Scientific Notation Calculator

How it works

Scientific notation writes any number as two parts multiplied together: a mantissa — a number from 1 up to (but not including) 10 — and a power of 10:

Number = mantissa × 10^exponent

For example, 6,420,000 becomes 6.42 × 10⁶, and 0.0000012 becomes 1.2 × 10⁻⁶. Both forms represent exactly the same value — scientific notation is just a shorter way to write it that also makes its size easy to compare at a glance, which is why it’s the standard way physicists, chemists, engineers and astronomers handle very large or very small quantities.

Standard number → scientific notation. Move the decimal point until exactly one non-zero digit sits in front of it — that shifted value is the mantissa. Count how many places the point moved: moving it left (for a number of 10 or more) gives a positive exponent, and moving it right (for a number smaller than 1) gives a negative exponent.

Scientific notation → standard number. Run the process in reverse: multiply the mantissa by 10 raised to the exponent, which is the same as moving the decimal point that many places — right for a positive exponent, left for a negative one — padding the gap with zeros as needed.

Toggle the conversion direction above, then enter either a standard number, or a mantissa and exponent, to see the other form worked out instantly. See Math Is Fun’s guide to scientific notation for more background on the convention this calculator follows.

Worked example

Amara is a first-year engineering student in Brisbane. Her lab report asks her to express two very different quantities in scientific notation: Australia’s population, and the width of a bacterium she measured under a microscope in that week’s biology prac.

Australia’s population is approximately 27,000,000 people. To convert it, Amara counts how many places the decimal point — sitting after the final zero — needs to move left until only one non-zero digit remains in front of it. Getting from 27000000. to 2.7000000 takes seven places, so the exponent is 7, and the digits left in front of the point, 2.7, are the mantissa:

27,000,000 = 2.7 × 10,000,000 = 2.7 × 10⁷

The bacterium she examined is about 0.0000012 metres wide (1.2 micrometres — a realistic width for many bacteria). This time the decimal point has to move right, since the number is smaller than 1. Counting from 0.0000012 to 1.2, the point moves six places, so the exponent is −6 and the mantissa is 1.2:

0.0000012 = 1.2 × 0.000001 = 1.2 × 10⁻⁶

Amara checks both answers the way her tutor showed her: multiply the mantissa back out by the power of 10 and confirm it returns the original number. 2.7 × 10,000,000 = 27,000,000 ✓, and 1.2 × 0.000001 = 0.0000012 ✓ — both conversions check out.

Quantity	Standard number	Scientific notation
Australia’s population (approx.)	27,000,000	2.7 × 10⁷
Bacterium width (approx.)	0.0000012 m	1.2 × 10⁻⁶ m

Notice the pattern: a number of 10 or more always gets a positive exponent, because the decimal point moves left to shrink it down to the mantissa; a number smaller than 1 always gets a negative exponent, because the point moves right to grow it up to the mantissa. That’s exactly what this calculator works out automatically, in either direction.