DIY Cost Tools
Decimal to Fraction Calculator
MATH CALCULATOR
Convert a decimal into a simplified fraction, mixed number, and percentage. The maximum denominator helps approximate repeating or rounded decimals.
How it works
The calculator uses continued-fraction approximation to find a nearby fraction whose denominator does not exceed your limit, then reports the remaining decimal error.
Formula
Fraction value = numerator ÷ denominator. Percentage = decimal × 100.
Example
For 0.375, the exact simplified fraction is 3/8 because 3 ÷ 8 = 0.375.
Important limits
- Rounded or repeating decimals may have many possible approximations.
- A larger denominator can improve precision but produces a less convenient fraction.
- Very large inputs are limited by JavaScript number precision.
Frequently asked questions
Why does the denominator limit matter?
It controls the tradeoff between a simple fraction and a closer approximation.
Can this handle negative decimals?
Yes. The sign is carried into the fraction and mixed number.
Choosing a fraction approximation
A terminating decimal can be converted exactly by writing it over a power of ten and reducing the result. Repeating or measured decimals may require an approximation, so the allowed maximum denominator determines how simple or precise the fraction will be.
For shop measurements, choose a denominator supported by the ruler or tool, such as 8, 16, 32, or 64, and compare the approximation error with the project tolerance. For mathematical work, preserve more decimal digits before conversion and reduce numerator and denominator by their greatest common factor. A displayed decimal may already be rounded, meaning the resulting fraction represents the displayed value rather than an unknown exact original measurement.
Review notes
The output was checked against standard fraction reduction and continued-fraction examples. Last reviewed September 30, 2026.