Scientific Notation Calculator

How to use the converter

Convert a number. Type it the way you have it: written out (0.000000000123), with thousands separators (602,214,076,000,000,000,000,000), or already in powers of ten (6.02214076 × 10^23, 6.02214076e23, 1.5E-4). You get:

• scientific notation, a × 10ⁿ with one non-zero digit before the point;
• E notation, the same number as calculators, spreadsheets and code write it (6.02214076E+23);
• engineering notation, with the exponent a multiple of 3 and the matching SI prefix (kilo, mega, micro, nano…);
• the number written out in full, its significant figures and its order of magnitude.

If you typed a power of ten, the main answer is the number written out; otherwise it is the scientific notation. The working shows how far the decimal point moves.

Calculate with two numbers. Enter each as a mantissa and a power of 10, pick ×, ÷, + or −, and the result comes back in scientific notation with the mantissas and exponents combined step by step.

How scientific notation works

a

the mantissa (also called the coefficient or significand)

n

the exponent, a whole number: how many places the decimal point moved

To convert, put the decimal point right after the first non-zero digit and count how many places it moved. Moving it to the left makes n positive (big numbers); moving it to the right makes n negative (small numbers). To write a number out, do the reverse: move the point n places right for a positive n, left for a negative one, filling with zeros.

Engineering notation lets the mantissa run from 1 to 999 so that n is always a multiple of 3, which lines up with the SI prefixes: 4.7 × 10⁻² becomes 47 × 10⁻³, that is 47 milli-units.

Arithmetic follows the rules for powers:

To add or subtract, first rewrite one number so both have the same exponent, then add or subtract the mantissas. Finally normalize: if the mantissa is 10 or more, divide it by 10 and add 1 to the exponent; if it is below 1, multiply it by 10 and subtract 1.

Worked examples

A large number. The Avogadro constant is exactly 602,214,076,000,000,000,000,000 per mole. Placing the point after the 6 moves it 23 places to the left, so it is 6.02214076 × 10²³, 6.02214076E+23 in E notation and 602.214076 × 10²¹ in engineering notation. It has 9 significant figures.

A small number. In 0.000000000123 the point moves 10 places to the right to sit after the 1, giving 1.23 × 10⁻¹⁰, or 123 × 10⁻¹² (123 pico-units) in engineering notation.

Multiplying. (3.2 × 10⁵) × (4.5 × 10³): the mantissas give 3.2 × 4.5 = 14.4 and the exponents 5 + 3 = 8, so 14.4 × 10⁸. The mantissa is above 10, so it is normalized to 1.44 × 10⁹. Both mantissas have two significant figures, so a measured result would be reported as 1.4 × 10⁹.

Adding. (3.2 × 10⁵) + (4.5 × 10³): rewrite 4.5 × 10³ as 0.045 × 10⁵, then 3.2 + 0.045 = 3.245, so the sum is 3.245 × 10⁵.

Significant figures and trailing zeros

Scientific notation makes precision visible: 1.2 × 10³ has two significant figures, 1.200 × 10³ has four. Written out as 1200, the two cases look the same. This converter therefore treats zeros at the end of a whole number as placeholders (1200 → 1.2 × 10³) unless you type a decimal point (1200. → 1.200 × 10³) or enter it in scientific notation. Zeros after a decimal point always count: 0.001200 → 1.200 × 10⁻³.

For counting and rounding significant figures on their own, use the significant figures calculator. For powers, logarithms and other functions, use the scientific calculator, and for byte sizes written with prefixes, the data storage converter.

Limits

Numbers from 10⁻¹⁰⁰⁰ to 10¹⁰⁰⁰ and up to 400 typed characters are converted exactly, digit for digit, so very long numbers are not rounded to the 15 to 17 digits that ordinary calculator arithmetic keeps. In the arithmetic mode, results are exact except quotients that do not terminate, which are rounded to 15 significant figures. The significant-figure rounding shown for × and ÷ is a convention for measured values, not a property of exact numbers.