Convert any number to or from scientific notation, get coefficient, exponent, and significant figures — and perform arithmetic in standard form.
Results update live as you type.
Scientific notation
E-notation
4.5678e-4
calculator form
Coefficient
4.5678
1 ≤ |a| < 10
Exponent
−4
power of 10
Sig figs
5
digits in a
| Quantity | Scientific Notation |
|---|---|
| Speed of light | 2.998 × 10⁸ m/s |
| Avogadro's number | 6.022 × 10²³ mol⁻¹ |
| Electron mass | 9.109 × 10⁻³¹ kg |
| Planck's constant | 6.626 × 10⁻³⁴ J·s |
| Boltzmann constant | 1.381 × 10⁻²³ J/K |
| Earth's mass | 5.972 × 10²⁴ kg |
The Method
Every non-zero number can be written as a × 10n where
1 ≤ |a| < 10 is the coefficient (or mantissa) and n is
an integer exponent. To convert a decimal to scientific form, move the decimal
point until exactly one non-zero digit is to its left; the number of places moved (and
its sign) is the exponent. Moving the point left by k places means the
exponent is +k; moving it right by k places means the exponent is −k.
Arithmetic combines coefficients and exponents using the rules of exponents.
Working for n = 0.00045678
About This Tool
A scientific notation calculator converts any decimal number into the standard form a × 10n, where a is a coefficient between 1 and 10 (in magnitude) and n is an integer exponent. It also reverses the operation: enter a coefficient and exponent, and the tool returns the equivalent decimal. The third panel performs arithmetic in scientific notation — addition, subtraction, multiplication, and division — and normalises the result back to standard form.
Scientists, engineers, and students rely on scientific notation because it makes very large and very small magnitudes readable, makes significant figures explicit, and makes arithmetic on extreme magnitudes simple — multiplying 6 × 10²³ by 1.6 × 10⁻¹⁹ is far easier than multiplying 602,000,000,000,000,000,000,000 by 0.00000000000000000016. It is the lingua franca of physics, chemistry, astronomy, geology, and any field that routinely deals with numbers spanning many orders of magnitude.
This calculator uses IEEE 754 double-precision floating-point arithmetic, accurate to about 15–17 significant figures with exponents up to roughly ±308. The conversion routine extracts the exponent via floor(log10(|n|)) and the coefficient by dividing the number by 10 to that power; the inverse is straightforward multiplication. Arithmetic operations are done in plain decimal, then the result is re-expressed in scientific form. Significant-figure counts are taken from the digits of the coefficient.
This free scientific notation tool runs entirely in your browser — no sign-up, no tracking, no data sent to any server. Use it for chemistry homework, physics worksheets, astronomy assignments, or any calculation that has to span many orders of magnitude.
Standard Form
Convert any decimal to a × 10n with 1 ≤ |a| < 10.
Reverse Conversion
Enter a coefficient and exponent — get back the decimal value.
Arithmetic in Standard Form
Add, subtract, multiply or divide two values in scientific notation.
Sig Figs & E-Notation
Count significant figures and toggle the calculator-style e-notation.
100% Free & Private
No account, no tracking — every calculation runs locally in your browser.
Physical Constants
Built-in reference table of common scientific constants in standard form.
Three panels cover every common conversion and computation.
Type any positive or negative decimal into the first field. Very large or very small magnitudes are fine — the tool handles 10⁻³⁰⁰ to 10³⁰⁰.
The headline shows a × 10n; the stat tiles split it into coefficient, exponent, e-notation, and significant figures.
Use the coefficient and exponent fields to go the other way — enter a and n to get the decimal value back.
In the arithmetic row, enter two numbers in standard form and pick + − × ÷. The result is given in both decimal and scientific notation.
The digit chart shows every digit of the decimal with the leading non-zero digit highlighted — that digit is the integer part of the coefficient.
Look up common physical constants — speed of light, Avogadro's number, Planck's constant — in standard form at the bottom of the results card.
