Scientific Notation Calculator
Convert any decimal number to scientific notation, or convert scientific notation back to an ordinary decimal number.
Calculator Inputs
For Decimal → Scientific, enter a plain number (no e). For Scientific → Decimal, enter mantissa-e-exponent form like 1.23e5 or -4.5e-3.
- Scientific Notation
- 1.23 × 10^5
- Decimal Value
- 123000
- Coefficient
- 1.23
- Exponent
- 5
About these results
CalcSpectrum calculators produce automated estimates using established formulas and the specific values you enter. Because real-world outcomes depend on input accuracy, mathematical assumptions, and rounding conventions, please verify critical figures with an appropriately qualified financial, tax, medical, legal, or other professional, as relevant.
How It's Calculated
Formula
Scientific 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.