What this calculator does
Powers of 10 are the backbone of the decimal system and scientific notation, from 10 to the power of 5 (100,000) to much larger or smaller values used in measurement and science. Because each extra exponent just adds another zero, the numbers are simple in principle but easy to miscount by hand once the exponent gets into double digits.
This power of 10 calculator takes any exponent, positive, negative or zero, such as 10 to the power of 5, 10 to the power of 10 or 10 to the power of 30, and returns 10 raised to that power directly, alongside a reference table listing 10⁰ through 10¹⁰ for the common cases that come up without retyping the exponent each time.
The formula
A positive integer exponent means repeated multiplication: 10ⁿ = 10 × 10 × …, n times, which is the same as writing a 1 followed by n zeros. A negative exponent flips that into a fraction, 10⁻ⁿ = 1/10ⁿ, and the reference table below simply evaluates the same formula for each whole-number exponent from 0 to 10.
| Term | Meaning |
|---|---|
| n | The exponent: how many times 10 is multiplied by itself, or the fraction taken if negative. |
| 10ⁿ | Ten raised to the power n, adding one zero to the result with every whole increase in n. |
| Scientific notation | A number written as a value between 1 and 10 multiplied by a power of 10, the standard way to express very large or small figures. |
The inputs explained
| Field | What to enter |
|---|---|
| Exponent (n) | The exponent to raise 10 to. Use a whole number such as 5 for "10 to the power of 5", or a negative value for a fraction. |
When to use it
Working out 10 to the power of 5, or any other exponent
A textbook or homework question asking for 10 to the power of 5, 10 to the power of 10 or 10 to the power of 30 is answered directly here, with the scientific notation and reciprocal shown alongside for context.
Reading large numbers in scientific notation
Figures written as a value times a power of 10, such as those in physics or chemistry, are easier to check against a plain number using the reference table of exponents from 0 to 10.
Understanding place value in the metric and decimal systems
Metric prefixes such as kilo (10³) and mega (10⁶) are all specific powers of 10, so the reference table doubles as a quick check on what each prefix actually multiplies by.
Worked examples
Every figure in the tables below is produced by this page’s own calculator at build time, so the numbers and the tool always agree. Select any row to load that scenario.
What is 10 to the power of 5, and other small exponents?
A range of small whole-number exponents from 3 to 10.
How large do powers of 10 get by the time n reaches 30?
A wider range of exponents from 5 up to 30, where results move into scientific notation.
Questions
What is 10 to the power of 5?
10 to the power of 5 is 100,000: a 1 followed by five zeros. Each whole increase in the exponent adds exactly one more zero to the result.
What is 10 to the power of 10?
10 to the power of 10 is 10,000,000,000, or 10 billion: a 1 followed by ten zeros.
What is 5 to the power of 10, or 3 to the power of 10?
Those use a different base, not 10, so they are not powers of 10 despite the similar phrasing. 5 to the power of 10 is 9,765,625 and 3 to the power of 10 is 59,049; the general-purpose exponents calculator handles any base and exponent.
How do I work out 10 to the power of a negative number?
A negative exponent gives a fraction: 10⁻ⁿ equals 1 divided by 10ⁿ. For example, 10 to the power of −3 is 1/1,000, or 0.001.
For any base rather than 10 specifically, see the exponents and roots calculator. For numbers converted to and from scientific notation directly, see the scientific notation calculator.