Everything you need to know about scientific notation, sig figs, and standard-form arithmetic.
Scientific notation expresses any number as a × 10n, where 1 ≤ |a| < 10 is the coefficient (or mantissa) and n is an integer exponent. For example 0.00045678 = 4.5678 × 10⁻⁴, and 1,234,000 = 1.234 × 10⁶. It compresses very large and very small numbers into a readable form and makes the magnitude (the order of 10) immediately visible.
Both put numbers in the form a × 10n, but scientific notation requires 1 ≤ |a| < 10 and any integer exponent, while engineering notation requires the exponent to be a multiple of 3 (so it aligns with SI prefixes like kilo-, mega-, giga-). For example, 47,000 is 4.7 × 10⁴ in scientific notation but 47 × 10³ in engineering notation, lining up with "47 kilo-".
E-notation is a plain-text form of scientific notation used by calculators, programming languages, and spreadsheets: 4.5678e-4 (or 4.5678E-4) means 4.5678 × 10⁻⁴. The "e" stands for "exponent of 10" — it's purely a typographical convenience, not a different mathematical notation.
To add or subtract, the exponents must match. Convert one number so it has the same exponent as the other (this temporarily moves it out of standard form), then add or subtract the coefficients, then re-normalise. Example: 1.5 × 10³ + 2.5 × 10² = 1.5 × 10³ + 0.25 × 10³ = 1.75 × 10³. This calculator does all the normalisation automatically.
Multiplication and division are easier than addition: multiply (or divide) the coefficients and add (or subtract) the exponents. (3 × 10⁴) × (2 × 10⁻²) = (3 × 2) × 10⁴⁺⁽⁻²⁾ = 6 × 10². Then re-normalise if the new coefficient falls outside 1 ≤ |a| < 10.
Significant figures are the digits that convey precision in a measurement. In scientific notation, every digit of the coefficient is significant — which is one of the major reasons scientists prefer this form. 4.5678 × 10⁻⁴ has five significant figures; 4.6 × 10⁻⁴ has only two. Trailing zeros are ambiguous in plain decimals (does 4500 have 2, 3, or 4 sig figs?) but unambiguous in scientific form: 4.500 × 10³ has four.
Three reasons. (1) Readability: 6.022 × 10²³ is easier than 602,200,000,000,000,000,000,000. (2) Explicit precision: you see exactly how many sig figs there are. (3) Easier arithmetic across magnitudes: multiplying numbers a few orders of magnitude apart becomes simple coefficient × coefficient and adding exponents, rather than counting zeros.
Yes. The rule is 1 ≤ |a| < 10 — that is, the magnitude is between 1 and 10. So −3.14 × 10⁵ is valid scientific notation for −314,000. The sign of the original number rides on the coefficient; the exponent only encodes the magnitude.
Strictly speaking, no — the constraint 1 ≤ |a| < 10 cannot be satisfied for zero. Most calculators (and this one) display 0 as 0 × 10⁰ as a convenience, but mathematically zero is just "zero" and is left in plain decimal form.
It uses IEEE 754 double-precision floating point — accurate to about 15–17 significant figures, with exponents up to roughly ±308. Numbers beyond that range will display as Infinity (or 0 in the case of extreme underflow). For arbitrary precision you would need a dedicated big-decimal library.
Two common reasons. (1) Floating-point representation: some decimals (like 0.1) cannot be stored exactly in binary, leading to a tiny round-off. (2) Normalisation: arithmetic can push the coefficient out of [1, 10), and the calculator shifts the exponent to re-normalise — this can change the number of trailing zeros shown.
Everywhere across the sciences. Astronomy uses it for stellar distances (1 light-year ≈ 9.46 × 10¹⁵ m); chemistry uses it for Avogadro's number (6.022 × 10²³); physics uses it for Planck's constant (6.626 × 10⁻³⁴ J·s); biology uses it for molecular concentrations and cell counts; and computing uses it implicitly in every float you ever print.