Proportion Calculator
Solve for any missing value in a ratio (A : B = C : D) with step-by-step cross-multiplication, fraction reduction, and percentages.
See also: Percentage Increase Calculator, Slope Calculator
How it is calculated
Cross Multiplication: If A / B = C / D, then A × D = B × C. Unknown X = (B × C) ÷ D
Worked example: Scaling a Recipe: 4 Servings Require 10 Eggs, How Many for 12 Servings?
A = 4 servings, B = 10 eggs, C = 12 servings, solve for D (eggs needed).
- Set up the proportion: 4 / 10 = 12 / D.
- Cross-multiply diagonal values: 4 × D = 10 × 12 = 120.
- Isolate D by dividing both sides by 4: D = 120 ÷ 4 = 30.
- Verify equality: 4 / 10 = 0.4 and 12 / 30 = 0.4.
D = 30 eggs required for 12 servings.
Frequently asked questions
What is a proportion in mathematics?
A proportion is a statement that two ratios or fractions are completely equal to each other.
How does cross-multiplication work?
Cross multiplication relies on multiplying the numerator of each side by the denominator of the other side (A × D = B × C), eliminating the fractions.
How do I solve for a different unknown (A, B, C, or D)?
Select the variable you want to solve for and the calculator rearranges the cross-multiplication for you: D = (B × C) ÷ A, C = (A × D) ÷ B, B = (A × D) ÷ C, and A = (B × C) ÷ D.
What happens if the divisor is zero?
The result is undefined, because division by zero is mathematically impossible. The calculator shows an error instead of a number — for example, solving for D requires A to be non-zero.
What is the scaling factor (k) in the results?
The scaling factor k equals C divided by A. It tells you how many times bigger the second ratio is than the first.
Can proportions handle decimals and negative numbers?
Yes. The inputs accept decimals and negative values within plus or minus 1,000,000. Keep the units consistent on both sides of the proportion, so that units of A match units of C and units of B match units of D.