Proportion Calculator
Enter any three values in the proportion A/B = C/D and instantly solve for the missing one, with the cross-multiplication steps shown.
Enter three values and leave one blank to solve the proportion A/B = C/D.
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.
Your data never leaves your device — 100% private processing.
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.
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
Get weekly tool tips & updates
New tools, power-user tips, and productivity hacks — delivered free every Friday.
No spam, ever. Unsubscribe with one click.
Why use Proportion Calculator?
- Step-by-step explanations alongside every calculation
- Printable or shareable result summaries
- Works entirely offline in your browser
- Built-in input validation prevents common mistakes
Common use cases
- Calculate loan repayments before applying
- Check compound interest on savings accounts
- Estimate tax owed before filing
- Work out break-even point for a new business
- Plan retirement savings contributions
Related Calculators
Ratio Calculator
Simplify ratios, scale them up, and solve for a missing value. Great for recipes, mixing, and aspect ratios. Free and private.
Percentage Calculator
Calculate percentages instantly. Find what X% of a number is, what percentage X is of Y, or calculate percentage change.
Fraction Calculator
Calculate fractions online. Add, subtract, multiply, and divide fractions and mixed numbers with step-by-step solutions. Free fraction calculator for students.
BMI Calculator
Calculate your Body Mass Index (BMI) instantly. Supports metric (kg/cm) and imperial (lbs/ft+in) units. Free online BMI calculator.
Age Calculator
Calculate your exact age in years, months, and days. Find your next birthday countdown and day of birth. Free online age calculator.
Scientific Calculator
Free online scientific calculator with trigonometric functions, logarithms, powers, and constants. Supports keyboard input and calculation history.
Explore all Calculators.