Proportion Calculator

A proportion states that two ratios are equal. It is commonly written as A divided by B equals C divided by D, where B and D are denominators. If three values are known, the fourth follows from cross-multiplication: A times D equals B times C. This calculator lets any one of the four positions be unknown. Leave that field empty, provide the other three numbers, and the solver rearranges the cross-product equation to isolate the missing value. Proportions are useful because equivalent ratios describe the same relationship at different scales. A recipe using two cups of flour for three servings can be scaled to eight servings without changing its balance. A map scale converts a short measured distance into a real-world distance. Unit prices, exchange rates, percentages, similar triangles, medication doses, photographic aspect ratios, and speed calculations all rely on proportional reasoning. The units may differ between the two sides, but corresponding positions must represent matching quantities. Cross-multiplication is a shortcut derived from ordinary algebra. Starting with A/B = C/D, multiply both sides by B and D to remove the denominators. The equation becomes A times D = B times C. To find A, divide B times C by D. To find B, divide A times D by C. To find C, divide A times D by B. To find D, divide B times C by A. The calculator selects the correct rearrangement based on the empty field and displays the result with unnecessary trailing zeros removed. A valid calculation requires exactly one unknown. Zero needs special care: a ratio with a zero denominator is undefined, and some arrangements can require division by zero even when the entered equation looks simple. The calculator reports that condition rather than displaying infinity. Decimal and negative inputs are supported mathematically, although practical quantities such as lengths or counts are often nonnegative. Keep units consistent and avoid rounding intermediate values when precision matters. To check an answer, substitute it into the original proportion and compare the cross products. For example, 2/3 = x/12 gives 2 times 12 = 3 times x, so x is 8. Both cross products equal 24. This verification works for every field position and is especially helpful when solving proportions by hand. Whether you are completing homework, resizing a design, scaling ingredients, or converting measurements, the tool provides the missing ratio value while keeping the governing relationship visible.