Proportion Calculator
Solve any proportion of the form a : b = c : d by entering three values and leaving the fourth empty. Cross-multiplication gives the missing term instantly, with the full working shown. Works with integers, decimals and negative numbers.
Enter three values
Enter three values and leave one empty, then press Solve proportion.
What a proportion is
A proportion states that two ratios are equal. Written as
a : b = c : d or equivalently a/b = c/d, it says
"the relationship between a and b is the same as the relationship between c
and d". Proportions are the mathematical backbone of scaling: recipes,
maps, currency exchange, unit conversion, similar triangles and population
estimates all rely on them.
The key property of any proportion is that the product of the outer terms equals the product of the inner terms — a rule known as cross-multiplication:
a × d = b × c
From this single equation, any one of the four values can be found if the other three are known.
Solving for each unknown
Rearranging a × d = b × c gives a formula for each variable:
| Unknown | Formula | Example (given 3 : 5 = 9 : ?) |
|---|---|---|
a | a = (b × c) / d | — |
b | b = (a × d) / c | — |
c | c = (a × d) / b | — |
d | d = (b × c) / a | d = (5 × 9) / 3 = 15 |
Division by zero is undefined, so if the value you are dividing by is zero
the calculator returns a clear error rather than Infinity.
Worked examples
Example 1 — Basic solve
Solve 3 : 5 = 9 : d for d.
Cross-multiply: 3 × d = 5 × 9 = 45. Divide:
d = 45 / 3 = 15. Check: 3 : 5 = 9 : 15 because
both reduce to 3 : 5.
d = 15
Example 2 — Scaling a recipe
A recipe uses flour and sugar in the ratio 4 : 1. You have
750 g of flour — how much sugar?
Set up: 4 : 1 = 750 : d. Cross-multiply:
4 × d = 1 × 750 = 750. Divide: d = 187.5.
Sugar = 187.5 g
Example 3 — Map scale
A map has a scale of 1 : 25000. Two towns are 4.2 cm apart on
the map — what is the real distance in km?
1 : 25000 = 4.2 : d. Cross-multiply:
1 × d = 25000 × 4.2 = 105000 cm = 1.05 km.
Distance = 1.05 km
Example 4 — Solve for a decimal
Solve 2.5 : 1.8 = a : 4.5 for a.
Cross-multiply: 2.5 × 4.5 = 1.8 × a →
11.25 = 1.8a. Divide: a = 6.25.
a = 6.25
Proportions in geometry
Similar triangles — triangles with the same shape but different sizes — have corresponding sides in proportion. If triangle ABC is similar to triangle DEF, then:
AB / DE = BC / EF = AC / DF
Because the ratios of corresponding sides are equal, you can use this proportion calculator to find a missing side length when you know the other side lengths. It is the same technique used in scale drawings, architectural plans and orthographic projections.
Common mistakes
-
Mixing up the order of terms. The order must be consistent
on both sides. If you write
red : blue = ? : ?, the second ratio must also be red : blue, not blue : red. -
Dividing by the wrong side. When solving for
d, divide bya— the term diagonally opposite tod. Check the formula table above if unsure. -
Adding instead of multiplying. Proportions use
multiplication, not addition. From
a/b = c/d, you cannot conclude(a+1)/(b+1) = c/d. - Ignoring units. The two ratios must be in the same units on both sides. If one side is in cm and the other in m, convert first.
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Frequently asked questions
Cross-multiplication solves proportions of the form a/b = c/d by multiplying the numerator of each side by the denominator of the other, giving a × d = b × c. Isolating the unknown then gives the answer.
Just leave the field you want to solve for empty. The calculator automatically detects which value is missing and solves for it using the appropriate rearrangement of a × d = b × c.
Enter them as decimals. For example, enter 1/2 as 0.5 and 2 1/2 as 2.5. You can also use the fraction to decimal converter to convert first if that is easier.
Proportions with a zero in a denominator are undefined. The calculator will return a clear error rather than producing Infinity or NaN.
Yes. Cross-multiplication works with negative numbers just as well as positive ones. Be careful with the signs when isolating the unknown.