utils.directory

Proportion Calculator

Solve a/b = c/d for any missing value as you type.

Fill in three values and leave one blank — the blank one gets solved.

How to use proportion calculator

  1. Type any three of the four values into the a, b, c and d boxes.
  2. Leave the box for the value you want to find empty.
  3. The solved equation and the missing value appear instantly as you type.
  4. Change any number to recalculate, or clear a different box to solve for that one instead.

Examples

Scale a recipe (2 / 4 = ? / 6)

A recipe uses 2 cups of flour for 4 servings. Leave c blank with a = 2, b = 4 and d = 6 to see that 3 cups serve 6 people.

Map scale (1 / 5 = 7 / ?)

If 1 cm on the map equals 5 km on the ground, a 7 cm route covers 35 km. Leave d blank to solve it.

Similar triangles (2 / 3 = ? / 15)

A 2 m pole casts a 3 m shadow. A tree casting a 15 m shadow is 10 m tall — leave c blank to find it.

What is Proportion?

A proportion states that two ratios are equal: a/b = c/d. If you know any three of the four values, you can always find the fourth — that is exactly what this calculator does. The method is cross-multiplication: the product of the means equals the product of the extremes, so a × d = b × c, and each value is one division away from the other three.

Proportions are everywhere. Cooks use them to scale recipes when a dish serves four but ten people are coming to dinner. Builders use them to convert scale drawings into real dimensions, and map readers translate centimeters on the page into kilometers on the ground. Students meet proportions in percent problems and similar triangles, and nurses rely on them to scale medication doses safely.

This page applies the standard cross-multiplication formulas locally in your browser. Fill in three of the four boxes and leave the fourth empty; the result updates with every keystroke, showing the complete solved equation alongside the missing value. Decimal answers are shown with up to six decimal places, and nothing you type is sent anywhere.

Frequently asked questions

How does cross-multiplication work?

In a/b = c/d the diagonal products are equal: a × d = b × c. Once three values are known, the fourth is one division away — for example d = (b × c) / a. This calculator performs that division for whichever box you left blank.

Can the answer be a decimal?

Yes. Proportions do not require whole numbers. If the division does not come out evenly, the result is shown with up to six decimal places, and trailing zeros are trimmed.

What if I leave two fields blank?

Then the proportion is underdetermined — infinitely many values could fit. The calculator asks you to leave exactly one field blank, which makes the solution unique.

Why does it say the proportion divides by zero?

Solving for d means computing b × c / a, so if a is 0 there is no finite answer. The same happens for the other positions — a zero in the wrong place makes the proportion unsolvable, and the calculator tells you so.

Can I solve percentage problems with this?

Yes. Write the proportion as part / whole = percent / 100. For example, to find what percent 30 is of 200, set a = 30, b = 200 and c = 1, then d gives the percentage.