Ratio Calculator: Solve A : B = C : D

What is a ratio proportion?

A ratio compares two quantities, written A : B — two cups of flour to three cups of sugar, for example. A proportion sets two ratios equal to each other: A : B = C : D. Whenever three of the four terms are known, the fourth is completely determined; this calculator solves for whichever one you leave blank.

Using the calculator

Type numbers into three of the four boxes — A, B, C, D — and leave exactly one blank; that's the value the calculator solves for. Every entry must be a positive number (whole or decimal, like 1.5); negative numbers aren't valid ratio terms here. Two guardrails keep the answer meaningful:

• Leaving zero, two, or all four boxes blank asks the calculator to solve for more (or fewer) unknowns than a single equation can determine, so it asks you to leave exactly one blank.
• If the term diagonally opposite the blank one is zero, the cross-multiplication would require dividing by zero, which has no answer — the calculator flags this rather than guessing.

Cross-multiplication: the rule behind every answer

A : B = C : D is the same statement as the fraction equation $\frac{A}{B} = \frac{C}{D}$. Multiplying both sides by $B$ and by $D$ clears the denominators and leaves:

$A \times D = B \times C$

Whichever term is missing, you isolate it by dividing the product of the two terms diagonally across from it by the one remaining known term. Solving for D, for instance, gives $D = \frac{B \times C}{A}$.

Step-by-step: solving 2 : 3 = x : 12

1. Identify the unknown. The third term, x, is missing from 2 : 3 = x : 12.
2. Cross-multiply. $2 \times 12 = 3 \times x$, so $24 = 3x$.
3. Solve. Divide both sides by 3: $x = 24 \div 3 = 8$.
4. Check. $2 \times 12 = 24$ and $3 \times 8 = 24$ — the cross products match, confirming 2 : 3 = 8 : 12.

The known side, 2 : 3, is already in lowest terms ($\gcd(2, 3) = 1$), so the calculator reports it unchanged alongside the answer.

Worked example: scaling a recipe

Ratios are the natural tool for scaling recipes up or down. Say a recipe calls for 2 cups of flour for every 3 cups of sugar, and you want to know how much flour matches 12 cups of sugar. Set up the proportion exactly like the calculator does:

$2 : 3 = x : 12$

Cross-multiplying gives $2 \times 12 = 3 \times x$, so $x = 24 \div 3 = 8$ cups of flour. The same method works for currency conversion, map scales, unit rates, or mixing paint — anywhere two quantities stay in a fixed relationship.

More worked examples

Reading the answer

The calculator returns the missing term as an exact value — a whole number when the proportion divides evenly, or a reduced fraction (with its decimal equivalent, rounded to at most six digits) otherwise. It also echoes the ratio on the side you already knew in full, simplified by its greatest common divisor, so you can double-check your original numbers at a glance.