Scientific notation calculator

Type a number in any form. An ordinary number like 0.000345 or 602,214,076,000,000,000,000,000 is turned into scientific notation, and one already in it, like 3.45 × 10^-4, 3.45e-4 or 3.45x10⁻⁴, is written out in full. Every form is shown together: scientific, E notation, engineering notation and the full number, each with its own copy button.

To work a sum, put + − × or ÷ between two numbers, as in (3 × 10^4) × (2 × 10^-2) or 6e8 / 3e2. The working shows each step the way it's taught. The arithmetic is exact, so 0.1 + 0.2 comes out as 0.3, and only a division that never ends is rounded, at 15 significant figures. Pick a number of significant figures to round the answer.

A number in scientific notation has two parts: a number from 1 up to (but not including) 10, and a power of ten that says how far to move the decimal point. 3.45 × 10⁴ means move the point 4 places right, giving 34,500. 3.45 × 10⁻⁴ means move it 4 places left, giving 0.000345. A positive power makes a big number and a negative one a small number; 10⁰ is 1, so the number is left as it is.

To convert, move the decimal point until exactly one non-zero digit sits in front of it, and count the places. Moving left gives a positive power and moving right a negative one. Leading zeros disappear, so the notation shows only the digits that matter. That's why scientists use it: the mass of an electron is 9.109 × 10⁻³¹ kg, which in full has 30 zeros after the point before the 9.

To multiply, multiply the front numbers and add the powers. (3 × 10⁴) × (2 × 10⁻²) is 6 × 10². To divide, divide the front numbers and subtract the powers. If the front number ends up 10 or more, or less than 1, move its point one place and change the power by 1 to put it right, so 30 × 10² becomes 3 × 10³.

Adding and subtracting need the same power first. Rewrite the smaller number with the larger power, so 2 × 10³ becomes 0.2 × 10⁴, then add the front numbers, so 3 × 10⁴ + 0.2 × 10⁴ = 3.2 × 10⁴. The power stays as it is.

Calculators and spreadsheets write 3.45 × 10⁻⁴ as 3.45E-4, where the E stands for times ten to the power of. Programming languages read the same form, in lower or upper case. Engineering notation keeps the power to a multiple of 3, as in 345 × 10⁻⁶, so it lines up with the metric prefixes: 10³ is kilo, 10⁻³ milli and 10⁻⁶ micro, so 345 × 10⁻⁶ amps is 345 microamps.

In British schools, scientific notation is called standard form, or standard index form. In American schools, standard form means the ordinary written-out number, 34,500, which this page shows as the number in full.