Ratio Calculator
This ratio calculator handles three closely related jobs: solving the missing term in A : B = C : x, reducing a two-number ratio, and finding what percentage A is of B.
Inputs may be non-negative whole numbers or decimals. All three known values in a proportion must be positive; the zero rules for the other modes are explained below. The answer includes the substituted formula.
Unknown term x
12
Formula and substitution: A : B = C : x → x = (B × C) ÷ A = (3 × 8) ÷ 2 = 12
How to solve a proportion for x
A proportion says that two ratios are equal: A : B = C : x. Cross-products are equal, so A × x = B × C. Isolating the unknown gives x = B × C ÷ A.
For 2 : 3 = 8 : x, substitute the values to get x = 3 × 8 ÷ 2 = 12. Checking the answer gives equal quotients: 2 ÷ 3 = 8 ÷ 12.
How to simplify a ratio
A ratio A : B compares the relative size of two quantities. With integers, divide both terms by their greatest common divisor. The GCD of 12 and 18 is 6, so 12 : 18 reduces to 2 : 3.
Decimals are first converted to integers without changing the relationship. For 1.5 : 2.25, multiplying both terms by 100 gives 150 : 225, which reduces to 2 : 3. The calculator performs this conversion exactly instead of rounding the inputs first.
Converting a ratio to a percentage
To find A as a percentage of B, divide A by B and multiply by 100%. The ratio 3 : 4 therefore gives 3 ÷ 4 × 100% = 75%.
Order matters: 4 compared with 3 is 133.333…%, not 75%. In a comparison over time, the new or compared value is usually A and the baseline is B.
Ratio and proportion examples
| Problem | Calculation | Answer |
|---|---|---|
| Simplify 12 : 18 | 12 ÷ 6 : 18 ÷ 6 | 2 : 3 |
| Simplify 1.5 : 2.25 | 150 : 225, then ÷ 75 | 2 : 3 |
| Convert 3 : 4 to percent | 3 ÷ 4 × 100% | 75% |
| Solve 2 : 5 = 8 : x | x = 5 × 8 ÷ 2 | 20 |
| Solve 6 : 9 = 10 : x | x = 9 × 10 ÷ 6 | 15 |
Units and limits
- Convert quantities to the same unit before comparing them: 2 m : 50 cm becomes 200 cm : 50 cm = 4 : 1.
- All known values A, B, and C must be greater than zero in A : B = C : x. A zero B makes the original A/B undefined; a zero C produces x = 0 and leaves C/x as the undefined expression 0/0.
- When simplifying, 0 : B and A : 0 are allowed if the other term is nonzero; 0 : 0 is undefined. In percentage mode, A may be zero but the divisor B must be greater than zero.
- A numerical ratio does not validate a recipe, material, or mixture. Follow the applicable specification and compare like units of mass or volume.
Frequently asked questions
How do I solve a proportion?
For A : B = C : x, use x = B × C ÷ A. In 2 : 3 = 8 : x, the missing term is 12.
How do I simplify a ratio?
Divide both terms by their greatest common divisor. Dividing 24 : 36 by 12 reduces the ratio to 2 : 3.
How do I turn a ratio into a percentage?
Divide the first number by the second and multiply by 100%. The number 30 is 30 ÷ 40 × 100% = 75% of 40.
Can a ratio contain decimals?
Yes. The calculator accepts decimal inputs and converts them to an exact integer ratio before reducing it.
What does a 1 : 4 ratio mean?
It means four equal parts of the second quantity for every one part of the first. Together the notation describes five parts, but it does not set the size of a part.
Why does the order of a ratio matter?
A : B and B : A are reciprocals. For example, 2 : 5 equals 0.4, while 5 : 2 equals 2.5.
Can a ratio or proportion contain zero?
A simplified ratio may be 0 : B or A : 0 when the other term is nonzero; 0 : 0 is undefined. Percentage mode allows A = 0 when B > 0. In A : B = C : x, the known values A, B, and C must all be positive.
Updated: 2026-08-16