The fourth term of a proportion
A proportion says two ratios are equal: A/B = C/X. Cross-multiplying gives A × X = B × C, so X = B × C ÷ A, as long as A is not zero. That is the whole calculator. If 3 pounds of apples cost $5.40, then 3 is to 5.40 as 8 is to X. X = 5.40 × 8 ÷ 3 = 43.20 ÷ 3 = 14.40. Eight pounds cost $14.40.
The unit-price check is the same arithmetic written out. One pound costs 5.40 ÷ 3 = $1.80. Eight pounds cost 8 × 1.80 = $14.40. If those two routes disagree, a digit was mistyped. The proportion does not know about bulk discounts. It assumes the ratio stays constant, which is right for a unit price, a recipe, a map scale, or similar triangles, and wrong for a price that changes at a quantity break.
Worked example: scaling a recipe
A recipe uses 2 cups of broth for 6 servings. You want 15 servings and need the new amount of broth.
- Set it up as 6 servings is to 2 cups as 15 servings is to X cups.
- Here A = 6, B = 2, and C = 15.
- X = 2 × 15 ÷ 6 = 30 ÷ 6 = 5.
- The scaled recipe needs 5 cups of broth. Per serving that is still 2 ÷ 6 = 1/3 cup, and 15 × 1/3 = 5.
Which number goes in which box
Keep the matching units on a diagonal that makes sense to you, and then be consistent. “3 pounds correspond to $5.40” means pounds are in A and C, and dollars are in B and X. Swapping B and C computes a different ratio and a wrong price. A has to be the number you will divide by, the one paired with B in the known ratio. If A is zero, there is no ratio to extend, and the calculator leaves the result blank.
Percentages are proportions too. “18 out of 100” is the same shape as “45 out of 250.” When the second term of the known ratio is 100, you are doing a percentage. The percentage calculator is labeled for that case. Use this page when neither side of the ratio is 100.