Raise any base to any exponent — positive, negative, zero, or fractional.
How it works
The result is the base multiplied by itself the number of times the exponent specifies: result = base^exponent. A negative exponent flips the result into a fraction (base⁻ⁿ = 1 ÷ baseⁿ), and any nonzero base raised to the power of 0 equals 1.
What this does not include
This is a plain power calculation, not a model of change over time — for a quantity growing continuously at a fixed rate, see this site’s exponential growth calculator instead.
How to use this calculator
- Enter the base.
- Enter the exponent.
A worked example
2¹⁰ = 1,024.
3⁴ = 81.
2⁻³ = 1/2³ = 0.125 — a negative exponent produces a fraction, not a negative number.
What the variables mean
| Variable | Meaning |
|---|---|
| Base | The number being raised to a power |
| Exponent | How many times the base is multiplied by itself (or divided, if negative) |
Edge cases worth knowing
A negative exponent means “reciprocal,” not “negative result.” 2⁻³ isn’t −8, it’s 1/8 = 0.125 — a very common point of confusion.
Zero raised to a negative exponent is undefined — it would require dividing by zero, so the calculator declines to show a result for that combination.
Why does anything to the power of 0 equal 1?
It follows from the pattern of dividing by the base each time you decrease the exponent by 1 — baseⁿ ÷ base = baseⁿ⁻¹, and continuing that pattern down to base⁰ always lands on 1.
What does a negative exponent mean?
It means “take the reciprocal” — 2⁻³ is 1 ÷ 2³, which is 1/8, or 0.125.
Can the base or exponent be a decimal?
Yes — a fractional exponent corresponds to a root (base^0.5 is the same as the square root of base), and a decimal base works exactly as you’d expect.
