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Scientific Notation Calculator

Convert any number to a coefficient-and-exponent pair, and see the metric prefixes those exponents map to.

Quick answer

Result

Scientific notation--
Coefficient--
Exponent--
E notation--

Computed in your browser from the number above.

How the conversion works

Scientific notation writes a number as a coefficient between 1 and 10, multiplied by a power of 10. It's a compact way to express very large or very small numbers without a long string of zeros.

How to convert by hand: move the decimal point until exactly one non-zero digit remains on the left. The number of places you moved is the exponent, positive for large numbers and negative for small ones. Example: 123456 becomes 1.23456 x 10^5.

To go back the other direction, multiply the coefficient by 10 raised to the exponent. A negative exponent means the number is smaller than 1, such as 4.5 x 10^-4 = 0.00045.

The metric prefixes this maps to

Every common metric prefix is just scientific notation at a fixed, named exponent, the same table NIST publishes for the International System of Units:

PrefixPower of 10
giga (G)10^9
mega (M)10^6
kilo (k)10^3
milli (m)10^-3
micro (ยต)10^-6
nano (n)10^-9

Enter 123000000 above and the exponent field will read 8, one short of the "mega" mark at 10^6, since 1.23 x 10^8 isn't a round multiple of a named prefix; prefixes only land exactly on multiples of three.

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FAQs

Why does the exponent round down instead of to the nearest whole number?

Rounding down (a floor operation on the base-10 logarithm) is what keeps the coefficient between 1 and 10, which is the definition of proper scientific notation. Rounding to the nearest exponent instead would sometimes push the coefficient below 1 or up to 10, breaking that convention.

What happens if I enter 0?

The calculator returns a plain 0 rather than trying to force it into a coefficient-and-exponent form. Zero has no meaningful scientific notation, since the logarithm step that finds the exponent is undefined at zero.

Is E notation the same thing as scientific notation?

Yes, just a different way of writing it down. 1.23456e5 and 1.23456 times 10 to the 5th power mean exactly the same number; E notation exists because calculators and plain text can't easily print a raised exponent, so the letter E stands in for "times ten to the power of."

How does this relate to metric prefixes like kilo or milli?

Metric prefixes are scientific notation with a name attached to specific round exponents. Kilo always means times 10 to the 3rd, milli always means times 10 to the negative 3rd, regardless of what's being measured; the reference table above lists the common ones.