About the Proportion Calculator
This proportion calculator solves equations of the form a/b = c/d when one of the four numbers is unknown. Pick which term to solve for, enter the other three, and it uses cross multiplication to find the missing value and shows the working.
Proportions turn up everywhere: scaling a recipe from 4 to 10 servings, converting a map distance using its scale, working out a unit price, mixing fertiliser or paint at a fixed ratio, or solving “if 3 pens cost $4.50, how much do 7 cost?” — the classic rule of three.
The method assumes the two quantities are directly proportional, meaning they rise and fall together at a constant rate. If one quantity goes down as the other goes up (more workers, fewer days), the relationship is inverse and needs a different setup.
With the default inputs, the missing value is 15. Change any value above to recalculate instantly.
How to use the proportion calculator
- 1Choose which of the four terms is unknown.
- 2Enter the other three values so that matching units line up (a with c, b with d).
- 3Read the missing value and the solved proportion.
- 4Check that both sides of the equation give the same ratio.
Formula and method
Two ratios are in proportion when they are equal. Multiplying both sides of a/b = c/d by b × d gives the cross-multiplication identity a × d = b × c, which can be rearranged to isolate any single unknown: d = bc/a, c = ad/b, b = ad/c or a = bc/d.
This is the “rule of three”: three known quantities determine the fourth. It only applies when the relationship is directly proportional, with a constant ratio between the paired quantities; the value you divide by must not be zero.
- a, b
- The known ratio (for example 250 g per 4 servings)
- c, d
- The second ratio, one of which may be unknown
Worked examples
2/5 = 6/?
Cross multiplying gives 2 × d = 5 × 6 = 30, so d = 30 ÷ 2 = 15. Both sides equal 0.4.
Recipe: 250 g flour for 4 servings — how much for 10?
Set up 250/4 = c/10. Then c = 250 × 10 ÷ 4 = 625 g of flour.
Unit price: 3 pens cost $4.50 — how many for $12?
Pair pens with pens and dollars with dollars: 3/b = 4.5/12. Then b = 3 × 12 ÷ 4.5 = 8 pens.
Map scale: 1 cm = 2.5 km, what is 7.4 cm?
With 1/2.5 = 7.4/d, d = 2.5 × 7.4 ÷ 1 = 18.5 km on the ground.
Frequently asked questions
How do you solve a proportion?+
Cross multiply: in a/b = c/d, a × d equals b × c. Put the unknown on one side and divide. For 3/4 = x/20, 4x = 60, so x = 15.
What is the rule of three?+
It is a shortcut for proportions: given three values of a direct proportion, multiply the two that are diagonal from the unknown and divide by the remaining one. It is the same as cross multiplication.
What is the difference between a ratio and a proportion?+
A ratio compares two quantities, such as 2:5. A proportion is an equation stating that two ratios are equal, such as 2:5 = 6:15.
How do I know if two quantities are proportional?+
Their ratio stays constant. If doubling one always doubles the other, they are directly proportional. If doubling one halves the other, they are inversely proportional and a/b = c/d does not apply.
Does it matter which numbers go on top?+
You can set it up either way as long as you are consistent: matching units in the same positions on both sides, such as grams over servings on the left and on the right.