Calculators

Scientific Notation Calculator

Convert numbers to scientific, E and engineering notation and do arithmetic in scientific notation.

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About this tool

Scientific notation writes a number as a coefficient between 1 and 10 multiplied by a power of ten, so 0.000456 becomes 4.56 × 10⁻⁴ and 602,200,000,000,000,000,000,000 becomes 6.022 × 10²³. This calculator has two parts. The converter accepts an ordinary decimal, E notation such as 6.02e23, or a typed form such as 6.02 × 10^23, and shows the number in scientific notation, E notation, engineering notation (exponents in multiples of three) and full decimal form. You can keep the digits as entered or round to between 1 and 15 significant figures. The arithmetic panel adds, subtracts, multiplies or divides two numbers written as coefficient and exponent, explains the rule used, and normalises the result. Calculations use standard double-precision numbers, so results are rounded to 12 significant figures and the range is about ±1.8 × 10³⁰⁸.

Why use it

  • Four formats at once: scientific notation, E notation, engineering notation and the full decimal.

  • Accepts the way people type it: 6.02e23, 6.02E23, 6.02 x 10^23, 6.02×10^23 and numbers with thousands separators all work.

  • Significant-figure rounding from 1 to 15 digits for lab reports and exam answers.

  • Arithmetic in scientific notation with the exponent rule explained for each operation.

  • Runs in your browser, so it works without an account or upload.

How to use

  1. Type a number in the converter, for example 0.000456, 6.02e23 or 6.02 × 10^23.
  2. Choose Auto to keep the digits you typed, or pick a number of significant figures to round to.
  3. Read the scientific, E, engineering and decimal forms in the table.
  4. To calculate, enter two coefficients and exponents and choose multiply, divide, add or subtract.
  5. Read the normalised answer and the rule that was applied.

When it helps

  • Writing very large or very small measurements, such as the speed of light or an atom's mass, in standard form.
  • Converting calculator E notation (like 1.6E-10) into the × 10ⁿ form your teacher expects.
  • Checking chemistry and physics homework that multiplies or divides values in scientific notation.
  • Expressing values in engineering notation to match SI prefixes such as kilo, mega or micro.

Examples

Small decimal

Input

0.000456

Expected result

4.56 × 10⁻⁴; E notation 4.56e-4; engineering 456 × 10⁻⁶

Rounded to 3 significant figures

Input

299792458, 3 significant figures

Expected result

3.00 × 10⁸; engineering 300 × 10⁶; decimal 300,000,000

Addition

Input

(3.2 × 10^5) + (4.1 × 10^4)

Expected result

3.61 × 10⁵ = 361,000

Tips

  • A negative exponent means a number smaller than 1; each step down moves the decimal point one place left.
  • Keep trailing zeros when they are significant: 3.00 × 10⁸ states more precision than 3 × 10⁸.
  • When adding, convert to the larger exponent first so the result needs less normalising.

Frequently Asked Questions

What is scientific notation?
A way of writing numbers as a × 10ⁿ, where the coefficient a is at least 1 and less than 10 and n is a whole number. 45,000 is 4.5 × 10⁴ and 0.0032 is 3.2 × 10⁻³.
What is the difference between scientific and engineering notation?
Engineering notation uses exponents that are multiples of three, so the coefficient can be from 1 up to 999. 45,000 is 4.5 × 10⁴ in scientific notation but 45 × 10³ in engineering notation, which lines up with the prefix kilo.
What does E notation mean?
E notation is how calculators and programming languages show powers of ten: 6.02e+23 means 6.02 × 10²³ and 4.56e-4 means 4.56 × 10⁻⁴.
How do you multiply numbers in scientific notation?
Multiply the coefficients and add the exponents, then normalise. (3 × 10⁴) × (2 × 10⁵) = 6 × 10⁹. For division, divide the coefficients and subtract the exponents.
How do you add numbers in scientific notation?
Rewrite both terms with the same power of ten, add the coefficients, then normalise. 3.2 × 10⁵ + 4.1 × 10⁴ = 3.2 × 10⁵ + 0.41 × 10⁵ = 3.61 × 10⁵.
How does significant-figure rounding work here?
Choosing, say, 3 significant figures rounds the coefficient to three digits, so 299,792,458 becomes 3.00 × 10⁸. Auto keeps the shortest form that represents the number you entered.
Why is the decimal form shown as a dash for some numbers?
Numbers with an exponent beyond ±60 would produce extremely long decimals, so only the scientific, E and engineering forms are shown for them.

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Glossary

Coefficient
The number multiplied by the power of ten, such as 6.02 in 6.02 × 10²³.
Exponent
The power of ten, which says how many places the decimal point moves.
Significant figures
The digits of a number that carry meaning about its precision.
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