Type a plain number or one already in e-notation. It converts both directions and gives the order of magnitude.
Scientific notation writes a number as m × 10ⁿ where the mantissa m is at least 1 and less than 10. The speed of light, 299,792,458 m/s, becomes 2.99792458 × 10⁸. Move the point left and the exponent goes up; move it right and it goes down.
Small numbers take negative exponents. 0.00045 is 4.5 × 10⁻⁴ — the exponent counts how many places the point moved, and its sign says which way.
Engineering notation restricts the exponent to multiples of three, so the mantissa can run from 1 to 999. 299,792,458 becomes 299.792458 × 10⁶ rather than 2.99792458 × 10⁸.
The point is that multiples of three line up with the SI prefixes — kilo, mega, giga, milli, micro, nano. An engineer reading 299.79 × 10⁶ Hz sees 299.79 MHz immediately. Scientific notation is tidier; engineering notation maps onto the units people actually speak.
The exponent alone is the order of magnitude, and comparing exponents is often more informative than comparing full values. Something at 10⁸ is a hundred times larger than something at 10⁶, and knowing that is usually enough to decide whether two quantities are even comparable.
It is also how calculators and programming languages display numbers too large or small to write out — 1.6e+60 is e-notation, the same idea with the "× 10" replaced by an e.
Scientific notation keeps the mantissa between 1 and 10, so the exponent can be any integer. Engineering notation restricts the exponent to multiples of three, letting the mantissa run from 1 to 999 so it lines up with SI prefixes like kilo, mega and nano.
It is shorthand for "× 10 to the power of" — 1.5e8 is 1.5 × 10⁸, or 150,000,000. It has nothing to do with Euler’s number. Calculators and programming languages use it because it is easy to type and display.
Move the decimal point right until exactly one non-zero digit sits before it, then make the exponent negative and equal to the number of places you moved. 0.00045 becomes 4.5 × 10⁻⁴.
The exponent by itself — the power of ten. Two quantities differing by one order of magnitude differ by a factor of ten. It is a fast way to check whether two numbers are even in the same league before comparing them precisely.
For arbitrary-precision arithmetic on very large integers, use the Big Number Calculator. Precision and significant figures are handled by the Rounding Calculator, and for exponent arithmetic see the Exponent Calculator and Log Calculator. Science tools that lean on the same notation: the Molecular Weight Calculator, the Molarity Calculator and the Weight on Other Planets table. Very large and very small numbers in context: Weight on Other Planets and the Density Calculator.