How to Use the Proportion Calculator
A proportion states that two ratios are equal: a : b = c : d. This calculator solves for any one of the four values when you know the other three. Select which position is unknown from the dropdown, fill in the three known values, and the result appears instantly. The formula comes from the cross-multiplication rule: b × c = a × d (product of means = product of extremes).
For example, if a:b = c:x and a = 2, b = 3, c = 4, then x = b × c / a = 3 × 4 / 2 = 6, meaning 2:3 = 4:6. The verification row confirms both sides of the cross-product are equal. Common real-world uses: map scale reading (1 in = 50 miles → 3 in = ?), scaling a recipe (2 cups flour for 12 cookies → ? cups for 30 cookies), and resizing images while maintaining aspect ratio.
The unknown can be placed at any of the four positions (a, b, c, or d) — the calculator covers all cases. Decimals and negative numbers are supported as long as the denominator in the formula is not zero.
Frequently Asked Questions
For a:b = c:d, multiplying the means (b × c) equals multiplying the extremes (a × d). This property is used to solve for any unknown term.
Map reading, recipe scaling, image resizing, unit price comparison, and similar triangle problems in geometry — anywhere two ratios must stay equal.
It shows b×c and a×d after substituting x, confirming the cross-products are equal. Both values should match, proving the proportion is satisfied.