Scientific Notation Calculator

This scientific notation calculator handles both jobs most people actually need: converting a decimal number to scientific notation (or standard form) and doing arithmetic on two numbers already written in scientific or e notation. The converter accepts any real number, positive or negative, and returns the standard form, engineering notation, coefficient, exponent, and the expanded decimal. The arithmetic panel adds, subtracts, multiplies, and divides two numbers and reports the answer in both scientific and decimal form.

1. Converter mode. Type a number in the top box. You can paste a long decimal like 0.0000543, a big integer like 602200000000000000000000, or a value already in e notation like 5.43e-5 or 6.022e23. The calculator detects the format and normalizes it to a × 10ⁿ with a coefficient between 1 and 10.
2. Arithmetic mode. Enter Number A and Number B in either decimal or e notation, pick an operation (+, −, ×, ÷), and read the result. For a multiplication like 6.022 × 10²³ multiplied by 1.38 × 10⁻²³, type 6.022e23 in A, 1.38e-23 in B, and select ×.
3. Read both forms. The result block shows scientific notation and the full decimal side by side. If the answer overflows standard decimal range (roughly above 10¹⁵ or below 10⁻¹⁰), only the scientific form is reliable. The mantissa is trimmed to six digits so the result stays readable.

Use this standard form calculator to check homework, convert between e notation and written form, or run quick engineering math where the exponents would otherwise be painful to track by hand. Every calculation runs locally in your browser, so nothing is sent to a server and you can change values as fast as you can type.

Scientific notation (also called standard form in the UK and most of the Commonwealth) is a compact way to write any real number as a coefficient times a power of ten. Every rule below follows from that single definition.

Standard Form: a × 10ⁿ

The general form is a × 10ⁿ where 1 ≤ |a| < 10 and n is an integer. The number a is called the mantissa or coefficient. The exponent n counts how many places the decimal point moves when you expand the number back to standard decimal form.

Worked example: 93,000,000 (distance from Earth to the Sun in miles)

Move the decimal left until one non-zero digit remains to its left:
  93,000,000.  →  9.3000000
  Places moved: 7 to the left  →  exponent = +7

Result: 93,000,000 = 9.3 × 10⁷

Negative Exponents for Small Numbers

When the number is smaller than 1, the decimal has to move right to get a coefficient between 1 and 10. Each place it moves right makes the exponent one unit more negative.

Worked example: 0.00042

Move the decimal right until the first non-zero digit is to its left:
  0.00042  →  4.2
  Places moved: 4 to the right  →  exponent = −4

Result: 0.00042 = 4.2 × 10⁻⁴

Negative signs on the whole number are kept on the coefficient, not the power of ten. So −0.00042 becomes −4.2 × 10⁻⁴, not 4.2 × 10⁻⁴ with a minus on the exponent.

Arithmetic Rules in Scientific Notation

Multiplication. Multiply the coefficients and add the exponents.

(a × 10ᵐ) × (b × 10ⁿ) = (a × b) × 10⁽ᵐ⁺ⁿ⁾

Worked example: (3.2 × 10⁵) × (2.5 × 10³)
  Coefficients: 3.2 × 2.5 = 8.0
  Exponents:    5 + 3     = 8
  Result:       8.0 × 10⁸

Division. Divide the coefficients and subtract the exponents.

(a × 10ᵐ) ÷ (b × 10ⁿ) = (a ÷ b) × 10⁽ᵐ⁻ⁿ⁾

Worked example: (7.2 × 10⁸) ÷ (2.4 × 10³)
  Coefficients: 7.2 ÷ 2.4 = 3.0
  Exponents:    8 − 3     = 5
  Result:       3.0 × 10⁵

Addition and subtraction. Match exponents first, then add or subtract the mantissas. You cannot add coefficients unless the powers of ten are identical.

Worked example: 2.5 × 10³ + 3.7 × 10²

Step 1: rewrite the smaller term to match the larger exponent.
  3.7 × 10² = 0.37 × 10³

Step 2: add coefficients, keep the common exponent.
  2.5 × 10³ + 0.37 × 10³ = 2.87 × 10³

Engineering Notation

Engineering notation is scientific notation with one extra constraint: the exponent must be a multiple of 3. That allows the mantissa to fall anywhere in the range 1 ≤ |a| < 1000, which lines up exactly with SI prefixes used in physics and electronics. 10³ is kilo, 10⁶ is mega, 10⁻³ is milli, 10⁻⁶ is micro, 10⁻⁹ is nano. A capacitor rated 2.2 × 10⁻⁶ F is commonly written 2.2 μF, and a supply of 1.5 × 10³ V is 1.5 kV.

Quick Reference: Decimal vs Scientific vs Engineering

Converting a number to scientific notation is not just cosmetic. It changes how errors propagate, how many significant figures are visible, and how comfortably the value fits on a page or a calculator screen. This section covers the practical reasons scientists, engineers, and programmers reach for standard form every day.

Why Scientists and Engineers Use It

The case is simple: very large and very small numbers are hard to read and easy to miscount in plain decimal form. 0.00000000000000000000000000000091 is an electron mass written out in kilograms, and nobody can verify the zero count by eye. Written as 9.109 × 10⁻³¹, the same value fits in a textbook margin and carries its precision on its sleeve. Scientific notation standardizes precision (the mantissa shows exactly how many digits were measured), avoids miscounted zeros, and makes multiplication and division trivial because exponents add and subtract instead of multiplying and dividing.

Real Examples You See in Physics, Chemistry, and Finance

The constants below show how wide a range scientific notation covers. None of these values would be readable in standard decimal.

Without standard form, a physics paper couldn't compare the electron mass (10⁻³¹) to the Earth's mass (10²⁴) without reserving half a page for zeros. In scientific notation, they differ by 55 orders of magnitude and the comparison takes one glance.

Significant Figures and Precision

The mantissa of a number in scientific notation should show only the digits you actually measured or computed with confidence. Writing the speed of light as 2.998 × 10⁸ m/s claims four significant figures. Writing it as 2.99792458 × 10⁸ m/s claims nine, and is only honest if your data actually supports that precision. Trailing zeros in plain decimal are ambiguous: 4,700 might have two, three, or four significant figures, and you cannot tell from the written form. Converted to scientific notation, that ambiguity disappears. 4.7 × 10³ is two sig figs, 4.70 × 10³ is three, and 4.700 × 10³ is four.

Calculator Display Conventions: E Notation

Most physical and software calculators cannot display the superscript 10ⁿ, so they use "E" or "e" as shorthand. 1.5E6 means 1.5 × 10⁶ = 1,500,000. The number before the E is the mantissa and the number after is the exponent. On a physical scientific calculator, press the EXP or EE key to enter the exponent (for example, 1.5 EXP 6 gives you 1.5 × 10⁶). In a spreadsheet, typing 1.5e6 or 1.5E6 is treated the same. Most calculators will round the mantissa to their display width, usually 8 to 12 digits, and silently drop anything past that. Programming languages follow the same convention: 1.5e6 in Python, JavaScript, and C compiles to the float 1500000.0.