Scientific Notation Converter
Convert numbers between standard decimal form and scientific notation (a × 10ⁿ, with 1 ≤ |a| < 10). Essential in science, engineering, and any context where values span many orders of magnitude — atomic masses, astronomical distances, financial figures, computer-memory sizes.
Last updated: September 2026
Formula below · 2 sources (mathsisfun.com, Wikipedia) · Updated Sep 2026
Compare with similar
About this calculator
Scientific notation expresses any non-zero number n as a · 10^b, where a is the coefficient (also called significand or mantissa) and b is an integer exponent, with the convention 1 ≤ |a| < 10. The exponent counts how many places the decimal point would move to recover the original number: positive exponents shift right (large numbers), negative shifts left (small numbers). For example, 6,022,000,000,000,000,000,000,000 = 6.022 × 10²³ (Avogadro's number); 0.0000000000667 = 6.67 × 10⁻¹¹ (Newton's gravitational constant). This calculator converts the number you enter into normalized scientific notation, a × 10ⁿ, and also shows the plain decimal form, so it works in both directions: type a decimal to get its scientific form, or type e-notation to get the decimal. Variables: n is the number to convert; enter it as a plain decimal without commas (300000000) or in e-notation (3e8 or 3.0e8). Edge cases: zero has no scientific notation in the strict sense (the exponent is undefined) — by convention it stays as "0"; negative numbers carry the sign with the coefficient (-3.14 × 10²); for very large or very small values (|n| ≥ 10²¹ or |n| < 10⁻¹²) only the scientific form is shown, because the decimal form would be unreadably long. The exponent for n is given by ⌊log₁₀(|n|)⌋. Scientific notation is also called "standard form" in UK schools and "exponential form" in some engineering contexts; "engineering notation" is a variant restricted to exponents that are multiples of 3 (so values map cleanly onto SI prefixes: kilo, mega, giga, nano, micro).
How to use
Example 1 — Very small number to scientific notation. Enter 0.000045. Result: "4.5 × 10⁻⁵ = 0.000045". ✓ Verify: 4.5 × 10⁻⁵ = 4.5 × 0.00001 = 0.000045 — the decimal point moved five places to the right to make the coefficient 4.5, so the exponent is −5. Useful for things like wavelengths of visible light (~5 × 10⁻⁷ m) or atomic radii (~10⁻¹⁰ m). Example 2 — Large number. Enter 1234500 (no commas). Result: "1.2345 × 10⁶ = 1,234,500". ✓ Moving the decimal point six places left gives the coefficient 1.2345, so the exponent is 6. You can also go the other way: enter 6.022e23 and the calculator returns 6.022 × 10²³ together with the full decimal form.
Frequently asked questions
What is the difference between scientific notation and engineering notation?
Scientific notation requires the coefficient to satisfy 1 ≤ |a| < 10 — exactly one non-zero digit before the decimal point. Engineering notation relaxes that constraint and requires the exponent to be a multiple of 3, so the coefficient can be anywhere from 1 up to (but not including) 1000. The reason: engineering notation aligns with SI prefixes (kilo = 10³, mega = 10⁶, giga = 10⁹, nano = 10⁻⁹, micro = 10⁻⁶), making physical quantities easier to read. For example, 47,000 Hz is 4.7 × 10⁴ Hz in scientific notation but 47 × 10³ Hz = 47 kHz in engineering notation, which matches how engineers actually pronounce the value. Scientific notation is more standardised in academic writing; engineering notation dominates spec sheets and lab equipment.
How do I add or subtract numbers in scientific notation?
First align the exponents — convert one number so both have the same exponent (it does not matter which one you adjust, but adjusting the smaller exponent up is conventional). Then add or subtract the coefficients, keeping the shared exponent. Finally, re-normalise so the coefficient lies in [1, 10). Example: 3.2 × 10⁵ + 1.1 × 10⁴ = 3.2 × 10⁵ + 0.11 × 10⁵ = 3.31 × 10⁵. For subtraction the procedure is identical. Multiplication and division are simpler: (a × 10ᵐ)(b × 10ⁿ) = (a · b) × 10ᵐ⁺ⁿ, and the same with subtraction of exponents for division. The key trap is forgetting to renormalise — if your coefficient grows above 10 or falls below 1 you need to shift the decimal and adjust the exponent accordingly.
Why does my calculator display 4e+5 instead of 4 × 10⁵?
Most calculators, programming languages, and spreadsheet apps use "e-notation" (4e+5 or 4E5) as ASCII shorthand for 4 × 10⁵ — it avoids the typographic complexity of a superscript exponent while preserving the same meaning. The "e" stands for "exponent of 10", not Euler's number; that is a common source of confusion for students. Conversion: read "aen" as "a × 10ⁿ". Examples: 2.5e-3 = 2.5 × 10⁻³ = 0.0025; 1.5e+10 = 1.5 × 10¹⁰ = 15,000,000,000. In scientific publications the superscript form is preferred; in spreadsheets, code, and calculator displays e-notation dominates because it is plain text. This calculator accepts e-notation as input and always displays the superscript form (4 × 10⁵).
What are the most common mistakes people make with scientific notation?
The first is forgetting to normalise the coefficient to satisfy 1 ≤ |a| < 10 — writing 25 × 10⁵ instead of 2.5 × 10⁶ is wrong by the standard definition (correct under engineering notation, though). The second is mishandling the sign of the exponent for small numbers: 0.005 = 5 × 10⁻³, not 5 × 10³. The third is confusing scientific notation's "e" with Euler's number (≈ 2.71828); in 3.14e2 the "e" means "× 10", not "× e". The fourth is dropping leading zeros or significant figures when converting between forms — 0.00120 should round-trip as 1.20 × 10⁻³ (three sig figs), not 1.2 × 10⁻³ (two sig figs). The fifth is computer floating-point rounding: very small or very large products in scientific notation can lose precision (1e-300 × 1e-300 underflows to 0 in standard doubles), and you may need arbitrary-precision arithmetic for sensitive scientific calculations.
When should I not use this calculator?
Skip it for arbitrary-precision arithmetic where you need exact representation of integers with hundreds of digits — JavaScript's number type holds only ~15–17 significant decimal digits, so very long integers lose precision when converted. Do not use it for symbolic math (irrational numbers, surds, fractions of π); use a CAS like SageMath, Mathematica, or SymPy instead. It is the wrong tool for unit conversion within scientific notation — you still need to know what the units mean (1.5 × 10⁻³ km is not the same as 1.5 × 10⁻³ m). Avoid it for high-precision physical constants where significant figures matter beyond about a dozen digits; reference NIST CODATA values directly. Finally, do not use it for engineering notation outputs (multiples of 3) — this calculator returns standard scientific notation, and for engineering use you may need to manually shift the exponent by 1 or 2.