Proportion Calculator

A proportion calculator solves five distinct types of relationships. Picking the wrong type gives a wrong answer even if your arithmetic is perfect. Know which type you are working with before you enter a single number. Each mode is explained below, with a real recipe-scaling example. Use the calculator to find your missing value, then verify your answer with the built-in check.

Select the proportion type that matches your problem. Enter three known values; leave the unknown blank. The calculator will find the missing term and show each step. Use the display options to control decimal places, 0 to 5, and choose whether to show calculation steps, simplify fractions, or verify the result. Click 'Calculate' to see the solution, verification, and a breakdown of the cross-multiplication property.

Every proportion mode uses the same core rule: the product of the means equals the product of the extremes. For a/b = c/d, that means a × d = b × c. If you know three of the four values, solve for the fourth by dividing the known product by the remaining known value. The calculator does exactly this, showing each step in the results panel.

For direct and inverse proportions, the calculator first checks whether you have three known values and one unknown, then applies the appropriate equation (y₁/x₁ = y₂/x₂ for direct, x₁ × y₁ = x₂ × y₂ for inverse). Continued proportions use the relationship b² = a × c. Compound proportions handle two variables at once, letting you mark whether each quantity is directly or inversely proportional to the result. In all cases, the calculator flags a zero-denominator error immediately, division by zero is impossible in a proportion.

Below is one example per mode. Each shows what you enter and what the calculator returns.

Basic Proportion (a/b = c/d)

Find the missing value when two ratios are equal. Try 2/3 = x/9. Enter a=2, b=3, c=blank, d=9. The calculator cross-multiplies: 2 × 9 = 3 × x, so x = 18 / 3 = 6. Result: 2/3 = 6/9.

Direct Proportion (y = kx)

Two quantities increase or decrease together at the same rate. Suppose 5 kg cost $10, so 8 kg cost x. Enter x₁=5, y₁=10, x₂=8, y₂=blank. The calculator uses y₁/x₁ = y₂/x₂: 10/5 = x/8, so x = 16. The constant of proportionality k = 10/5 = 2.

Inverse Proportion (xy = k)

One quantity increases as the other decreases. Suppose 4 workers take 12 days, so 6 workers take x days. Enter x₁=4, y₁=12, x₂=6, y₂=blank. The calculator uses x₁ × y₁ = x₂ × y₂: 4 × 12 = 6 × x, so x = 48 / 6 = 8. The constant k = 48.

Continued Proportion (a/b = b/c)

Three quantities where the ratio of the first to the second equals the ratio of the second to the third. Suppose x/6 = 6/4. Enter a=blank, b=6, c=4. The calculator uses b² = a × c: 36 = a × 4, so a = 9. The middle term (b) is the mean proportional.

Compound Proportion

Two quantities affect the result. Suppose 3 workers working 4 hours paint 12 walls. How many walls do 5 workers working 6 hours paint? Enter: q1 initial = 3, q1 final = 5, q2 initial = 4, q2 final = 6, result initial = 12, result final = blank. The calculator applies the compound proportion formula, letting you check a box if a quantity is inversely proportional (e.g., more workers means less time).

A lasagna recipe serves 4 and calls for 2 cups of ricotta. You need to serve 10 people. This is a direct proportion: more people, more ricotta.

Set the proportion: 4 people / 2 cups = 10 people / x cups. Enter a=4, b=2, c=10, d=blank in the basic mode. The calculator cross-multiplies: 4 × x = 2 × 10, so x = 20 / 4 = 5. You need 5 cups of ricotta.

Now check the cooking time. The recipe says 45 minutes at 180°C for a 4-person lasagna. Cooking time does not scale proportionally with size, a larger lasagna takes longer because heat penetrates more slowly. This is not a direct proportion. Use the calculator in inverse mode or check a separate roasting guide. The calculator warns you when a proportion does not fit a zero denominator or when the cross-multiplication fails, but it cannot detect a non-proportional relationship.

After you get a result, always verify it. The calculator provides a verification step in the results panel: it substitutes your answer back into the original proportion and checks that the cross-products are equal. For a basic proportion, it shows a × d = b × c. If the two products match, your answer is correct.

You can also check manually: enter the solved value into the original equation and see if both sides reduce to the same decimal or fraction. For the recipe example, 4/2 = 10/5 → 2 = 2. If the calculator returns a verification failure, one of your inputs is wrong or the proportion type does not match the problem.

A common error is entering values in the wrong order, for example, swapping numerator and denominator in a basic proportion. The calculator cannot guess your intent. Always double-check that you placed each value in the correct field. If the result looks too large or too small, try a rough mental check: in direct proportion, the answer should be between the two known values; in inverse proportion, it should move in the opposite direction.

A proportion calculator solves only relationships where two ratios are equal. If your problem involves a fixed fee plus a variable cost, that is additive, not multiplicative, and a proportion will give you the wrong answer. Likewise, problems involving compound units like pressure (force/area) or density (mass/volume) are direct proportions only if you keep the other variable constant. The calculator is for arithmetic proportions, not calculus or statistical analysis. If you need a unit converter or a financial ratio, use a dedicated tool. The one thing that most often goes wrong is selecting the wrong proportion type, double-check whether your quantities move together or apart before you calculate.