Proportion Calculator
Solve for any missing value in a proportion A/B = C/D. Enter three known values, choose what to find, and get the answer with full cross-multiplication steps shown.
Last updated: March 2026
How to Use the Proportion Calculator
- Choose the unknown value — use the dropdown to select which variable (A, B, C, or D) you want to solve for.
- Enter the three known values — type numbers into the three active fields. The unknown field is automatically disabled.
- Read the answer instantly — the missing value appears as soon as you finish typing. No Calculate button needed.
- Review the cross-multiplication steps — the results panel shows the full equation setup, cross products, and algebraic solution.
- Verify the result — the final row confirms that A/B equals C/D with the computed value substituted in.
Understanding Cross-Multiplication
A proportion states that two fractions are equal: A/B = C/D. The most reliable method for solving a proportion with one unknown is cross-multiplication. The rule states that if A/B = C/D, then A × D = B × C. This works because multiplying both sides of the equation by B × D clears both denominators simultaneously, leaving a simple algebraic equation.
For example, to solve 3/4 = x/20: cross-multiply to get 3 × 20 = 4 × x, which simplifies to 60 = 4x. Dividing both sides by 4 gives x = 15. You can verify this is correct by substituting back: 3/4 = 15/20 = 0.75. Both sides equal 0.75, confirming the answer.
The same logic applies regardless of which variable is unknown. To find A given B, C, and D: A = (B × C) / D. To find B: B = (A × D) / C. To find C: C = (A × D) / B. All four formulas are derived from the same cross-product equation A × D = B × C.
When Cross-Multiplication Cannot Be Used
Cross-multiplication is undefined when either denominator (B or D) equals zero, because division by zero has no meaning in arithmetic. Additionally, cross-multiplication in its standard form applies to direct proportions only. Inverse proportions (where A × B = C × D) require a different setup.
Direct vs Inverse Proportion Explained
Two quantities are in direct proportion when they increase and decrease together at the same rate. If you double one quantity, the other also doubles. The ratio A/B stays constant. Common examples include unit pricing (more items = more cost), distance and time at constant speed, and recipe scaling. The general form is y = kx where k is the constant of proportionality.
Two quantities are in inverse proportion when one increases as the other decreases, so their product remains constant: A × B = k. If you double one quantity, the other halves. Real-world examples include workers and time (more workers finish a job faster), gear ratios (larger gear = slower rotation), and pressure and volume of a gas (Boyle's Law). The general form is y = k/x.
This calculator solves direct proportions (A/B = C/D). For inverse proportion problems, rearrange the relationship as A × B = C × D and solve algebraically, or use the ratio calculator.
Proportions in Maps and Scale Drawings
Scale is one of the most practical applications of proportion. A map scale of 1:50,000 means every 1 cm on the map represents 50,000 cm (500 m) in reality. If you measure 3.5 cm between two cities on the map, set up 1/50,000 = 3.5/x and solve: x = 175,000 cm = 1.75 km. Architectural blueprints, engineering drawings, and model kits all use the same proportional reasoning.
Unit Rates and Proportional Relationships
A unit rate simplifies a ratio so the denominator is 1. For example, 240 miles driven in 4 hours = 60 miles per 1 hour. Once you know the unit rate, you can set up a direct proportion to solve for any unknown: 60/1 = x/7 hours → x = 420 miles. Proportional reasoning underpins currency exchange, nutritional labels, speed conversion, and countless everyday comparisons.
How to Solve a Proportion If...
How do I solve 5/8 = x/40?
x = 25. Cross-multiply: 5 × 40 = 8 × x → 200 = 8x → x = 25. Verify: 5/8 = 25/40 = 0.625.
How do I find the missing denominator in 7/x = 21/9?
x = 3. Cross-multiply: 7 × 9 = x × 21 → 63 = 21x → x = 3. Verify: 7/3 = 21/9 = 2.333...
How do I scale a recipe for 6 servings to 9 servings if it calls for 2 cups of flour?
3 cups of flour. Set up 2/6 = x/9. Cross-multiply: 2 × 9 = 6 × x → 18 = 6x → x = 3 cups.
If 1 inch on a map equals 25 miles, how many miles is 3.5 inches?
87.5 miles. Proportion: 1/25 = 3.5/x → x = 25 × 3.5 = 87.5 miles.
A car travels 150 miles in 2.5 hours. How far in 4 hours at the same speed?
