Proportion Calculator
Solve A/B = C/D by leaving the unknown blank
A / B = C / D. Fill any three values and leave the unknown one blank.
How to Use
- 1Enter three of the four values A, B, C and D.
- 2Leave the unknown value blank. Any position works.
- 3Press Solve (or just type) to get the missing number.
- 4Fill all four values to check whether the proportion is true.
Proportion Rules
- ProportionA/B = C/D
- Cross multiplyA·D = B·C
- Solve for DD = B·C ÷ A
- Scale factork = C ÷ A = D ÷ B
Quick Examples
Tap an example to load it above.
Everything about the Proportion Calculator
Cross multiplication, the rule of three, and everyday proportion problems.
A proportion says two ratios are equal: A/B = C/D. If you know any three of the values, cross multiplication finds the fourth, a technique also called the rule of three. This proportion calculator solves for whichever value you leave blank and shows the cross-multiplication working.
Example: 6/8 = 9/D. Cross multiply: 6 × D = 8 × 9 = 72, so D = 72 ÷ 6 = 12. Check: 6/8 = 0.75 and 9/12 = 0.75. ✓
Why it works: multiplying both sides of A/B = C/D by B·D clears the fractions and leaves A·D = B·C, and the "cross products" are always equal in a true proportion.
Everyday proportion problems
- 1Recipes
2 cups flour for 3 servings, so how much for 8? 2/3 = C/8 → C = 16/3 ≈ 5.33 cups.
- 2Maps & models
A 1:50,000 map: 3 cm on paper = 150,000 cm = 1.5 km on the ground.
- 3Prices
5 kg costs $12, so what do 8 kg cost? 5/12 = 8/D → D = 96/5 = $19.20.
- 4Similar triangles
Matching sides of similar shapes are proportional, which is the basis of scale drawings and indirect measurement.
Direct vs inverse proportion
A/B = C/D handles direct proportion, where more of one means proportionally more of the other. If more of one means less of the other (more workers, less time), that is inverse proportion and uses A·B = C·D instead. This calculator solves the direct form, which covers most textbook and everyday cases.
Frequently Asked Questions
How do I solve a proportion?
Cross multiply and divide. In A/B = C/D the cross products are equal: A·D = B·C. To find the missing value, multiply the two numbers diagonal to it and divide by the number opposite it. Example: 3/4 = x/20 → x = 3×20 ÷ 4 = 15.
What is cross multiplication?
Multiplying diagonally across the equals sign: the numerator of each side times the denominator of the other. A/B = C/D becomes A·D = B·C. It works because it is just multiplying both sides of the equation by B·D.
What is the rule of three?
The classical name for solving a direct proportion from three known values: multiply the two values that sit diagonal to the unknown, then divide by the remaining value. It is exactly what this calculator does.
How do I check if two ratios form a true proportion?
Enter all four values and the calculator compares the cross products. 2/3 and 8/12: cross products 2×12 = 24 and 3×8 = 24 are equal, so the proportion is true. Unequal cross products mean the ratios differ.
Can a proportion have decimals or fractions?
Yes. Proportions work with any positive or negative numbers: 2.5/4 = x/10 → x = 6.25. Enter decimal values directly; the calculator keeps full precision and rounds only the display.
Is this proportion calculator free and does it work on mobile?
Yes. It is 100% free with no sign-up, works in any modern browser, and shows the cross-multiplication steps so you can present the working in class.