Scientific Notation Calculator

Scientific notation is a way to express very large or very small numbers compactly as a coefficient multiplied by a power of 10, written as a × 10ⁿ. It is widely used in mathematics, science, and engineering because it simplifies arithmetic with extreme values — for example, 345,000,000 becomes 3.45 × 10⁸.

Move the decimal point so that only one non-zero digit sits to the left of it. Count the number of places you moved — that count becomes the exponent of 10. Moving left gives a positive exponent; moving right gives a negative one. For example, 0.00456 becomes 4.56 × 10⁻³.

They represent the same value in different formats. Scientific notation writes the number as a × 10ⁿ (e.g. 3.456 × 10⁵), while E-notation uses the letter 'e' as shorthand for '× 10^' (e.g. 3.456e5). E-notation is commonly used in calculators, programming languages, and spreadsheets.

Engineering notation is similar to scientific notation, but the exponent is always a multiple of 3 (e.g. 10³, 10⁶, 10⁹). This aligns with common unit prefixes like kilo (10³), mega (10⁶), and giga (10⁹), making it practical in electrical engineering and physics.

Multiply the two coefficients together and add the exponents: (a × 10ⁿ) × (b × 10ᵐ) = (a × b) × 10^(n+m). If the resulting coefficient is not between 1 and 10, adjust it and modify the exponent accordingly.

To add or subtract, first convert both numbers to the same power of 10, then add or subtract the coefficients. For example, 3.5 × 10⁴ + 2.1 × 10³ = 3.5 × 10⁴ + 0.21 × 10⁴ = 3.71 × 10⁴. This calculator handles that conversion automatically.

The order of magnitude is the exponent (n) when a number is written in scientific notation (a × 10ⁿ). It gives a rough sense of scale — for example, 3.4 × 10⁵ has an order of magnitude of 5. Two numbers that differ by one order of magnitude differ by a factor of roughly 10.

Yes. This calculator accepts numbers in standard decimal form (e.g. 345600), E-notation (e.g. 3.456e5), and caret notation (e.g. 3.456x10^5 or 3.456 × 10^5). All formats are recognized and converted automatically.