What the exponent calculator does
Enter a base and an exponent and the calculator returns the power — plus the negative power (the reciprocal) and the half power (the square root of the result), which are the two related values people most often need next. It handles fractional and negative exponents and very large results, and runs in your browser. Use it for compound growth, scientific notation, data sizes, probability and anything else that repeats a multiplication.
The rules of exponents
bⁿ = b × b × … × b (n times) 2⁵ = 32
b⁰ = 1 (any non-zero base)
b⁻ⁿ = 1 / bⁿ 2⁻³ = 1/8 = 0.125
b^(1/n) = ⁿ√b 8^(1/3) = 2
b^(m/n) = ⁿ√(bᵐ) 27^(2/3) = (³√27)² = 9
bᵐ × bⁿ = bᵐ⁺ⁿ bᵐ ÷ bⁿ = bᵐ⁻ⁿ (bᵐ)ⁿ = bᵐⁿ (ab)ⁿ = aⁿbⁿPowers worth knowing
| Power | Value | Where it appears |
|---|---|---|
| 2¹⁰ | 1,024 | One kibibyte; the reason 'kilo' in computing is 1,024 |
| 2²⁰ | 1,048,576 | One mebibyte |
| 2³² | 4,294,967,296 | 32-bit address space; IPv4 addresses |
| 2⁶⁴ | 1.8 × 10¹⁹ | 64-bit integers |
| 10³, 10⁶, 10⁹, 10¹² | thousand, million, billion, trillion | SI prefixes kilo, mega, giga, tera |
| 1.05¹⁰ | 1.629 | 10 years at 5% growth — a 63% increase |
| 1.07¹⁰ | 1.967 | 10 years at 7% — nearly doubling (Rule of 72) |
| 0.5¹⁰ | 0.000977 | Ten halvings — ten half-lives leave under 0.1% |
| e¹ | 2.71828 | Continuous growth base |
Exponential growth and decay
Growth: future = present × (1 + rate)^periods $1,000 × 1.06¹⁵ = $2,397
Decay: remaining = initial × (1 − rate)^periods 100 g × 0.9⁵ = 59 g
Half-life: remaining = initial × 0.5^(time / half-life)The base carries the rate, the exponent carries the time. Small differences in the base compound into large differences in the result: over 30 years, 6% turns $1,000 into $5,743 while 8% turns it into $10,063. The Compound Interest Calculator explores this with a table.
Scientific notation
Very large and very small numbers are written as a number between 1 and 10 times a power of ten: the speed of light is 3 × 10⁸ m/s, an electron's mass 9.1 × 10⁻³¹ kg. The calculator shows results above about 10²¹ in this form (displayed as 1e21). To multiply numbers in scientific notation, multiply the leading parts and add the exponents.
Common mistakes
−3²is −9, not 9: the exponent binds before the minus.(−3)²is 9.2³²is not 2 × 32 — exponents are repeated multiplication, not multiplication.- A negative exponent does not make the result negative; it makes it a fraction.
0⁰is defined as 1 in most contexts (and by this calculator), but is treated as undefined in some branches of analysis.- Fractional exponents of negative bases are usually not real:
(−8)^(1/3)is −2 by convention, but(−8)^(0.5)has no real value.