Percent to Fraction CalculatorFree online math calculator — instant results, no sign-up
Convert a terminating percentage to a reduced fraction.
Sign in to save results and favorites.
About the Percent to Fraction Calculator
The Percent to Fraction Calculator converts a terminating percentage into a fraction in lowest terms. It accounts for both the percent sign and any decimal places, so the default input of 12.5% becomes 1/8.
- Percentage
- The value to convert, expressed in percent units (%), with a default of 12.5.
Formula and method
N = p × 10^d; D = 100 × 10^d; g = gcd(|N|, D); F = (N/g)/(D/g). For p = 12.5 and d = 1: F = 125/1000 = 1/8.
- pThe entered percentage value, without the percent sign.
- dThe number of decimal places in the terminating input.
- NThe integer numerator obtained by multiplying p by 10^d.
- DThe denominator 100 × 10^d, accounting for percent units and decimal places.
- gThe greatest common divisor of |N| and D, used to reduce the fraction.
- FThe reduced fraction equivalent to the entered percentage.
Divide the percentage by 100, then multiply the numerator and denominator by a power of ten that makes both integers. Reduce the resulting fraction by dividing both integers by their greatest common divisor. With the default input, 12.5% = 12.5/100 = 125/1000; dividing both integers by 125 gives 1/8.
Worked example
These are the calculator's starting values and the results it actually produces for them.
Inputs
- Percentage12.5
Results
- Fraction1/8
How to use the Percent to Fraction Calculator
- 1Enter the value in the Percentage field, or leave the default value of 12.5.
- 2Check that the entry is a percentage rather than a decimal proportion.
- 3Run the calculation to convert the percentage to a fraction and reduce it.
- 4Read the Fraction output; for the default input, it is 1/8.
Reading your result
The Fraction row shows the entered percentage as an equivalent ratio in lowest terms. For 12.5%, the output 1/8 means one part out of eight equal parts of a whole. The numerator and denominator have no common factor greater than one.
Limitations
This tool is intended for finite, terminating percentage inputs. The fraction is exact for the value entered, but if that percentage was rounded from another value, the fraction does not recover the original value. Repeating decimals, symbolic expressions, and nonnumeric entries are outside the stated scope. Very long decimal inputs may be subject to the implementation's precision limits.
Common questions
Why does 12.5% become 1/8 rather than 12.5/1?+
Percent means per hundred, so 12.5% is 12.5/100. Clearing the decimal gives 125/1000, which reduces to 1/8.
Should I divide the percentage by 100 before entering it?+
No. Enter 12.5 for 12.5%; the calculator performs the division by 100 as part of the conversion.
Why is the output 1/8 instead of 125/1000?+
The calculator returns a reduced fraction. Both 125 and 1000 are divisible by 125, so their ratio simplifies to 1/8 without changing its value.
Can a rounded percentage produce an exact fraction?+
Yes, the fraction is exact for the terminating percentage entered. However, if 12.5% is a rounded measurement, 1/8 represents that rounded value, not necessarily the original measurement.
Does the calculator save my information?+
Calculations run in your browser. While signed in, inputs and results are automatically recorded in account history; saving a result creates a separate saved record.
You might also like
Scientific Calculator
Full scientific calculator with trig, logs, powers, memory and degree/radian modes.
Fraction Calculator
Add, subtract, multiply and divide fractions.
Percentage Calculator
Percent of a number, what percent, and percent change.
Random Number Generator
Generate random integers in a range.
Percent Error Calculator
Error between an observed and true value.
Exponent Calculator
Raise a base to any power.
Results are estimates for informational purposes and are not financial, medical or legal advice.