— Everyday Math
Proportion Calculator
Solve a proportion where two ratios are equal: a : b = c : d. Enter the three known values, choose the missing position, and the calculator cross-multiplies to find the fourth, with support for inverse proportion too.
Value of d
12
- Completed proportion
- 2 : 3 = 8 : 12
- Cross-product check
- 2 × 12 = 3 × 8 = 24
- Simplified a : b
- 2 : 3
— How it works
For a : b = c : d, the cross-products are equal: a × d = b × c. Rearranged for the unknown, e.g. d = (b × c) ÷ a. Inverse proportion instead keeps the product constant: a × b = c × d.
Cross-multiplying to find the unknown
When two ratios are equal — a : b = c : d, the same as the fractions a/b = c/d — their cross-products are equal too: a × d = b × c. That single fact solves for any missing value. If the unknown is d, rearrange to d = (b × c) ÷ a; if it is a, then a = (b × c) ÷ d, and so on for each position. Pick which letter you are solving for, enter the other three, and the calculator does the cross-multiplication and shows the check — the two cross-products that should match.
Worked example — 2 : 3 = 8 : x: Cross-multiply: 2 × x = 3 × 8, so x = (3 × 8) ÷ 2 = 12. Check: 2 × 12 = 24 and 3 × 8 = 24 — equal, so it balances.
Where proportions show up
Proportions are the maths behind scaling anything that keeps a fixed relationship. Doubling a recipe: if 2 cups of flour need 3 eggs, then 5 cups need 5 × 3 ÷ 2 = 7.5 eggs. Reading a map: if 1 cm represents 50 km, then 3.4 cm is 170 km. Currency, unit conversion, mixing ratios, similar triangles, fuel for a journey — all are “three knowns, one unknown” proportions. The trick in a word problem is lining the quantities up consistently on each side: keep the same units in the same positions (cups with cups, eggs with eggs) and the cross-multiplication takes care of the rest.
Direct vs inverse proportion
Most proportions are direct: as one quantity grows, the other grows in step, so the ratio stays fixed (more flour needs proportionally more eggs). But some relationships are inverse — as one quantity rises, the other falls, keeping their product constant. The classic case is speed and time: at twice the speed a journey takes half as long, because speed × time = distance is fixed. For an inverse proportion the rule changes from a × d = b × c to a × b = c × d. Switch the proportion type under the advanced options and the calculator solves it the inverse way; choosing the wrong type is the most common mistake in these problems, so it is worth asking whether “more means more” or “more means less”.
— Reader questions
How do I solve a proportion?
Cross-multiply. For a : b = c : d the cross-products are equal (a × d = b × c), so rearrange for the unknown — for example d = (b × c) ÷ a. Enter the three values you know, choose the position to solve, and the calculator finds the missing one.
What is cross-multiplication?
It is the step that turns a/b = c/d into a × d = b × c by multiplying each side by both denominators. Because those two products must be equal, you can solve for whichever value is missing. The calculator shows both products as a check.
How do I solve 2 : 3 = 8 : x?
Cross-multiply: 2 × x = 3 × 8, so x = 24 ÷ 2 = 12. Leave the d position as the unknown, enter 2, 3 and 8, and the calculator returns 12 with the check 2 × 12 = 3 × 8 = 24.
What is the difference between direct and inverse proportion?
In direct proportion both quantities move together and the ratio is constant (a : b = c : d). In inverse proportion one rises as the other falls and the product is constant (a × b = c × d) — like speed and time for a fixed distance. Choose the type under the advanced options.
Can I solve for any of the four values?
Yes. Use the “solve for” control to pick a, b, c or d as the unknown; that field is hidden and you fill the other three. The calculator rearranges the cross-multiplication accordingly.