Power of 2 Calculator — 2ⁿ
Raise 2 to any exponent and see the result — with handy computing context for powers like 2¹⁰ (1 KiB), 2²⁰ (1 MiB) and 2³².
1 KiB (kibibyte)
- 1
Exponent
10 - 2
2ⁿ
2 ^ 10 = 1,024
How does this calculator work?
Powers of 2 (2ⁿ) double with every unit increase in n, forming the backbone of binary computing. 2¹⁰ = 1 024 (1 KiB), 2²⁰ = ~1 M, 2³⁰ = ~1 G. Negative n gives fractions; 2⁰ = 1. Enter any real exponent for the exact result.
Formula
How this is calculated
Powers of 2 are central to computing and digital electronics because binary (base-2) numbers double with each additional bit. 2¹ = 2, 2² = 4, 2³ = 8 — each step doubles the previous value. This doubling explains why computer memory and address spaces come in sizes like 256 (2⁸), 1 024 (2¹⁰ = 1 KiB), 1 048 576 (2²⁰ = 1 MiB), and so on. The IEC prefixes kibibyte (KiB), mebibyte (MiB) and gibibyte (GiB) precisely represent these binary powers.
Negative exponents give fractions: 2⁻¹ = 0.5, 2⁻⁴ = 0.0625. Fractional exponents are also valid — 2^0.5 = √2 ≈ 1.414. The calculator evaluates 2ⁿ for any real n using 64-bit floating-point arithmetic.
Note that very large n (above about 1023) exceeds the maximum representable double-precision float and will overflow to Infinity. For exact large integers JavaScript BigInt can represent 2ⁿ up to any size, but this calculator returns the floating-point approximation.
Frequently asked questions
Computers use binary (base 2), so each additional bit doubles the number of addressable locations. Hardware address buses map cleanly to powers of 2, making 1 KiB = 2¹⁰ = 1 024 bytes a natural unit rather than an exact 1 000.
2⁰ = 1. Any nonzero number raised to 0 equals 1. In computing, a register with 0 bits holds exactly 1 state.
An n-bit number can represent 2ⁿ distinct values. An 8-bit byte holds 2⁸ = 256 values (0–255), a 16-bit integer holds 65 536 values, a 32-bit integer roughly 4.3 billion, and a 64-bit integer about 1.8 × 10¹⁹.
Also known as
TG we-Calculate Editorial Team. (2026). Power of 2 Calculator — 2ⁿ [Online calculator]. TG we-Calculate. https://we-calculate.com/calculator/power-of-2-calculator
TG we-Calculate Editorial Team. "Power of 2 Calculator — 2ⁿ." TG we-Calculate. 2026. https://we-calculate.com/calculator/power-of-2-calculator.
TG we-Calculate Editorial Team, "Power of 2 Calculator — 2ⁿ," TG we-Calculate, 2026. [Online]. Available: https://we-calculate.com/calculator/power-of-2-calculator
@misc{wecalculate_power_of_2_calculator, title = {Power of 2 Calculator — 2ⁿ}, author = {{TG we-Calculate Editorial Team}}, howpublished = {\url{https://we-calculate.com/calculator/power-of-2-calculator}}, year = {2026}, note = {TG we-Calculate} }
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