Solve A / B = C / D
Enter three values. The blank field is the value the calculator will find.
What is a proportion?
A proportion is an equation that says two ratios are equal. It is often written as two fractions, such as A/B = C/D. For example, 2/5 = 8/20 because both fractions represent the same relationship.
How to solve a proportion
Enter the two values in one fraction and one known value in the other. Then leave the unknown value blank and select Solve proportion. The calculator uses cross multiplication to find the missing value.
Worked example
Suppose 2/5 = X/20. Cross multiplication gives 2 × 20 = 5 × X. Therefore, X = 40 ÷ 5 = 8. The completed proportion is 2/5 = 8/20.
Where proportions are used
Proportions are useful for scaling recipes, converting measurements, working out prices by quantity, map scales and comparing rates. For example, if 8 hours of work earns £120, then 25 hours earns £375 when the rate stays the same.
Direct and inverse proportion
In a direct proportion, both quantities move in the same direction: if one doubles, the other doubles. In an inverse proportion, one quantity increases while the other decreases, such as more workers completing the same task in fewer hours. This calculator solves direct proportional relationships written as equal ratios.
Check that the relationship really stays constant
If four identical notebooks cost 10, seven cost 17.50 at the same unit price. But adding a fixed delivery charge changes the relationship between item count and total bill. Apply a proportion to the variable item cost, then add the fixed charge separately.
Frequently asked questions
How many fields should I leave blank?
Leave exactly one unknown blank and supply the other three values. Keep corresponding quantities in the same positions.
How do I solve 3/5 = x/20?
Cross multiplication gives 5x = 60, so x = 12.
Can a denominator be zero?
No. The fractions in a valid proportion need nonzero denominators; cross multiplication does not make an undefined fraction valid.
When is scaling by a proportion appropriate?
Use it when the relationship stays constant, such as an unchanged unit price or recipe ratio. Fixed charges and tiered pricing can break that assumption.
Is inverse proportion set up in the same way?
No. In direct proportion the ratio stays constant; in inverse proportion the product stays constant. Rearrange the relationship correctly before using an equal-ratio calculation.