Ratio calculator
Simplify a two-part ratio, use it to divide a total, or solve one missing value in an equivalent proportion.
First side of the ratio; use a whole number when simplifying.
Second side of the ratio; use a whole number when simplifying.
- Original ratio
- 12 : 18
- Greatest common divisor
- 6
- Scale factor
- ÷ 6
Relative size of the two parts
The two bars share a scale and supplement the exact numeric labels; length and colour are not the only way the relationship is shown.
Both sides were divided by the same greatest common divisor, so the relationship is unchanged.
Included
- Two-part ratios with non-negative values
- Whole-number simplification using the greatest common divisor
- Dividing a non-negative total between two ratio parts
- Solving one missing fourth term in a positive proportion
Not included
- Negative ratios or ratios with three or more parts
- General symbolic equations or more than one unknown value
- Unit conversion or checking whether quantities use compatible units
- Recipe, mixture, dosage or safety guidance
What this means
A ratio compares two quantities in a fixed order. 12:18 and 2:3 describe the same relationship because both sides of 12:18 can be divided by their greatest common divisor, 6.
When a total is divided in a ratio, each side receives its fraction of all ratio parts. For 2:3, there are five parts altogether: the first share is 2/5 of the total and the second is 3/5.
A proportion states that two ratios are equal. In a:b = c:x, the missing value is x = b × c ÷ a. This calculator requires all three known proportion terms to be greater than zero so the displayed solution is unique and valid.
Formula & worked example
Simplify: divide both sides by gcd(a, b) Divide a total: left = total × a ÷ (a + b); right = total × b ÷ (a + b) Solve a:b = c:x: x = b × c ÷ a
Simplify the ratio 12:18
- Greatest common divisor of 12 and 18
- 6
- First side: 12 ÷ 6
- 2
- Second side: 18 ÷ 6
- 3
The simplified ratio is 2:3. Multiplying both sides by 6 reconstructs the original 12:18 ratio.
How this calculation works
The calculation follows the formulas, definitions and assumptions explained on this page. The references below support the method and any stated boundaries.
Official sources
- OpenStax Prealgebra 2e — Solve proportions and their applications — Equality of valid ratios and solving a proportion by equal cross-products