Calculator tool
How this calculator works
Use the explanation to understand the formula, assumptions, and practical limits behind the calculator result.
What a ratio tells you
A ratio compares two quantities in the form . The calculator simplifies the pair by dividing both parts by their greatest common factor, then shows the decimal value , the percentage of relative to , and the missing value in an equivalent proportion.
For example, 12:8 simplifies to 3:2. If , then because both sides keep the same relationship.
When ratio outputs become undefined
Some ratio-derived values need division. If both parts are zero, the ratio itself is undefined. If , decimal and percentage forms cannot be calculated. If , the equivalent proportion cannot solve by dividing through .
Use the simplified ratio when comparing mixtures, map scales, recipes, or relative quantities. Use the warnings when a zero input changes which outputs are mathematically meaningful.
Frequently asked questions
What does it mean to simplify a ratio?
It means dividing both parts by the same common factor until no larger shared factor remains. 12:8 becomes 3:2.
Why can a ratio output be undefined?
Because decimal, percentage, and proportion forms require division. Division by zero has no valid finite result.
Is a ratio the same as a fraction?
They are closely related, but a ratio compares two quantities while a fraction is often read as part of a whole. The same numbers can be useful in both forms depending on the question.
How do I solve an equivalent proportion?
Keep the same relationship on both sides. If and is non-zero, then .
