The ratio calculator simplifies two positive quantities, generates an equivalent ratio from a new first term, and solves a missing fourth proportional value. It supports whole-number and decimal inputs.
How to use this calculator
Choose a mode and enter A and B. Simplification divides both by their greatest common divisor when values are integers. Equivalent mode uses C as the new A and finds the matching B. Missing-value mode solves A:B = C:D.
Formula & calculation method
Equivalent B = B × C/A; missing D = B × C/AEquivalent and missing-value modes use the same scale factor C/A. For integer simplification, the calculator scales decimal inputs to integers before finding the greatest common divisor, then reduces the pair.
Worked example
The ratio 12:18 simplifies to 2:3. If the first term becomes 6 in an equivalent ratio, the second is 9. In 12:18 = 6:D, D is also 9 because both sides use the same proportion.
Why this is useful
The three modes address common recipes, scale drawings, mixtures, and proportional reasoning without converting every problem to decimals manually. Simplified output makes relationships easier to communicate.
Limitations to keep in mind
Ratios require consistent units and meaningful positive quantities. This tool handles two-term ratios only and does not determine whether a real-world relationship is genuinely proportional outside the supplied numbers.
Frequently asked questions
Can a ratio contain zero?
This calculator requires positive terms because its proportion and scaling modes divide by A. Zero also changes interpretation in many ratio problems.
Do A and B need the same units?
For a meaningful direct ratio, express compared quantities consistently. Convert unlike units before entering them.
How is a decimal ratio simplified?
Decimals are scaled by powers of ten to whole numbers, reduced by their greatest common divisor, and displayed in simplest integer terms.