A ratio compares quantities by division while keeping their relative sizes visible as parts.
Use ratios for mixtures, scale, allocation, recipes, aspect relationships, and any comparison where proportional structure matters.
The relationship
The defining equation
a:b = (a÷k):(b÷k)
Dividing every part by the same nonzero factor k preserves the ratio.
See the structure
Shrink every part by the same factor
2 : 3=4 : 6same relative parts
Worked example
Simplify 1.5 : 2.25
1.5:2.25 = 6:9 = 2:3
Interpret with care
What the result does—and does not—mean
A ratio alone does not say whether it means part-to-part, part-to-whole, a rate, or a scale. Keep units and interpretation explicit.
Quick guide
How to use this calculator
Enter the known values using ordinary signed decimals.
Choose an interpretation or relationship when the calculator provides one.
Read the exact result, decimal preview, and any domain explanation.
Calculation method
Use the stated percentage or ratio relationship
Clear denominators, then divide all terms by their greatest common divisor.
The calculator keeps finite-decimal inputs as exact reduced fractions and rejects a zero reference or denominator whenever the requested relative quantity would be undefined.
Worked example
Worked interpretation
1.5 : 2.25 simplifies to 2 : 3.
Clear denominators, then divide all terms by their greatest common divisor.
Supported inputs
Precision and limits
Input precision
Each value may contain up to 30 digits and 15 decimal places. Scientific notation, fractions typed with a slash, and thousands separators are not accepted.
Exactness
Finite decimals are converted to reduced rational numbers. Detected repeating digits appear in parentheses, while previews that exceed the display limit end with an ellipsis; the exact fraction remains available.
Lists and ratios
List-based tools accept 2–12 entries separated by commas, colons, semicolons, or new lines. Ratio parts must satisfy the positivity rules shown by the calculator.
