Proportion Calculator

Written byOleh Soloninupdated 5 October 2026

Relationship

Where the unknown is

Only needed when the unknown is somewhere else.

Result

x35
Formula4 : 10 = 14 : x → x = 10 × 14 ÷ 4 = 35
Ratio b ÷ a2.5
Cross-multiplication check4 × 35 = 140, 10 × 14 = 140

Cross-multiplication in one step

Solves a proportion a : b = c : d with the unknown in any of the four places, and inverse proportion, by cross-multiplication, with the working and a check.

A proportion says two ratios are equal: a : b = c : d. Its key property is cross-multiplication: the product of the outer terms equals the product of the inner ones, a × d = b × c. So any term follows from the other three: d = b × c ÷ a, c = a × d ÷ b, b = a × d ÷ c, a = b × c ÷ d.

For 4 : 10 = 14 : x, x = 10 × 14 ÷ 4 = 35. Check: 4 × 35 = 140 and 10 × 14 = 140. If 4 servings take 10 spoons of flour, 14 servings take 35.

How to use

Choose the relationship: direct proportion or inverse proportion.
For a direct proportion, choose where the unknown sits and enter the three known numbers.
Read x, the working and the check: the products of the outer and inner terms must match.

How to solve a proportion

1. Write it so that like quantities sit in like places: servings with servings, spoons with spoons. 2. Cross-multiply the known terms. 3. Divide by the remaining known term. 4. Check that a × d equals b × c.

Inverse proportion is when one quantity grows as the other shrinks by the same factor: 4 workers finish in 10 days, so 5 workers take 4 × 10 ÷ 5 = 8 days. Here the product stays the same: a × b = c × x.

Worked out with this calculator.
Proportion	Working	x
4 : 10 = 14 : x	10 × 14 ÷ 4	35
4 : 10 = x : 35	4 × 35 ÷ 10	14
4 : x = 14 : 35	4 × 35 ÷ 14	10
x : 10 = 14 : 35	10 × 14 ÷ 35	4
100 : 2400 = 15 : x	2400 × 15 ÷ 100	360

What this calculator shows

The value of x and the working
The ratio b ÷ a
A cross-multiplication check
The answer for inverse proportion

What to keep in mind

You cannot divide by zero: the term you divide by must be non-zero.
For inverse proportion the unknown is x in a · b = c · x.

FAQs

How do I solve a proportion?

Cross-multiply the known terms and divide by the third: in 4 : 10 = 14 : x, x = 10 × 14 ÷ 4 = 35. The check is that outer and inner products are equal.

How do I find a missing middle term?

Divide the product of the outer terms by the known middle term: in 4 : x = 14 : 35, x = 4 × 35 ÷ 14 = 10. Choose where the unknown is in the calculator.

What is inverse proportion?

A relationship where one quantity falls by the same factor the other rises, so their product is constant: a × b = c × x. Four workers take 10 days, five take 8.

Can I do percentages as a proportion?

Yes: 100% is to the whole as the percentage is to the part. 15% of 2400 is 100 : 2400 = 15 : x, so x = 360.

How do I find the missing term of a proportion?

Cross-multiply and divide. In 4 : 10 = 14 : x that gives x = 10 × 14 ÷ 4 = 35, and the check balances: 4 × 35 = 140 and 10 × 14 = 140.

How does an inverse proportion differ?

In a direct proportion both quantities grow together; in an inverse one their product stays fixed. The same numbers taken inversely give x = 4 × 10 ÷ 14 ≈ 2.857: 3.5 times the workers take a 3.5th of the time, if everyone works at the same pace.

Worked example

Scaling a recipe

Input: 4 : 10 = 14 : x

Output: x = 35

Note: If 4 servings need 10 spoons, 14 servings need 35. Check: 4 × 35 = 140 and 10 × 14 = 140.

Useful links

All tools in Math & Statistics

Proportion Calculator

Result

Related tools

Ratio Calculator

Percentage Calculator

Recipe scaler: adjust ingredients for more or fewer servings

Useful links