Power of 2 Calculator. Enter any exponent and the Power of 2 Calculator instantly computes 2 raised to that power. You can also check whether a given number is a power of 2. Results include the calculated value, the expanded multiplication form, and whether your number qualifies as an exact power of 2. Also try the Modulo Calculator.
An exponent of 2 refers to raising the number 2 to a given power. For example, 2 to the power of 5 (written as 2⁵) means multiplying 2 by itself 5 times: 2 × 2 × 2 × 2 × 2 = 32. The exponent tells you how many times the base (2) is used as a factor. See also our calculate Long Addition.
To calculate 2ⁿ, multiply 2 by itself n times for positive exponents. For example, 2³ = 2 × 2 × 2 = 8. For a negative exponent, take the reciprocal: 2⁻³ = 1 / 2³ = 1/8 = 0.125. For n = 0, any base raised to the zero power equals 1, so 2⁰ = 1.
2 to the power of -1 equals 0.5. A negative exponent means you take the reciprocal of the positive power, so 2⁻¹ = 1 / 2¹ = 1/2 = 0.5.
2 to the power of 8 equals 256. You multiply 2 by itself 8 times: 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 = 256. Powers of 2 up to 2¹⁰ (1024) are commonly memorized in computing and mathematics.
2 to the power of 30 equals 1,073,741,824 — just over one billion. Powers of 2 grow very rapidly; 2³⁰ is approximately 1 GB when used in the context of computer memory (1 gibibyte = 2³⁰ bytes).
2 to the power of 3 equals 8. This is often called '2 cubed' and represents 2 × 2 × 2. It's one of the most common powers of 2 used in everyday math and computer science.
A positive integer n is a power of 2 if dividing it by 2 repeatedly always yields a whole number until you reach 1. Mathematically, n is a power of 2 if n > 0 and (n & (n - 1)) === 0 using bitwise logic. For example, 64 is a power of 2 because 64 = 2⁶, but 48 is not.
Computers use binary (base-2) arithmetic, so powers of 2 appear everywhere in computing — memory sizes (RAM, storage), data structure sizing, color depths, and more. For example, 1 kilobyte = 2¹⁰ = 1024 bytes, and 1 megabyte = 2²⁰ = 1,048,576 bytes. You might also find our Double Factorial (n!!) — Double Factorial useful.