Proportion Calculator

A proportion is an equation stating that two ratios are equal. Written as A/B = C/D (or A:B = C:D), it asserts that the relationship between A and B is the same as between C and D. Proportions are among the most practical tools in mathematics, used for scaling recipes, converting currencies, calculating distances on maps, solving similar triangle problems in geometry, and performing unit conversions of all kinds.

The fundamental property of proportions is cross-multiplication: if A/B = C/D, then A × D = B × C. This works because multiplying both sides by B × D eliminates the denominators. To find an unknown X in A/B = X/D, rearrange: X = (A × D) / B. To find X in A/B = C/X, rearrange: X = (B × C) / A. These two forms cover every proportion problem you encounter.

Consider the classic example: if 3 pounds of apples cost $6, how much do 5 pounds cost? Set up the proportion 3/6 = 5/x (or 3:6 = 5:x). Cross-multiply: 3x = 30, so x = 10. Five pounds cost $10. Always set up proportions consistently — put matching units in corresponding positions (pounds over dollars on both sides, not pounds over dollars on one side and dollars over pounds on the other).

Proportions connect directly to the concept of unit rate. If a car travels 150 miles in 3 hours, its speed is 50 mph. To find how far it travels in 7 hours: 150/3 = x/7, giving x = 350 miles. In geometry, similar figures have proportional sides — if two triangles are similar and one side is 6 cm while the corresponding side in the larger triangle is 9 cm, all sides scale by the factor 9/6 = 1.5.

Common mistakes include setting up inconsistent ratios (mixing up which quantities go on top versus bottom), dividing when you should multiply, and forgetting that a proportion requires four terms with one unknown. Verify your answer by checking that both ratios simplify to the same value. This calculator supports both forms — solving for the unknown in the third or fourth position — and handles the cross-multiplication automatically so you can focus on setting up the problem correctly.