Proportion Calculator

A proportion states that two ratios are equal. The relationship A : B = C : D is equivalent to A/B = C/D and to the cross-multiplication identity A × D = B × C. The calculator uses these identities to solve for a missing term or to confirm that four values form a valid proportion. Reduced ratios express the same relationship using the greatest common divisor to give the pair in lowest terms.

• Proportion: A : B = C : D, equivalent to A / B = C / D, or A × D = B × C.
• Ratio reduction: for ratio a : b, divide both a and b by their greatest common divisor (GCD).
• Percentage difference: | (a/b) − (c/d) | / ( (a/b + c/d) / 2 ) × 100.

The proportion calculator solves the equation A : B = C : D for a missing term, or checks whether four given values already form a valid proportion. The relationship is equivalent to the fraction equality A/B = C/D and to the cross-multiplication identity A × D = B × C.

• Any three of the four values, A, B, C, and D, are enough to solve for the fourth; supplying all four instead checks whether the two ratios are equal.
• Accepted values are integers, common fractions such as 3/4, or decimals with up to two places such as 2.5; a leading minus sign covers negative values where the context allows them.
• The blank term is isolated by rearranging the cross-multiplication identity: A = (B × C) / D, B = (A × D) / C, C = (A × D) / B, or D = (B × C) / A.
• A Solved value reports the computed missing term; a Check result instead states whether A × D equals B × C when all four values are present.
• Original and Reduced ratios are shown for both A : B and C : D; reduction divides both sides by their greatest common divisor to give the pair in lowest terms.
• A Percentage Difference reports how far apart two unequal ratios sit, and a Steps breakdown lists each multiplication and division in the order it was applied.
• Entries persist between visits, so a returning session restores the last set of numbers.

A worked example shows the pattern. To find what a scale value of 10.5 represents when a value of 1 equals 100 percent, setting A = 1, B = 100, and C = 10.5 and leaving D blank returns D = (100 × 10.5) / 1 = 1050. Reversing the question, with A = 1, B = 100, and D = 1050 left C blank, returns C = 10.5, the scale factor that moves a quantity from 100 to 1050. Internal math keeps exact fraction values, while the solved field rounds to two decimal places for readability.

Proportional reasoning turns one known relationship into an answer for a related quantity. The same A : B = C : D structure scales recipes, converts map distances, resizes design assets, and checks financial ratios. The list below outlines where the calculator applies.

• Education: Solve and verify A : B = C : D homework problems, confirm reduced ratios, and check equivalence between two fractions without working the cross-multiplication by hand.
• Cooking: Scale a recipe up or down while holding ingredient ratios fixed. If 2 cups of flour pair with 1 cup of milk, the same relationship gives the milk needed for any flour amount.
• Design and mapping: Resize images, layouts, and scale models without distortion. Convert a map scale such as 1 cm to 4 km into ground distance, or find the pixel width that keeps an asset proportional.
• Finance: Compare price-to-value ratios, normalize figures across different bases, and check whether two cost relationships match before acting on them.
• Engineering: Confirm gear and pulley ratios, validate scale-model dimensions, and verify that tolerance relationships hold across two measurements.
• Data analysis: Normalize metrics to a common base, compare conversion rates, and assess relative performance between two groups.

Each scenario reduces to the same step: identify three known quantities, place them so that equal ratios sit on each side of the equation, and solve for the fourth. Because the calculation runs on exact fractions rather than rounded decimals, repeated scaling does not accumulate error, and the reduced-ratio output makes it quick to confirm that two relationships truly match.

Work through common scenarios to see how the formulas apply.

• Price comparison: If 3 items cost 18, the cost of 7 items follows from A = 3, B = 18, C = 7, solving for D: D = (18 × 7) / 3 = 42.
• Recipe scaling: If 2 cups of flour match 1 cup of milk, the milk needed for 3 cups of flour follows from A = 2, B = 1, C = 3, solving for D = 1.5.
• Model scale: If 1 cm on a map equals 4 km, checking whether 3 cm equals 12 km sets A = 1, B = 4, C = 3, D = 12; since A × D = B × C (12 = 12), the ratios match.

The Solved field shows the computed missing value. The Check field states whether A × D equals B × C. Original and Reduced ratios are shown for both sides for comparison. The Percentage Difference reports how far the two ratios differ when they are not equal. The Steps section explains the formula applied and each operation in order.

What formats are accepted? Integers, fractions like 5/8, and decimals with up to two places are all accepted. A leading minus sign covers negative values when the context allows them.

What happens with zeros? Division by zero is prevented. If B or D is zero when forming a ratio, the calculation is flagged rather than computed.

How are results rounded? The solved value displays rounded for readability, while internal steps keep precise fractional values to maintain accuracy.

Can I only check proportions? Yes. Supplying all four values checks whether they satisfy A × D = B × C and shows the percentage difference when they do not.