Exponent Calculator
Raise any number to any power — including negative and fractional exponents like 27^(1/3) = 3 — with the exponent rules shown. Free, runs in your browser.
Exponent and Power Calculator
How to Use the Exponent Calculator
Enter the base
Type the number you want to raise to a power — the base. It can be a whole number, a decimal, or negative.
Enter the exponent
Type the power. It can be positive, negative (for reciprocals), or fractional (for roots) — for example 1/3 as 0.3333 or simply enter the decimal.
Read the result
The answer appears instantly, to twelve significant figures, with the value shown in the familiar base-and-superscript notation.
Understand the rule
A short note explains which exponent rule applies — repeated multiplication, reciprocal, or root — so you learn the why, not just the answer.
Exponents, From Whole to Fractional
One Idea, Stretched
An exponent starts as the simplest shorthand in mathematics: 2³ just means 2 × 2 × 2 = 8, "multiply the base by itself this many times". But the real beauty of exponents is how that one idea stretches consistently to cases where "multiply yourself three times" stops making literal sense. What is 2⁰? The rules force it to be 1, because dividing 2³ by 2 each time — 8, 4, 2, 1 — lands you there. What is a negative exponent? 2⁻¹ continues the same halving pattern past 1 to give ½, so a negative exponent means "reciprocal": x⁻ⁿ = 1 ÷ xⁿ. And what is a fractional exponent? 27^(1/3) is the cube root of 27, which is 3, because raising it to the third power must give back 27. This calculator handles all of these — whole, zero, negative, and fractional exponents — and tells you which rule is doing the work, so the consistency behind the notation becomes visible rather than mysterious.
That consistency is not a curiosity; it is what makes exponents one of the most powerful tools in science and finance. Compound interest, population growth, radioactive decay, sound and earthquake scales, computer storage sizes — all are described by exponents, because all involve a quantity multiplying by a fixed factor over and over. The same notation that says "2 cubed" also says "grows by 5% for 30 years" or "halves every 8 days". Fractional exponents, in particular, are the bridge between powers and roots: writing a square root as x^(1/2) or a cube root as x^(1/3) lets you manipulate roots with the same simple algebra you use for whole-number powers, which is why scientific and engineering calculators treat them as one operation. This tool, and the sin/cos/log functions across the site, all sit on the same exponent engine underneath.
"A negative exponent is a reciprocal; a fractional exponent is a root. Exponents are one idea stretched to stay consistent — and that consistency is their power."
A Note on Negatives
There is one case where the real numbers genuinely run out: a negative base raised to a fractional power. Asking for (-8)^(1/2) — the square root of −8 — has no real answer, because no real number squared gives a negative, and this calculator says so clearly rather than returning a confusing value. (The answer does exist in the complex numbers, which the site's Complex Number Calculator handles.) For odd roots it is different: (-27)^(1/3) is a perfectly good −3, because a negative times a negative times a negative is negative. These edge cases are exactly where casual calculators trip up, and where understanding the rule matters. Whether you are doing homework on indices, working with scientific notation, or just settling what 2¹⁰ is, this calculator gives the exact answer and the reason behind it, instantly and privately in your browser.
10 Facts About Exponents
A whole-number exponent means repeated multiplication: 2³ = 2×2×2.
Any non-zero number to the power 0 is 1.
A negative exponent is a reciprocal: 2⁻¹ = ½.
A fractional exponent is a root: 27^(1/3) is the cube root of 27 = 3.
To multiply powers of the same base, add the exponents.
A negative base with a fractional power has no real value (it is complex).
But odd roots of negatives are fine: (−27)^(1/3) = −3.
Compound interest, decay, and growth are all described by exponents.
The word "exponent" was coined by Michael Stifel in 1544.
Exponents underpin sin, cos, and log on every scientific calculator.
Frequently Asked Questions
- A negative exponent means the reciprocal: x⁻ⁿ equals 1 ÷ xⁿ. So 2⁻¹ is ½, and 2⁻³ is 1/8. The calculator computes this directly and explains the reciprocal rule in the working below the answer.
- A fractional exponent is a root. x^(1/2) is the square root of x, x^(1/3) is the cube root, and so on. For example 27^(1/3) = 3 because 3 × 3 × 3 = 27. Enter the fraction as a decimal (1/3 ≈ 0.3333) or use the Nth Root calculator for exact root notation.
- Because of the pattern of dividing by the base each time the exponent drops by one: 2³ = 8, 2² = 4, 2¹ = 2, 2⁰ = 1. Keeping that consistent rule forces the value 1 for any non-zero base. The calculator notes this when you enter an exponent of 0.
- Because the square root of a negative number has no real value — no real number squared is negative. The calculator says so rather than returning a misleading result. The answer does exist as a complex number, which the Complex Number Calculator can show. Odd roots of negatives, like (−27)^(1/3) = −3, are fine and do compute.
- Yes — both the base and the exponent can be decimals. This is exactly what you need for growth and decay calculations, like 1.05^30 for thirty years of 5% growth, or roots written as decimal powers.
- Results are shown to twelve significant figures using the shared, tested math engine. For whole-number powers the answer is exact; for fractional powers it follows standard high-precision floating-point behaviour, the same as a scientific calculator.
- When multiplying powers of the same base, you add the exponents: xᵃ × xᵇ = xᵃ⁺ᵇ. When dividing, you subtract them. These index laws are why fractional and negative exponents behave so consistently, and they are the foundation for logarithms.
- Yes. The calculation runs in your browser — nothing is uploaded, stored, or logged — and it works offline once loaded.
- Completely free, with no account, sign-up, or limit. It runs entirely in your browser and collects no data. Use it as often as you like.
- They are two views of the same maths. This tool raises a base to a power; the Nth Root calculator takes roots and writes them in radical notation (√, ∛). A fractional exponent here, like ^(1/3), is exactly a cube root there. Use whichever notation matches your problem.
Related News
You may be interested in these recent stories from our newsroom.
No related news yet for this tool. Our editorial team publishes new pieces every week.
Browse all news →75 more free tools
Calculators, converters, security tools — no signup.