Proportion Calculator

1. Enter three of the four values a, b, c and d.
2. Leave the one you want to find blank.
3. Read the missing value.
4. See the full proportion and check it holds.

Here is what each result means:

A proportion is a statement that two ratios are equal, written a over b equals c over d. It says the first pair relates in the same way as the second. So 2 over 3 equals 4 over 6, because both reduce to the same ratio. Proportions let you scale one known relationship up or down to find an unknown.

They are everywhere in daily life: scaling a recipe, converting units, reading a map, mixing paint, or working out a price for a different quantity. Whenever two quantities change together at a fixed rate, a proportion connects them, and solving it fills in the missing piece.

It uses cross multiplication, the fact that in a true proportion the diagonal products are equal.

1. Cross-multiply the two diagonals to set them equal.
2. Rearrange to isolate the unknown value.
3. Divide to solve, then check the diagonals match.

Proportions come from ratios; to simplify or scale a ratio itself, use the ratio calculator.

Solve 2 / 3 = x / 9 for x.

Calculation: cross-multiply to get 2 x 9 = 3 x, so 18 = 3x and x = 6. Check it: 2 over 3 and 6 over 9 both reduce to two-thirds, so the proportion holds.

Which value is missing decides how you rearrange.

Each formula comes from the single rule that the diagonal products a d and b c are equal.

The two ideas are closely related but not the same.

A proportion links two ratios and lets you solve for an unknown, while a ratio on its own just compares two numbers.

Which Value Is Missing

The formula changes depending on whether you solve for a, b, c or d, though all come from cross multiplication.

A Zero in the Wrong Place

Solving needs the value you divide by to be nonzero, or the proportion cannot be completed.

The Size of the Known Values

Larger or smaller knowns scale the unknown up or down in the same proportion.

Scaling Recipes

Adjust ingredient amounts for a different number of servings.

Maps and Models

Convert a scale distance to a real one, or the reverse.

Prices and Rates

Find the cost of a different quantity at the same unit rate.

1. Multiplying Straight Across

Multiply the diagonals, a with d and b with c, not the tops together and bottoms together.

2. Leaving More than One Blank

You can solve for only one unknown. Enter the other three values.

3. Mixing Up the Order

Keep the two ratios in the same order, so like quantities line up top and bottom.

4. Dividing by Zero

The value you divide by must be nonzero, or there is no solution.

5. Forgetting to Check

Confirm the diagonal products match once you have the answer.

The method is exact; only the displayed decimals are rounded.

It is a statement that two ratios are equal, written a over b equals c over d. It says two pairs of numbers relate in the same way, which lets you scale one to find an unknown in the other.

Cross-multiply: set the product of the diagonals equal, so a times d equals b times c, then solve for the unknown. If 2 over 3 equals x over 9, then 18 equals 3x, so x is 6.

It is the rule that in a true proportion the two diagonal products are equal. Multiplying a by d and b by c gives the same value, which you use to solve for a missing term.

A ratio compares two quantities, like 2 to 3. A proportion is a statement that two ratios are equal. A proportion links two ratios so you can solve for an unknown.

Yes. Leave any one of a, b, c or d blank and enter the other three. The calculator rearranges cross multiplication to find whichever is missing.

If the value you would divide by is zero, the proportion cannot be solved. Cross multiplication needs a nonzero denominator to isolate the unknown.

They scale recipes, convert map distances, adjust prices for different quantities, mix ingredients, and change units, anywhere two quantities keep a fixed relationship.

No. The proportion works whatever form the ratios take, as long as they are truly equal. 2 over 3 and 6 over 9 form a valid proportion even though one is not reduced.

No. The calculation runs in your browser and nothing you enter is stored or sent anywhere, unless you choose Save, which keeps the result only on this device.

• Proportionality (mathematics) (Wikipedia).
• Proportions explained (Maths Is Fun).
• Ratios (Maths Is Fun).