Proportion calculator
Enter three numbers of A/B = C/D, get the missing one instantly.
A/B = C/D — A and C on top, B and D below.
How do I solve a proportion?
Cross-multiply and divide. In 3/4 = 9/x, multiply across: 3 × x = 4 × 9 = 36, so x = 36 ÷ 3 = 12.
What if the unknown is on top?
It works the same way. In 2/5 = x/20: 5 × x = 2 × 20 = 40, so x = 8. Pick which of the four places holds the unknown.
How do I check my answer?
Both sides should give the same decimal. 3/4 = 0.75 and 9/12 = 0.75, so x = 12 is right. The calculator shows both sides.
Where are proportions used?
Scaling recipes, maps and drawings, unit prices and mixing. If 2 cups of flour make 12 cookies, 30 cookies need 2/12 = x/30, so x = 5 cups.
What is the difference between a ratio and a proportion?
A ratio compares two numbers, like 3 : 4. A proportion says two ratios are equal, like 3 : 4 = 9 : 12. The ratio calculator simplifies and scales ratios; this one solves for a missing term.
What is the difference between direct and inverse proportion?
In a direct proportion both quantities grow together: twice the flour makes twice the cookies. In an inverse proportion one grows as the other shrinks: twice as many workers finish the same job in half the time. This calculator solves the direct case, A ÷ B = C ÷ D.
Can the unknown term be zero or negative?
A term in the denominator cannot be zero, because division by zero is not defined. Negative numbers work in the same cross-multiplication, as long as you keep the signs.
Why cross-multiplying works
The proportion A ÷ B = C ÷ D says two fractions are equal. Multiply both sides by B × D and the fractions clear: A × D = B × C. Whatever term is unknown, it equals the product of the diagonal pair divided by the remaining term. For instance, if D is unknown, D = B × C ÷ A. The calculator applies this to whichever of the four boxes you leave empty, and it shows both fractions as decimals so you can see that they match.
Worked examples
A map scale says 1 inch represents 24 miles. How far apart are two towns that are 3.5 inches apart on the map? 1 ÷ 24 = 3.5 ÷ x, so x = 24 × 3.5 ÷ 1 = 84 miles. A car uses 12 gallons for 330 miles; at the same rate, 5 gallons cover 330 × 5 ÷ 12 = 137.5 miles. If 2 parts of a mix call for 3 cups of water, then 7 parts need 3 × 7 ÷ 2 = 10.5 cups.
Common mistakes
The most common error is putting the terms in the wrong places: if the first fraction is inches to miles, the second must also be inches to miles, not miles to inches. A second is mixing units inside a fraction, for example minutes in one place and hours in another, so convert first. A third is using a direct proportion on an inverse relationship, such as workers and time, or speed and travel time. After solving, check that your answer is the right size: if you doubled one quantity, the answer should have doubled too.
Sources: OpenStax Prealgebra 2e, the sections on ratios and rates and on solving proportions and their applications. Related: ratio calculator, percentage calculator, scale calculator and recipe scaler.