Proportion solver — find the missing term in a/b = c/d

How to use the proportion solver

1. Read your problem as a/b = c/d. For “3 is to 4 as x is to 20”, a = 3, b = 4, c = x and d = 20.
2. Type the three known values into the boxes a, b, c and d.
3. In the remaining box type x, or leave it empty.
4. Read the Solution line. If the answer is not a whole number, an As a fraction line appears as well.
5. Check the Cross multiplication box to see the formula the tool used with your numbers.

What it does and when to use it

A proportion says two ratios are equal. You meet them when you scale a recipe, read a map, convert currency at a fixed rate, enlarge a photo without stretching it, or work out similar triangles in geometry. In each case three numbers are known and one is missing.

The solver is useful for checking homework and for quick real-life scaling. If your problem starts with a percentage rather than a ratio, the percentage calculator has ready-made modes. For adding or dividing fractions, use the fraction calculator.

How it works

Two fractions are equal exactly when their cross products are equal:

a/b = c/d ⇔ a × d = b × c

The tool rearranges this rule for whichever term is missing:

• a = b × c ÷ d
• b = a × d ÷ c
• c = a × d ÷ b
• d = b × c ÷ a

All values are stored as exact fractions of whole numbers, so nothing is rounded during the calculation. The decimal is shown exactly when it ends within 12 digits; otherwise you get 12 significant figures and the exact fraction.

Step by step for 3/4 = x/20:

1. Cross multiply: 3 × 20 = 4 × x.
2. Work out the known side: 60 = 4x.
3. Divide both sides by 4: x = 60 ÷ 4 = 15.

The tool shows the same thing in one line: c = a × d ÷ b = 3 × 20 ÷ 4 = 15.

Worked examples

Basic proportion. a = 3, b = 4, c = x, d = 20 gives c = 15.

Map scale. A map has a scale of 1 : 50,000 and two towns are 3.2 cm apart on it. Enter a = 1, b = 50000, c = 3.2, d = x. The tool returns d = 160,000. That is 160,000 cm on the ground, which is 1.6 km.

An answer that is not whole. x/8 = 5/12. The solver gives a = 3.33333333333… and As a fraction: 10/3. In class you would write 3⅓.

Limits and tips

• Keep the units on matching sides. If a is in grams and b is in people, c must also be grams and d people.
• Exactly one box must be unknown. The tool does not solve two-unknown problems.
• To go further with equations, the quadratic solver handles x² problems.
• Everything is calculated in your browser; nothing you type is sent anywhere.