Proportion Calculator
Find the missing fourth value d in any proportion a/b = c/d when three values are known. Perfect for scaling recipes, converting units, solving map distances, and cross-multiplication problems.
About this calculator
A proportion states that two ratios are equal: a/b = c/d. When d is unknown, cross-multiplication gives a × d = b × c, so d = (b × c) / a. This calculator solves for d given values of a, b, and c using exactly that formula. Proportions are fundamental in unit conversion, scaling drawings, calculating ingredient amounts, and working with similar geometric figures. The key requirement is that a ≠ 0 and b ≠ 0; dividing by zero is undefined. Proportional reasoning underpins much of everyday arithmetic — any time a consistent rate or ratio is applied to a new quantity, you're using a proportion.
How to use
Suppose a recipe calls for 2 cups of flour (a = 2) to make 8 cookies (b = 8), and you want to know how much flour (d) you need to make 20 cookies (c = 20). Enter a = 2, b = 8, c = 20. The calculator computes d = (b × c) / a = (8 × 20) / 2 = 160 / 2 = 80 ÷ 2 = 80/2 = 5. You need 5 cups of flour to make 20 cookies, maintaining the same ratio of 1 cup per 4 cookies.
Frequently asked questions
How does cross-multiplication work to solve a proportion?
Cross-multiplication states that if a/b = c/d, then multiplying the numerator of each fraction by the denominator of the other gives equal products: a × d = b × c. To isolate d, divide both sides by a, yielding d = (b × c) / a. This technique works because multiplying both sides of an equation by the same non-zero value (in this case b × d) preserves equality. It is one of the most widely taught algebraic techniques in middle-school mathematics.
What is the difference between a ratio and a proportion?
A ratio is a comparison of two quantities, written a : b or a/b. A proportion is a statement that two ratios are equal, such as a/b = c/d. Every proportion contains two ratios, but a single ratio on its own is not a proportion. When you scale a recipe, enlarge a photo, or convert miles to kilometres, you set up a proportion by asserting that the original ratio equals the new ratio — then solve for the unknown fourth term.
When should I use a proportion calculator instead of a percentage calculator?
Use a proportion calculator when you know three of the four values in a direct a/b = c/d relationship and need the fourth — typically in scaling, unit conversion, or recipe adjustment scenarios. A percentage calculator is more appropriate when you want to express one quantity as a fraction of 100 for comparison purposes, such as finding a discount or a score. In practice, many percentage problems can be reframed as proportions (e.g., 15% = 15/100 = x/200), so the two tools are complementary.