Solve for X Proportion Calculator: cross-multiplication with steps

How it works

Direct: A/B = C/D ⇒ A × D = B × C ⇒ x = (product of the two known diagonal terms) ÷ (the known term on x’s diagonal); e.g. A/B = C/x ⇒ x = B × C ÷ A · Inverse: A × B = C × D ⇒ e.g. x = A × B ÷ C

Two equal ratios form a proportion, A/B = C/D. Multiplying across the diagonals always gives equal products, A × D = B × C, so when three terms are known the fourth follows: multiply the two known terms on one diagonal and divide by the known term that shares a diagonal with x. Choose where x sits; the default is the classic A/B = C/x, the “rule of three”. In a direct proportion both quantities move together: 3 kg costs 45, so 7 kg costs 45 × 7 ÷ 3 = 105. In an inverse proportion one quantity rises as the other falls, so the products are equal instead: if 4 workers take 12 days, 6 workers take 4 × 12 ÷ 6 = 8 days. For the inverse case, enter the first pair as A and B and the second pair as C and D. When all the known terms are whole numbers the calculator also gives x as an exact fraction (and mixed number), checks the answer by comparing the two ratios or products, and lists equivalent pairs with the same ratio. Denominators B and D cannot be zero.

Worked example

For 3/4 = 9/x (the default): cross-multiply to get 3 × x = 4 × 9 = 36, and divide by 3 to get x = 12. Check: 3 ÷ 4 = 0.75 and 9 ÷ 12 = 0.75, so 3/4 = 9/12, and the scale factor from A to C is × 3. If instead the proportion were inverse, 3 × 4 = 9 × x would give x = 12 ÷ 9 = 4/3 = 1 1/3.

Sources: CalculatorSoup: Solve for X in Fractions (cross-multiplication examples) · Basic Mathematics: Solving proportions (5/x = 10/16, 8/10 = n/25) · Vaia: Solve 2/15 = 18/x (worked solution) · Calculator.net: Ratio Calculator (proportion solver)

Frequently asked questions