Ratio Calculator guide
Reduce a multi-part ratio to whole-number terms or solve the missing value in a proportion.
What this tool does
The Ratio Calculator has two independent operations. Ratio simplification accepts two to eight non-negative terms separated by colons, slashes, or commas. Decimal terms are scaled to integers using up to six decimal places, then divided by their greatest common divisor. For example, 1920:1080 becomes 16:9, while 1.5:3 becomes 1:2.
The proportion solver uses the relationship a:b = c:x. Cross multiplication gives x = b × c ÷ a. The first term cannot be zero because that would require division by zero. Negative values are permitted in the proportion solver because signed mathematical ratios can be meaningful, but the simplifier accepts non-negative terms for a clear conventional result.
Decimal scaling is practical rather than symbolic. Repeating decimals and values written with more than six meaningful decimal places may be approximated before reduction. Use a fraction or algebra system when exact rational representation is required.
How to use it
- For simplification, type the ratio terms such as
24:36. - Select Simplify ratio and review the whole-number output.
- For a proportion, enter known values for
a,b, andc. - Select Solve x to calculate the fourth value.
- Substitute the result back into both ratios to verify the relationship.
Units must be compatible before simplifying or comparing ratios. Convert lengths, weights, currencies, or rates to consistent units first.
For width-and-height scaling, use the Aspect Ratio Calculator. For percentage change or a part-to-total comparison, use the Percentage Calculator.
Benefits
- Simplifies ratios with two to eight terms
- Supports common separators and finite decimals
- Handles zero terms when the ratio is not entirely zero
- Solves a common fourth-proportional equation
- Shows errors for undefined inputs
- Performs calculations locally
Understanding equivalent ratios
An equivalent ratio preserves relative proportions, not the original scale. Reducing 20:30 to 2:3 does not mean the quantities equal two and three units. It means both original quantities share a factor of ten. When rounding a solved result for real materials or people, state the rounding rule and check whether whole units are required.