Power Calculator

What an exponent means

xⁿ means x multiplied by itself n times: 2⁵ = 2 × 2 × 2 × 2 × 2 = 32. The calculator also handles exponents that are negative, decimal or fractional.

The rules of exponents

Worked examples

• 2¹⁰ = 1,024 — why a kilobyte was historically 1,024 bytes.
• 10⁻³ = 0.001 — the prefix "milli".
• 27^(1/3) = 3, the cube root of 27.
• 1.05¹⁰ = 1.629: money growing 5% a year for 10 years is multiplied by about 1.63.

Powers and growth

Exponents describe anything that grows by a fixed percentage: savings with compound interest, inflation, population or the spread of an epidemic. A value multiplied by 2 every period grows to 2¹⁰ = 1,024 times its size after 10 periods and over a million times after 20. This "exponential growth" is why small differences in a rate matter so much over long periods.

Scientific notation

Very large or small numbers are written as a number between 1 and 10 times a power of 10: the speed of light is about 3 × 10⁸ m/s; a red blood cell is about 8 × 10⁻⁶ m wide. Multiplying such numbers means multiplying the first parts and adding the exponents.

Special cases

• A negative base with a fractional exponent (for example (−8)^0.5) has no real result; the calculator shows an error.
• 0⁰ is conventionally taken as 1 in most contexts.
• Very large results may be shown rounded; for precise work with huge numbers, use scientific software.

Formulas and content last reviewed: October 2026 · About