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Scientific Notation Calculator — Convert & Calculate

Convert numbers to and from scientific notation. Add, subtract, multiply and divide numbers in scientific notation instantly.

What is this calculator?

This scientific notation calculator converts any real number into scientific notation (a × 10^b) and engineering notation (a × 10^b where b is a multiple of 3). It also performs arithmetic on numbers in scientific notation, though the current version focuses on conversion.

Formula

Scientific notation expresses a number as a coefficient (a) times a power of 10 (10^b), where 1 ≤ |a| < 10 and b is an integer. Engineering notation restricts b to multiples of 3. The calculator uses the standard algorithm: move the decimal point to obtain a coefficient between 1 and 10, count the moves as the exponent (positive for left, negative for right).

Example

For input value 123400, the calculator outputs coefficient 1.234, exponent 5, scientific notation 1.234 × 10^5, and engineering notation 123.4 × 10^3. For 0.000567, it outputs coefficient 5.67, exponent -4, scientific notation 5.67 × 10^-4, and engineering notation 567 × 10^-6.

How to use

  1. 1Enter any real number in the 'value' field. This can be a decimal, integer, or number in scientific notation (e.g., 2.5e3). The number must be between -1×10^300 and 1×10^300.
  2. 2Click the 'Calculate' button. The calculator processes the input by identifying the decimal point and moving it to create a coefficient between 1 and 10 (or between 1 and 1000 for engineering notation). The number of places moved becomes the exponent.
  3. 3The results show four outputs: Coefficient (the mantissa), Exponent (power of 10), Scientific Notation (standard form), and Engineering Notation (exponent multiple of 3). Use the scientific notation for general purposes; use engineering notation when working with SI prefixes (e.g., kilo, mega, micro).

Frequently Asked Questions

How do you convert a number like 0.00045 to scientific notation?
Move the decimal point to the right until you get a number between 1 and 10. For 0.00045, move the decimal 4 places to the right to get 4.5. The exponent is -4 because you moved right. So scientific notation is 4.5 × 10^-4.
What is the difference between scientific notation and engineering notation?
Scientific notation requires the coefficient to be between 1 and 10 (absolute value). Engineering notation requires the exponent to be a multiple of 3, so the coefficient is between 1 and 1000. For example, 1234 becomes 1.234×10^3 in scientific and 1.234×10^3 in engineering (since exponent 3 is a multiple of 3), but 0.01234 becomes 1.234×10^-2 in scientific and 12.34×10^-3 in engineering.
Can this calculator handle very large or very small numbers?
Yes, it accepts numbers up to ±1×10^300 and as small as ±1×10^-300. This covers most scientific and engineering applications, including Avogadro's number (6.022×10^23) and Planck's constant (6.626×10^-34).
What does the 'Coefficient' output mean?
The coefficient is the significant digits of the number, also called the mantissa. In scientific notation, it is always between 1 and 10 (or -10 and -1 for negative numbers). For example, for 0.00045, the coefficient is 4.5. It represents the precision of the number.
Is there an official standard for scientific notation?
Yes, scientific notation follows the IEEE standard for floating-point arithmetic (IEEE 754) and is widely used in ISO 80000-1 for quantities and units. The notation a × 10^b is universally accepted in science and engineering.
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