Exponential Notation Calculator

Background.

Numbers in science and engineering swing across enormous ranges. Avogadro's constant is 6.02214076 × 10²³ per mole, a 24-digit number if written out in full, and the speed of light, 299,792,458 metres per second, is usually quoted as 2.998 × 10⁸. Exponential notation tames them by splitting a number in two: a coefficient that holds the significant digits and a power that holds the scale. 3.2 × 10⁴ means 3.2 multiplied by ten four times, or 32,000; 3.2 × 10⁻⁴ means 3.2 divided by ten four times, or 0.00032.

This page runs the notation in reverse. Give it a coefficient, a base and an exponent and it multiplies them out into an ordinary number. The base is usually 10, but any positive base works, which makes it just as handy for powers of two in computing (5 × 2¹⁰ = 5,120) or a growth factor raised to a number of periods. The exponent can be negative, giving fractions, or fractional, giving roots: 10 to the power 0.5 is the square root of 10, about 3.1623.

What it does not do is tidy up. Scientific notation proper keeps the coefficient at 1 or more but below 10, so 32 × 10³ and 0.32 × 10⁵ are non-standard ways of writing 3.2 × 10⁴. All three expand to the same 32,000 here, but none is rewritten into standard form for you.

Two limits matter at the extremes. Results are kept to ten decimal places, so anything much smaller than 10⁻¹⁰ loses its digits, and a value such as the electron's charge, 1.602 × 10⁻¹⁹ coulombs, comes back as 0. At the other end, a result beyond about 1.8 × 10³⁰⁸, the largest number ordinary double-precision arithmetic can hold, is shown as infinity rather than a number.

What is exponential notation calculator?

Exponential notation writes a number as a coefficient multiplied by a base raised to an exponent, c × bⁿ. With base 10 and a coefficient of at least 1 but less than 10 it is called scientific notation; engineering notation instead restricts the exponent to multiples of three, so values line up with prefixes such as kilo, mega and micro. Expanding the notation means carrying out the multiplication to recover the ordinary decimal value.

How to use this calculator.

1. 01Enter the coefficient, the number in front of the multiplication sign. It may be negative, and a negative coefficient gives a negative result.
2. 02Enter the base: leave it at 10 for scientific or engineering notation, use 2 for binary quantities, or any other positive number. Zero and negative bases are refused.
3. 03Enter the exponent, using a minus sign for values smaller than one, so 10⁻³ is entered as −3. A calculator display of 3.2E4 means coefficient 3.2, base 10, exponent 4.
4. 04Read the expanded value. If a tiny number comes back as 0, it fell below the ten-decimal-place limit; switch to a smaller unit, such as nanometres instead of metres, so the exponent sits closer to zero.

The formula.

value = c × bⁿ. The base b, which must be positive, is raised to the exponent n, and the result is multiplied by the coefficient c. For a whole-number exponent, bⁿ is b multiplied by itself n times, and b⁻ⁿ is 1 ÷ bⁿ. For a fractional exponent, b^(p/q) is the q-th root of b raised to the power p, which is why the base has to be positive: a negative number has no real square root. Every step of 1 in the exponent multiplies the value by the base, so with base 10 an exponent that is off by one makes the answer ten times too big or too small, the commonest slip when copying numbers between notations. The coefficient only scales the result in proportion.

A worked example.

Frequently asked questions.

References& sources.

1. [1]OpenStax, Rice University. College Algebra 2e, 2021. Algebra and function chapters. Retrieved 2026-08-06.
2. [2]OpenStax, Rice University. Precalculus 2e, 2021. Trigonometry and analytic geometry chapters. Retrieved 2026-08-06.
3. [3]NIST/SEMATECH. e-Handbook of Statistical Methods, 2012. Chapter 1.3 and Chapter 4. Retrieved 2026-08-06.