A proportion states that two ratios are equal — this solves for whichever one of the four numbers is missing, the classic recipe-scaling and map-scale question.
How it works
Given three of the four values in “a is to b as c is to d,” cross-multiplication solves for the missing fourth value.
What this does not include
This does not include solving a proportion with more than one unknown — exactly one of the four values must be left blank for the calculator to solve it.
How to use this calculator
- Enter three of the four values and leave the one you want solved for blank.
A worked example
Recipe scaling: 2 cups of flour makes 12 cookies. How much flour makes 30 cookies? 2/12 = x/30 → x = (2 × 30) ÷ 12 = 5 cups.
Map scale: 1 inch represents 5 miles. How many miles does 3.5 inches represent? 1/5 = 3.5/x → x = (5 × 3.5) ÷ 1 = 17.5 miles.
What the variables mean
| Position | Role in “a is to b as c is to d” |
|---|---|
| a, b | The known ratio |
| c, d | The scaled ratio — with exactly one of the two left blank to solve for |
Edge cases worth knowing
Exactly one of the four values must be missing. With all four filled in there’s nothing left to solve for, and with two or more missing, the system is underdetermined — neither case produces a result.
Cross-multiplication works because it’s a direct algebraic consequence of the two ratios being equal — multiplying both sides of a/b = c/d by bd gives ad = bc, which rearranges to isolate any single unknown.
Frequently asked questions
What’s a real-world example of a proportion problem?
Scaling a recipe (if 2 cups of flour makes 12 cookies, how much flour makes 30 cookies?) or reading a map scale (if 1 inch represents 5 miles, how many miles does 3.5 inches represent?) are both classic proportion problems.
Why does cross-multiplication work?
It’s a direct algebraic consequence of two fractions being equal — multiplying both sides of a/b = c/d by bd gives ad = bc, which rearranges to solve for any single unknown.
What if I enter all four values?
The calculator needs exactly one blank to solve for — with all four filled in, there’s nothing to solve, so no result is shown.
