Scientific Notation Calculator
Convert any decimal number to scientific notation, or convert scientific notation back to an ordinary decimal number.
How It's Calculated
Formula
n = a \times 10^{p}, \quad 1 \le |a| < 10Scientific notation writes a number as a coefficient between 1 and 10 (in absolute value) multiplied by a power of 10 — for example, 123000 becomes 1.23 × 10^5, and 0.00456 becomes 4.56 × 10^-3. It's a compact way to write very large or very small numbers without a long string of zeros. This calculator converts in both directions: from an ordinary decimal number to its canonical scientific notation, or from scientific notation text (like 1.23e5 or -4.5e-3) back to an ordinary decimal number. Zero is a special case with no meaningful power-of-10 form, so it's shown explicitly as 0 × 10^0. This tool does not evaluate arbitrary math expressions — only a single plain decimal number or a single strict scientific-notation value is accepted, and results are limited to the range JavaScript's native Number type can represent exactly (roughly 10^-308 to 10^308); values outside that range are rejected as overflow or underflow rather than silently truncated.
Worked Examples
Convert 123000 to scientific notation
- 123000 = 1.23 × 100000
- 100000 = 10^5
- Result: 1.23 × 10^5
Convert 4.56e-3 to decimal
- 4.56e-3 means 4.56 × 10^-3
- 10^-3 = 0.001
- 4.56 × 0.001 = 0.00456
- Result: 0.00456
Frequently Asked Questions
What is the canonical coefficient range?
For any nonzero number, the coefficient (the 'a' in a × 10^n) is always between 1 and 10, not including 10 itself: 1 <= |a| < 10. This calculator always normalizes results into that range, so 45.6 × 10^2 is reported as its canonical form, 4.56 × 10^3, instead.
How is zero represented in scientific notation?
Zero has no meaningful power-of-10 form, since any power of 10 multiplied by 0 is still 0. This calculator represents it explicitly as 0 × 10^0 rather than leaving it undefined.
Can I type a full math expression here?
No. This calculator only accepts a single plain decimal number (for Decimal → Scientific mode) or a single strict scientific-notation value like 1.23e5 (for Scientific → Decimal mode). It does not evaluate expressions such as 2 + 3 or parse multiple numbers at once.
What happens with extremely large or small numbers?
This calculator works within the finite range JavaScript's native Number type can represent exactly, roughly 10^-308 to 10^308. A value outside that range — for example 1e400 — is rejected as an overflow (or underflow, for values too small to represent as a nonzero number) rather than silently rounded to Infinity or 0.