Fraction ↔ Percentage Calculator
Formula: n/d × 100 = p (p is shown as a percentage).
Fraction ➜ Percentage
Percentage ➜ Fraction
Results (live)
Actions
Quick summary
Reference
| Topic | Rule / Info |
|---|---|
| Fraction → Percentage | ( p% = dfrac{n}{d} times 100 ). |
| Percentage → Fraction | ( p% = dfrac{p}{100} ) then reduce by the greatest common divisor. |
| Notes | Denominator must be nonzero. Values can be negative or > 100% (improper fractions or > 1). |
Important Notes
This calculator uses standard fraction and percentage conversion rules. For fraction-to-percentage conversion, it divides the numerator by the denominator and multiplies the result by 100. For percentage-to-fraction conversion, it writes the percentage over 100 and simplifies the fraction when possible.
- The denominator cannot be zero. A fraction with a denominator of 0 is undefined, so the calculator cannot convert it.
- Percentages above 100% are valid. Improper fractions such as 5/4 convert to percentages greater than 100%, such as 125%.
- Negative values are valid. A negative fraction converts to a negative percentage, such as -1/4 = -25%.
- Repeating decimals may be rounded. Fractions like 1/3 convert to repeating percentages such as 33.333…%, so displayed results may be rounded for readability.
- Decimal percentages may create approximate fractions. Very long decimal percentages can produce large fractions before simplification, depending on the entered precision.
Best use: Use this calculator for math homework, quick conversions, grades, ratios, discounts, probability, and general percentage work. For official reporting, financial documents, engineering work, or school assignments with required rounding rules, always check the required decimal places or fraction format.
Use this Fraction to Percentage Calculator to convert a fraction into a percentage or convert a percentage back into a simplified fraction.
Calculation Method
To convert a fraction to a percentage:
Percentage = numerator ÷ denominator × 100
To convert a percentage to a fraction:
p% = p/100
Then simplify the fraction when possible.
Example
Convert 3/4 to a percentage:
3 ÷ 4 = 0.75
0.75 × 100 = 75%
Therefore, 3/4 = 75%.
Important Note
The denominator cannot be zero. Improper fractions can produce percentages above 100%, and repeating decimal results may be rounded for display.