Ratio Calculator
Simplify a ratio and scale it to a new equivalent ratio using any known value.
Simplified ratio
How we calculated it
About the Ratio Calculator
Ratios describe how quantities relate without forcing the comparison onto a percentage scale. This calculator simplifies that relationship and can solve equivalent proportions while preserving the original order of the terms.
A ratio does not require the quantities to be identical in size, but they should represent compatible or intentionally comparable things. Convert units first when both sides measure the same type of quantity.
How to Use the Ratio Calculator
- Enter the two or more quantities in the order you want them compared.
- Convert measurements to compatible units before simplifying when they represent the same physical quantity.
- Calculate the simplified ratio and any equivalent ratio requested.
- Keep the original order because reversing a ratio changes its meaning.
How the Calculation Works
For two whole-number quantities a and b, the simplified ratio a:b is found by dividing both values by their greatest common divisor.
For proportional problems, equivalent ratios preserve the same quotient. If a/b = c/d and one value is unknown, cross multiplication can be used to solve for it.
Worked example
Ratio Calculator Worked Example
Simplify 18:24
The greatest common divisor of 18 and 24 is 6. Divide both terms by 6: 18 ÷ 6 = 3 and 24 ÷ 6 = 4. The simplified ratio is 3:4.
Result guide
Understanding Your Ratio Calculator Result
A simplified ratio preserves the relationship but not the original scale. A ratio of 3:4 could represent 3 to 4, 30 to 40 or 75 to 100.
Before you rely on the answer
Assumptions and Limitations
- Quantities are entered in the intended order.
- Compatible measurements are converted to a common unit before comparison.
- Zero terms are interpreted carefully because division-based forms may become undefined.
Practical tip
Using This Result in Practice
Write a short label beside each side of a ratio, such as water:concentrate. This prevents a correct numerical ratio from being used in the wrong direction.
Related calculations
Useful Calculations to Continue With
If one part of an equivalent ratio is unknown, use the Proportion Calculator to solve the cross-multiplication problem.
If you want the relationship expressed per 100 rather than as a ratio, use the Percentage Calculator.
Common questions
Ratio Calculator FAQ
How do you simplify a ratio?
Divide every term by their greatest common factor. For 18:24, dividing both by 6 gives 3:4.
Is 2:3 the same as 3:2?
No. The order matters. 2:3 means two units of the first quantity for every three of the second.
Do ratio quantities need the same units?
If they measure the same physical type, convert them to the same unit first. Some intentional ratios, such as speed, compare different units and should retain that meaning.