240 miles. Set up 150/2.5 = x/4 → x = (150 × 4) / 2.5 = 600 / 2.5 = 240 miles.
If 5 workers finish a job in 12 days, how many days for 3 workers (direct proportion model)?
20 days. Workers and time are inversely proportional, but using proportion form: 5/3 = d/12 is incorrect. The inverse form gives 5 × 12 = 3 × d → d = 20 days.
A shirt costs $45. If sales tax is applied at 8%, what is the proportion setup for the tax amount?
$3.60 tax. Set up 8/100 = x/45 → x = (8 × 45) / 100 = 360/100 = $3.60.
If 3/5 of a class are girls and there are 30 students, how many are girls?
18 girls. 3/5 = x/30 → x = (3 × 30) / 5 = 90 / 5 = 18.
People Also Search For
What is the proportion formula?
The proportion formula is A/B = C/D, or equivalently A × D = B × C (cross-product form). Given any three of the four values, you rearrange to isolate the unknown: for D, use D = (B × C) / A; for C, use C = (A × D) / B; for B, use B = (A × D) / C; for A, use A = (B × C) / D.
How to solve proportions step by step
Step 1: Write the proportion A/B = C/D. Step 2: Cross-multiply to get A × D = B × C. Step 3: Isolate the unknown variable. Step 4: Simplify and verify. Always substitute your answer back into the original proportion to confirm both sides are equal.
What does proportional mean in math?
Two quantities are proportional when their ratio remains constant. If x and y are proportional, then y/x = k for some constant k, which means y = kx. Doubling x doubles y; tripling x triples y. This constant ratio is called the constant of proportionality.
Proportion vs ratio — what is the difference?
A ratio is a comparison of two quantities (e.g., 3:4). A proportion is an equation stating two ratios are equal (e.g., 3/4 = 6/8). Every proportion contains two ratios, but a single ratio alone is not a proportion.
How to check if two ratios form a proportion
Cross-multiply and check if the products are equal. For 2/3 and 8/12: 2 × 12 = 24 and 3 × 8 = 24. Since 24 = 24, the ratios are proportional. If the cross-products differ, the ratios are not proportional.
Frequently Asked Questions
What is a proportion?
A proportion is a mathematical statement that two ratios are equal: A/B = C/D. It expresses a relationship between four numbers where the ratio of the first pair equals the ratio of the second pair.
How do I solve 3/4 = x/20?
Cross-multiply: 3 × 20 = 4 × x → 60 = 4x → x = 15. Select "Find C" in the calculator, enter A=3, B=4, D=20, and the answer 15 appears instantly.
Why does cross-multiplication work?
Cross-multiplication works because multiplying both sides of A/B = C/D by B × D eliminates both denominators. The left side becomes A × D and the right side becomes B × C, giving the equivalent equation A × D = B × C with no fractions.
Can proportions include decimals or fractions as inputs?
Yes. Any real number (positive, negative, or decimal) is valid as long as no denominator (B or D) equals zero. The cross-multiplication algebra works identically for decimal and fractional inputs.
What is a proportional relationship?
A proportional relationship is one where two quantities always maintain the same ratio. On a graph, a proportional relationship is a straight line through the origin. The equation is y = kx where k is the constant of proportionality.
How do maps use proportions?
A map scale like 1:100,000 is a ratio. To find real distances, set up the proportion (map distance) / 1 = (real distance) / 100,000 and solve. For example, 4.5 cm on the map → 4.5 × 100,000 = 450,000 cm = 4.5 km in reality.
What is the constant of proportionality?
The constant of proportionality (k) is the fixed ratio between two proportional quantities: k = y/x or k = A/B. In a proportion A/B = C/D, both ratios equal the same constant k.
Is this calculator accurate for large numbers?
Yes. The calculator uses JavaScript floating-point arithmetic, which handles numbers up to about 10^308 accurately. For extremely large integers (more than 15–16 significant digits), slight rounding may occur due to floating-point limitations.
Does this calculator store my data?
No. All calculations happen locally in your browser. No values are sent to any server, and nothing is stored after you close the page.
What is inverse proportion and how is it different?
In inverse proportion, the product of two quantities is constant (A × B = k), unlike direct proportion where the ratio is constant (A/B = k). This calculator solves direct proportions. For inverse proportion, rearrange your problem into the form A × B = C × D before using the cross-product property.