Enter values into any two of the input fields to solve for the third.
The exponent calculator evaluates power expressions and can solve for any one of the three quantities involved — the result, the base, or the exponent. Enter any two of them and the calculator finds the third, showing the working behind the answer. Written as an, exponentiation is one of the most fundamental operations in mathematics, and this tool handles it in every direction: computing a power, finding a root, or determining an unknown exponent.
Exponents appear throughout math and science — in compound growth, scientific notation, area and volume formulas, physics, computing, and finance. Being able to move fluidly between a base, its exponent, and the resulting value is a core skill, and this calculator makes each of those calculations quick and reliable.
Exponentiation is a mathematical operation, written as an, involving two numbers: the base a and the exponent (or power) n. When n is a positive integer, exponentiation corresponds to repeated multiplication of the base — that is, an is the product of multiplying n copies of a together. For example, 25 means 2 × 2 × 2 × 2 × 2 = 32. Here 2 is the base, 5 is the exponent, and 32 is the result.
The expression an is read as "a raised to the power of n" or "a to the nth." Two special cases have their own names: a2 is called "a squared," and a3 is called "a cubed," reflecting their geometric connection to the area of a square and the volume of a cube.
Exponents follow a set of consistent rules that make working with them predictable. These identities extend the idea of repeated multiplication to zero, negative, and fractional exponents:
What makes this calculator especially useful is that it works no matter which value is missing:
Enter the base and the exponent, and the calculator computes the power. For 2 and 5, it returns 25 = 32. This is straightforward exponentiation.
Enter the exponent and the result, and the calculator finds the base by taking a root. If a5 = 32, then the base is the fifth root of 32: a = 321/5 = 2. Finding the base is equivalent to computing a root.
Enter the base and the result, and the calculator finds the exponent using logarithms. If 2n = 32, then n = log(32) ÷ log(2) = 5. Finding the exponent is equivalent to computing a logarithm.
This three-way flexibility means the single tool replaces a power calculator, a root calculator, and a logarithm calculator in one.
You can enter e in the base field to use Euler's number (approximately 2.71828) as the base. This is enormously useful because e is the natural base of exponential growth and decay, appearing throughout calculus, continuous compound interest, probability, and the sciences. The expression ex is called the natural exponential function, and its inverse is the natural logarithm (ln). Entering e as the base lets you evaluate natural exponentials directly.
Beyond simple whole-number powers, exponents extend to some cases that surprise newcomers but follow logically from the rules above:
The calculator handles all of these, giving high-precision decimal results.
Exponentiation sits at the center of a trio of related operations, and this calculator touches all three because it can solve for any part of the expression an = r. When you know the base and exponent and want the result, you are doing exponentiation. When you know the result and the exponent and want the base, you are taking a root. When you know the base and the result and want the exponent, you are taking a logarithm. They are three ways of looking at the same fundamental relationship among the three numbers.
This is why, historically, roots and logarithms were developed as the "inverse" operations of raising to a power — each undoes exponentiation from a different starting point. Recognizing this connection is often the key that makes the whole topic click: a square root is just the question "what number, squared, gives this?", and a logarithm is the question "to what power must I raise the base to get this?". The calculator answers whichever of these three questions your blank field represents.
Exponents take a high priority in the order of operations, evaluated after parentheses but before multiplication, division, addition, and subtraction (the "E" in PEMDAS). This matters because it changes the answer of expressions that mix operations. For instance, 3 × 22 means 3 × 4 = 12, not (3 × 2)2 = 36 — the exponent is applied to the 2 alone before the multiplication. Similarly, −32 conventionally means −(32) = −9, because the exponent binds tighter than the negation, whereas (−3)2 = 9. Being careful about what the exponent actually applies to is one of the most common places errors creep in, so when in doubt, use parentheses to make your intent explicit.
One of the most practical everyday uses of exponents is scientific notation, a compact way of writing very large or very small numbers using powers of ten. Instead of writing 300,000,000, scientists write 3 × 108; instead of 0.0000001, they write 1 × 10−7. The exponent on the 10 simply counts how many places the decimal point moves — positive for large numbers, negative for small ones. This notation is indispensable in physics, chemistry, astronomy, and engineering, where quantities routinely span dozens of orders of magnitude, from the mass of an electron to the distance across the observable universe. Powers of ten also underlie the metric system's prefixes: kilo is 103, mega is 106, milli is 10−3, and so on.
Exponents describe not just static numbers but processes that change over time. Exponential growth occurs whenever a quantity increases by a constant percentage each period — money earning compound interest, a population multiplying, or a rumor spreading. Because the growth compounds on an ever-larger base, the totals climb slowly at first and then explosively, which is why exponential trends so often catch people by surprise. Exponential decay is the mirror image: radioactive material losing half its mass each half-life, a hot object cooling, or a drug clearing from the bloodstream. Both are modeled with exponential expressions, frequently using e as the base, and understanding them is essential to fields from finance to epidemiology.
Exponents are written in several ways depending on context. In print and formal math they appear as a small raised number, as in an. In plain text, email, and many programming languages, the caret symbol is used instead: a^n means the same thing. Some languages, such as Python, use a double asterisk (a**n). Spreadsheets accept the caret, so typing =2^5 in a cell returns 32. Whatever the notation, the meaning is identical: the base is raised to the power of the exponent. When you see the caret in this calculator's help text, read it simply as "to the power of."
Certain exponents show up so often they have special significance. Squaring (raising to the power of 2) connects to area — the area of a square is its side length squared — and appears in the Pythagorean theorem, statistics (variance), and physics (kinetic energy). Cubing (the power of 3) connects to volume, since the volume of a cube is its edge length cubed. And powers of two are the heartbeat of computing: 210 = 1024 (a kilobyte), 220 is a megabyte, and 230 a gigabyte. The number of values a group of bits can represent is always a power of two — eight bits give 28 = 256 possibilities — which is why so many limits in technology (256 colors, 65,536 rows, and so on) are powers of two rather than round decimal numbers. Recognizing these patterns makes many technical figures instantly meaningful.
An exponent, written as the small raised number in an, tells you how many times to multiply the base a by itself. For positive integers, 25 means 2 multiplied by itself five times, equaling 32.
Use a logarithm: the exponent equals log(result) ÷ log(base). For 2n = 32, that is log(32) ÷ log(2) = 5. Enter the base and result and the calculator does this for you.
A fractional exponent represents a root. a1/n is the nth root of a, so 81/3 is the cube root of 8 (which is 2). More generally, am/n is the nth root of am.
It follows from the exponent rules: an ÷ an equals a0, and any non-zero number divided by itself is 1. So a0 = 1 for every non-zero base.
A negative exponent means the reciprocal of the positive power: a−n = 1 ÷ an. For example, 2−3 = 1/23 = 1/8 = 0.125.
e (Euler's number, about 2.71828) is the base of the natural exponential function ex, which describes continuous growth and decay. It appears throughout calculus, finance (continuous compounding), statistics, and the sciences. Enter e in the base field to use it here.
This Exponent Calculator is provided for educational and general informational purposes. Results are computed to high precision using standard mathematical functions; round them as appropriate for your application.