommended per 10 kg body weight, a 65 kg person needs (400 × 65)/10 = 2,600 mg. In photography: maintaining aspect ratio when resizing images.
Worked examples
Solve for x
Inputs: 3/4 = x/20
Result: x = 15
Scale a recipe
Inputs: 2/4 = x/8
Result: x = 4 cups
Missing denominator
Inputs: 5/x = 20/8
Result: x = 2
Glossary
- Proportion
- An equation stating that two ratios are equal: A/B = C/D.
- Cross-multiplication
- The rule that if A/B = C/D then A×D = B×C, used to solve for an unknown term.
- Scale factor
- The ratio by which all dimensions of a shape or recipe are multiplied when scaling up or down.
- Direct proportion
- A relationship where two quantities increase or decrease at the same rate; if x doubles, y doubles.
Related reading
Frequently Asked Questions
Why use Proportion Calculator?
- Solves A/B = C/D for any single unknown using full step-by-step cross-multiplication working
- Displays every intermediate step so you can follow the method and learn the technique
- Handles non-integer solutions and returns the result to full decimal precision
- Substitutes the answer back to verify correctness before displaying the final result
Common use cases
- Scale a recipe from 4 servings to 7 while keeping every ingredient proportional
- Convert a map measurement to a real-world distance using the stated map scale ratio
- Calculate the correct medication dose for a patient's body weight from a reference dose
- Resize an image to a target width while maintaining the original aspect ratio exactly
- Solve a missing-value proportion word problem for a maths or science assignment
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