Quick answer
The power of two is 2ⁿ. 2^10 = 1,024.
Enter an exponent. The calculator returns 2 raised to that power.
Related tools: Power Converter: Convert watts, kilowatts, horsepower and BTU per hour. Power Calculator: Mechanical power from work and time, or force and velocity. Power Factor Calculator: Power factor, phase angle and reactive power from real and apparent power.
How to use the Power of 2 Calculator
- Enter exponent n (a whole number, between -60 and 1000).
- Press Calculate to see the result, and use Reset to start again.
| Input | What to enter | Allowed values |
|---|---|---|
| Exponent n | A whole number | ≥ -60, ≤ 1000 |
Formula and method
Formula
result = 2ⁿ
IEEE-754 double precision; shown to at most 6 decimal places.
BigInt exponentiation for n ≥ 0; reciprocal for negative n.
Worked examples
These examples are verified: each one is an automated test case that the live calculator must reproduce exactly.
Example 1
Inputs: Exponent n = 10.
| Result | Value |
|---|---|
| 2^10 | 1,024 |
Example 2
Inputs: Exponent n = -3.
| Result | Value |
|---|---|
| 2^-3 | 0.125 |
Example 3
Inputs: Exponent n = 64.
| Result | Value |
|---|---|
| 2^64 | 18,446,744,073,709,551,616 |
The first line is the headline result (2^10). IEEE-754 double precision; shown to at most 6 decimal places.
Why powers of 2 matter
Computers use binary, so memory sizes are powers of two: 2^10 = 1,024 (KiB), 2^20 = 1,048,576 (MiB), 2^30 = 1,073,741,824 (GiB). Each extra bit doubles the number of values.
Edge cases
2^0 = 1 and negative exponents give fractions: 2^−3 = 0.125. Very large exponents overflow. Doubling each day from 1 gives 2^29 = 536,870,912 after 30 days.
Powers of two in computing
2¹⁰ = 1,024. Other useful values are 2⁸ = 256, 2¹⁶ = 65,536, 2²⁰ = 1,048,576 and 2³² = 4,294,967,296.
n bits can represent 2ⁿ distinct values, so 8 bits give 256 values (0 to 255). A negative exponent gives a fraction: 2⁻¹ = 0.5.
What happens with invalid input
These messages are produced by the calculator itself, so you know what to fix.
- Exponent n: entering "1001" shows "Exponent n must be at most 1000." beside that field and no result.
Choosing between the Power of 2 Calculator and similar calculators
Each row shows what a related calculator on this site asks for and what it returns, so you can pick the one that matches your question.
| Calculator | You enter | It returns |
|---|---|---|
| [Power Converter](/converters/power-converter/) | value, from and to | Horsepower (mechanical) → Watt (W) |
| [Power Calculator](/science/power-calculator/) | use | Power |
| [Power Factor Calculator](/math/power-factor-calculator/) | real power and apparent power | Power factor |
| [Slope Calculator](/math/slope-calculator/) | x₁, y₁ and x₂ | Slope |
| [LCM Calculator](/math/lcm-calculator/) | numbers | Least common multiple |
Background: algebra
Many algebra calculators rest on the same ideas: write the problem in a standard form, identify the coefficients, apply the formula and check the answer by substituting it back. For a quadratic ax² + bx + c = 0 the roots are (−b ± √(b² − 4ac)) ÷ 2a, and the discriminant b² − 4ac decides the kind of roots: positive gives two real roots, zero gives one repeated root and negative gives two complex conjugate roots.
If a = 0 the equation is linear, not quadratic. A sign slip on the −b term shifts both roots by the same amount, so substitute your roots back to check.
Assumptions and limitations
- 2^0 = 1
- Negative exponents give fractions
If a required value is empty, not a number, or outside its allowed range, the form marks that field with a message and shows no result instead of a misleading number. The automated checks deliberately try invalid entries for exponent n to confirm this.
Frequently asked questions
What is 2^16?
2¹⁶ = 65,536, the number of values a 16-bit unsigned integer can hold.
What is 2^8?
256, the number of byte values.
What is 2^−1?
2⁻¹ = 1 ÷ 2 = 0.5.
How many values can 8 bits hold?
2⁸ = 256 values, from 0 to 255 when unsigned.
What is 2 to the power of −1?
It is 1/2 = 0.5.
What does the Power of 2 Calculator calculate?
Compute 2 raised to an integer power exactly. It returns 2^10.
What formula does the Power of 2 Calculator use?
result = 2ⁿ. BigInt exponentiation for n ≥ 0; reciprocal for negative n.
What do I need to enter in the power of 2 Calculator?
You enter Exponent n.
How is the result rounded or limited?
IEEE-754 double precision; shown to at most 6 decimal places. 2^0 = 1.
What are the limits of this calculator?
2^0 = 1. Negative exponents give fractions.
What is an example of a power of 2 result?
With exponent n 10, the 2^10 is 1,024.
Related calculators
- Power Converter — Convert watts, kilowatts, horsepower and BTU per hour.
- Power Calculator — Mechanical power from work and time, or force and velocity.
- Power Factor Calculator — Power factor, phase angle and reactive power from real and apparent power.
- Slope Calculator — Slope, angle, distance and line equation through two points.
- LCM Calculator — Least common multiple of two or more numbers.
- Factor Calculator — List every factor of a positive whole number.
Sources
- OpenStax, Algebra and Trigonometry 2e (Rice University): exponents, radicals, logarithms and inverse trigonometric functions
Content last reviewed 2026-11-04. Formulas and worked examples are checked by automated tests against independently computed values.