This free online scientific notation calculator converts standard numbers into scientific notation and back again. Use it to quickly express very large or very small numbers as a mantissa multiplied by a power of 10, or to expand scientific notation into a standard number.
A number in scientific notation has two parts: a mantissa (also called the coefficient or significand) and a power of 10. The mantissa must be at least 1 and less than 10, ignoring any minus sign. The exponent tells you how many places the decimal point has moved.
A negative number keeps its minus sign on the mantissa: −4,500 becomes −4.5 × 10^3. The sign of the exponent is a separate matter and only says whether the size is large or small.
| Quantity | Standard form | Scientific notation |
|---|---|---|
| Speed of light in vacuum (m/s) | 299,792,458 | 2.99792458 × 10^8 |
| Avogadro constant (per mole) | 602,214,076,000,000,000,000,000 | 6.02214076 × 10^23 |
| One lakh | 1,00,000 | 1 × 10^5 |
| One crore | 1,00,00,000 | 1 × 10^7 |
| One lakh crore | 10,00,00,00,00,000 | 1 × 10^12 |
| Wavelength of green light, about 520 nm (m) | 0.00000052 | 5.2 × 10^-7 |
The Indian place-value system groups digits in twos after the first thousand, which makes very large figures such as budget totals hard to compare at a glance. Converting them to powers of ten removes that problem: ₹45 lakh crore is 4.5 × 10^13 rupees, whichever digit grouping you started with.
Phone calculators, spreadsheets and programming languages often write scientific notation with the letter E: 1.23E5 or 1.23e+5 both mean 1.23 × 10^5, and 5.2E-7 means 5.2 × 10^-7. When you type the mantissa and exponent into the "Scientific → Standard" section here, enter 1.23 and 5 rather than the E form.
Your browser itself switches back to E format for very large or very small results. Expanding 6.022 × 10^23 will display 6.022e+23, because writing out 24 digits gives no extra information. Numbers between roughly one millionth and 10^21 are shown in full.
Scientific notation makes precision explicit. Written as 123000, it is unclear whether the trailing zeros were measured or are just placeholders. Writing 1.23 × 10^5 says three figures are meaningful, while 1.230 × 10^5 claims four. This converter drops trailing zeros from the mantissa, so if your result must show a particular number of significant figures, add the zeros back when you write it down.
Engineering notation is a close relative in which the exponent is always a multiple of 3, so it lines up with prefixes such as kilo (10^3), mega (10^6) and micro (10^-6). For example, 52,000 ohms is 5.2 × 10^4 in scientific notation but 52 × 10^3, or 52 kΩ, in engineering notation.