Calculator
Enter a percentage value; options control rounding and display.
Example Data
| Percentage | Fraction | Simplified | Mixed Number | Decimal |
|---|---|---|---|---|
| 12.5% | 125/1000 | 1/8 | 1/8 | 0.125 |
| 33.5% | 335/1000 | 67/200 | 67/200 | 0.335 |
| 150% | 150/100 | 3/2 | 1 1/2 | 1.5 |
| -7.25% | -725/10000 | -29/400 | -29/400 | -0.0725 |
Formula Used
A percentage means “per one hundred.” If p is the percent value, then:
- p% = p / 100
- If p has decimals, write it as n / 10^k, then: (p / 100) = n / (10^k × 100)
- Simplify by dividing numerator and denominator by gcd(numerator, denominator).
This calculator keeps exact fractions for finite-decimal inputs (before optional rounding).
How to Use This Calculator
- Type a percentage value (you can include a % sign).
- Choose rounding if your input has many decimals.
- Keep “Simplify” on to get lowest terms.
- Press “Convert to Fraction” to see results above.
- Use CSV/PDF buttons to export your latest result.
FAQs
1) Why do we divide by 100?
Because percent literally means “per one hundred.” So 45% equals 45/100, which can then be reduced.
2) Does the calculator simplify the fraction?
Yes, when “Simplify fraction” is enabled. It divides numerator and denominator by their greatest common divisor to reach lowest terms.
3) What if my percent has decimals?
Finite decimals become exact fractions by using a power-of-ten denominator, then multiplying by 100 for the percent conversion.
4) Why might rounding be helpful?
Very long decimals can create huge denominators and exceed integer limits. Rounding keeps calculations stable while staying close to your input.
5) Can I convert values over 100%?
Yes. For example, 150% becomes 3/2, which can also be shown as the mixed number 1 1/2.
6) How are negative percentages handled?
The sign stays with the numerator. For example, -7.25% converts to -29/400 after simplification.
7) Are the steps shown exact?
Yes for finite-decimal inputs before rounding. If you choose rounding, steps reflect the rounded input you selected.
8) What do CSV and PDF downloads include?
They export your latest calculation: input percent, raw and simplified fractions, mixed number, and decimal value for easy sharing.