Ratio Calculator
A ratio compares two quantities — three parts flour to one part water, a 16 : 9 screen, two cats for every three dogs. This ratio calculator does the two jobs people most often need: it reduces a ratio to its simplest whole-number form by cancelling the common factor, and it scales a ratio up or down by solving for a missing term. Reach for it when adapting a recipe, mixing paint or fuel, reading a map scale, or checking that two ratios describe the same relationship.
Calculate
Default result: 3.00
Ratio Calculator · Result
calculators.dev
Simplified first term
12 × 8 × 3
- Simplified second term
- 2.00
- Missing term x (where a/b = c/x)
- 2.00
Reviewed by the calculators.dev team · Last updated 2026-06-23
How to calculate
Enter the two terms of your ratio in the first two boxes. The calculator finds the largest number that divides both — their greatest common divisor — and cancels it to show the simplest form, so 12 : 8 becomes 3 : 2. To scale the ratio, enter the known term of the second ratio in the third box; the tool then solves a / b = c / x, giving the value of x that keeps the two ratios equivalent. Change any number and every result updates as you type.
Simplify: divide both terms by gcd(a, b), the greatest common divisor, so a : b becomes (a ÷ g) : (b ÷ g). Scale: a proportion a / b = c / x is solved by x = c × b ÷ a. A ratio and a proportion are two views of the same idea — a ratio names the relationship, a proportion sets two ratios equal so a missing term can be found.
Example calculation
The ratio 12 : 8 shares a common factor of 4, so dividing both terms by 4 reduces it to 3 : 2 — the simplest whole-number form. Using the same two terms as a proportion, 12 / 8 = 3 / x solves to x = 2, because 3 stands in the same relationship to 2 as 12 does to 8.
- simplifiedA
- 3
- simplifiedB
- 2
- solvedX
- 2
Assumptions
- Simplification to whole numbers applies when both terms are integers; a ratio with a decimal term is left as entered, since it has no integer reduction.
- Order matters: 3 : 2 is not the same as 2 : 3, so keep the terms in the sequence the original ratio uses.
- The first term divides the proportion when solving, so it cannot be zero.
Common mistakes
- Reducing only one side of the ratio — both terms must be divided by the same common factor to stay equivalent.
- Flipping the order of the terms when scaling, which gives the reciprocal instead of an equivalent ratio.
- Confusing a 3 : 1 ratio with a 3 : 4 fraction of the whole — a 3 : 1 mix is three parts out of four, not three quarters of one part.
Frequently asked questions
How do I simplify a ratio?
Divide both terms by their greatest common divisor. For 12 : 8 the common factor is 4, so the ratio reduces to 3 : 2.
What is the difference between a ratio and a proportion?
A ratio compares two quantities (a : b). A proportion states that two ratios are equal (a / b = c / x), which lets you solve for a missing term.
Can a ratio have decimals?
Yes, but a decimal ratio has no whole-number reduction, so the calculator leaves it as entered. Multiply both terms by ten to clear one decimal place if you want integers.
Why can't the first term be zero?
Solving the proportion divides by the first term, and division by zero is undefined, so the calculator asks for a non-zero value instead of returning a broken result.