Proportion Calculator
Solve a/b = c/d. Fill in three terms and leave exactly one blank to solve for it.
Solved for d6.000000
Cross Product6.000000
A proportion states that two ratios are equal, written a/b = c/d. When one of the four terms is unknown you can find it by cross multiplication. This solver takes any three of the terms a, b, c, and d, leaves the blank one as the unknown, and returns its value along with the cross product used to get there.
Formula
a/b = c/d ⇒ a × d = b × c
- a, b
- Numerator and denominator of the first ratio
- c, d
- Numerator and denominator of the second ratio
How it works
- Enter three of the four terms in the equation a/b = c/d and leave exactly one box empty — that empty box is the value you want to find.
- The solver cross multiplies (a × d = b × c) and rearranges to isolate the missing term, dividing the cross product by the known term on the other diagonal.
- The result shows the solved value and the cross product, so you can check that the two ratios are genuinely equal.
Worked example
A recipe uses 3 cups of flour for every 4 cookies. How much flour scales to 20 cookies (3/4 = c/20)?
- Set up the proportion 3/4 = c/20 with c unknown.
- Cross multiply: c × 4 = 3 × 20, so 4c = 60.
- Solve: c = 60 ÷ 4 = 15.
You need 15 cups of flour, found by solving for c.
Frequently asked questions
- What is cross multiplication?
- Cross multiplication turns the equation a/b = c/d into a × d = b × c by multiplying each numerator by the opposite denominator. It removes the fractions so the unknown term can be isolated with one division.
- Which term should I leave blank?
- Leave the single term you want to find empty and fill in the other three. The solver requires exactly one blank; with zero or more than one blank the proportion cannot be solved uniquely.
- How is this different from a ratio calculator?
- A ratio calculator simplifies or scales a ratio you already know. This proportion solver instead finds a missing term in the equation a/b = c/d, which is the classic solve-for-x problem from cross multiplication.
- Can the terms be decimals or negatives?
- Yes. Any real numbers work as long as the term you divide by is not zero. If solving would require dividing by zero the proportion has no solution and no result is shown.