Math Runs locally Ready to use Built-in examples No tracking

Scientific Notation Calculator

Enter any number (123000, 1.23e5, 1.23 × 10⁵) to get scientific notation, engineering notation, e notation and the plain decimal form; switch to arithmetic for exact + − × ÷.

The speed of light is about three hundred million metres per second, and Avogadro's number is 6.02 × 10²³. Astronomy, chemistry and chip fabrication are full of numbers that are painful to write out, which is exactly why scientific notation was invented. This tool converts any notation into standard and engineering form, back into an ordinary number, and performs arithmetic between two large numbers.

Conventions: in standard scientific notation the mantissa lies in [1, 10) (6.02 × 10²³); in engineering notation the exponent must be a multiple of 3 (22 × 10³ rather than 2.2 × 10⁴), which lines up with the k/M/G prefixes. For arithmetic, addition and subtraction align the exponents first, while multiplication and division multiply mantissas and add exponents — this tool follows those rules and normalises the result.

—

How to use

  1. Enter a number (several notations are accepted) and read the four representations.
  2. In engineering notation, check whether the exponent is a multiple of 3 — it maps to the k/M/G prefixes.
  3. Switch to the operations tab to do arithmetic in scientific notation.
  4. Copy the result — use × 10ⁿ in papers and e-notation in code.

How it works

How to convert to scientific notation

The conversion rule is one sentence: move the decimal point so it sits after the first non-zero digit, and the number of places moved becomes the exponent — left is positive, right is negative. 123000 → 1.23 × 10⁵ (five places left); 0.00045 → 4.5 × 10⁻⁴ (four places right). For integers there is a shortcut: the exponent is the digit count minus one, so 299792458 (9 digits) gives an exponent of 8.

Engineering notation versus scientific notation

Engineering notation is numerically identical to scientific notation; the only difference is that the exponent must be a multiple of 3, leaving the mantissa between 1 and 1000, which maps directly onto thousands, millions and billions. The same value becomes 1.23 × 10⁵ in scientific notation and 123 × 10³ in engineering notation. Avogadro's number 6.022 × 10²³ has an exponent of 23, not a multiple of 3, so engineering notation writes it as 602.214 × 10²¹.

Why 0.1 + 0.2 equals 0.3 here

For addition and subtraction, align the exponents (convert to the same n) before adding the mantissas; for multiplication and division, work on the mantissas directly and add or subtract the exponents. This tool avoids binary floating point entirely — input is split into "integer × 10ⁿ" and computed in BigInt — so 0.1 + 0.2 gives exactly 0.3. Division keeps 12 significant digits with rounding and is marked "approximate" when it does not terminate.

Calculation basis: scientific notation a × 10ⁿ with 1 ≤ |a| < 10, while engineering notation requires the exponent to be a multiple of 3. Decimal arithmetic is implemented exactly with BigInt (addition, subtraction and multiplication are lossless; division keeps 12 significant digits, rounded), and the constants come from the 2019 SI definitions.

Code example

JavaScript Normalised and engineering notation 

function toSci(n) {
  if (n === 0) return "0";
  const exp = Math.floor(Math.log10(Math.abs(n)));
  const mant = n / 10 ** exp;
  return { sci: mant + "e" + exp, exp, mant };
}

function toEng(n) {                       // exponent forced to a multiple of 3
  const exp = Math.floor(Math.log10(Math.abs(n)) / 3) * 3;
  return (n / 10 ** exp) + "e" + exp;
}

toEng(22000);   // "22e3" (i.e. 22k)

Python Formatting and parsing 

f"{6.022e23:.3e}"    # "6.022e+23"

# Engineering notation (exponent a multiple of 3):
from decimal import Decimal

n = 22000
exp3 = (len(str(abs(n))) - 1) // 3 * 3
n / 10 ** exp3, exp3      # (22.0, 3) → 22k

# Parsing user input: float("1.23e5") is accepted directly

FAQ

How do I convert scientific notation back to an ordinary number?

Move the decimal point of the mantissa by the exponent: positive exponents move right, negative move left, padding with zeros when needed. 2.5 × 10³ → 2500; 2.5 × 10⁻³ → 0.0025; 6.022 × 10²³ → 6022 followed by 20 more zeros.

How are significant figures counted?

Start at the first non-zero digit and count through to the last digit. 1.23 × 10⁵ has three significant figures, and 299792458 written as 2.99792458 × 10⁸ has nine. This tool drops trailing zeros automatically (3.0e8 becomes 3 × 10⁸, one significant figure), because whether an omitted zero is significant depends on measurement precision, which the input cannot reveal.

What is the difference between engineering notation and scientific notation?

Only the exponent rule: engineering notation requires an exponent that is a multiple of 3 and a mantissa between 1 and 1000, so the value reads directly as thousands, millions or billions. 1.23 × 10⁵ becomes 123 × 10³; 5.29177210903 × 10⁻¹¹ becomes 52.9177210903 × 10⁻¹².

Why use scientific notation at all?

Three practical reasons. It writes very large and very small values compactly (the speed of light, 299792458 m/s, becomes 2.99792458 × 10⁸). Multiplication and division reduce to adding and subtracting exponents, which makes estimating magnitudes fast (10⁸ × 10⁻³ = 10⁵). And significant figures can be counted at a glance, so you do not miscount the zeros in something like 0.000000001.

Why does 0.1 + 0.2 not equal 0.3?

Because computers store decimals in binary, and both 0.1 and 0.2 can only be approximated; double-precision addition yields 0.30000000000000004. This tool avoids binary floating point, splitting input into "integer × 10ⁿ" and computing in BigInt, so the result is exactly 0.3 — and 1.1 × 1.1 is exactly 1.21.

Why is a division result marked "approximate"?

1 ÷ 3 = 0.333… is a repeating decimal that cannot be written in finite digits. This tool keeps 12 significant digits with rounding, so it marks the result "approximate"; results that terminate (1 ÷ 8 = 0.125, 10 ÷ 4 = 2.5, 1 ÷ 1000000 = 1 × 10⁻⁶) are marked "exact".

What is the largest exponent I can enter?

A single input is limited to exponents within ±5000, while the exponent of a result may exceed that (1e2000 × 1e2000 = 1 × 10⁴⁰⁰⁰). Beyond ±5000 it reports that the exponent is out of range — a safeguard against constructing hundred-thousand-digit integers that freeze the page, not a mathematical limit.

Can I paste 1.23 × 10⁵ straight from a paper?

Yes. Superscript digits, multiplication signs (× or *), the ^ operator, e-notation, thousands separators and full-width minus signs are all recognised automatically: 1.23 × 10⁵, 1.23e5, 1.23×10^5 and 1.23*10^5 all give the same result.