Scientific Notation Calculator

What this calculator does

The Scientific Notation Calculator converts an ordinary number into scientific notation, E-notation, and engineering notation. It also performs arithmetic on two values written in scientific notation and reports the result in both decimal and scientific form.

Scientific notation is useful when a number is too large or too small to write comfortably in ordinary decimal form. It is common in astronomy, chemistry, physics, engineering, and computer science, where values may span many orders of magnitude.

How to use this calculator

1. Choose Convert a number or Scientific arithmetic.
2. For conversion, enter the number and the display precision.
3. For arithmetic, enter X and its exponent, choose an operation, and enter Y and its exponent when the operation needs it.
4. Click Calculate.

The default conversion is 1,568,938, which becomes 1.568938 × 10⁶. The default arithmetic example is 1.23 × 10⁷ plus 3.45 × 10², which equals 12,300,345.

Scientific notation formulas

A number in scientific notation has the form:

b × 10^n

Here, b is the significand and n is an integer exponent. In normalized scientific notation, the significand is at least 1 and less than 10. In engineering notation, the exponent is a multiple of three, so the significand may be between 1 and 1,000.

For arithmetic, the calculator converts each input to a decimal value, applies the operation, and converts the result back:

X = x × 10^a
Y = y × 10^b
X + Y, X − Y, X × Y, X ÷ Y, X^Y, √X, X²

What the results mean

The result panel shows the primary result and its equivalent forms. For conversion, the same number appears as scientific notation, E-notation, engineering notation, and an ordinary real number. For arithmetic, the panel shows X, Y, the decimal result, the scientific result, and the E-notation.

The precision setting controls the number of digits shown after the decimal point. It does not change the underlying calculation; it only controls display rounding.

Assumptions and limitations

• The calculator works with real numbers. Complex results are not supported.
• Exponents must be whole numbers between −1,000 and 1,000.
• Precision must be between 0 and 100 digits after the decimal point.
• Division by zero is rejected.
• A negative base with a non-integer exponent is rejected because the result is not real.
• Results larger than 10^5,000 are rejected to keep the page responsive.
• The calculator does not perform symbolic simplification or carry significant-figure rules.

Frequently asked questions

What is the difference between scientific and engineering notation?

Both use a significand times a power of ten. Scientific notation restricts the significand to the range 1 to 10. Engineering notation restricts the exponent to a multiple of three, so the significand can range from 1 to 1,000. Engineering notation is common in electronics and engineering because it aligns with prefixes such as kilo, mega, milli, and micro.

What is E-notation?

E-notation is a compact way to write scientific notation using the letter e. For example, 1.568938 × 10⁶ becomes 1.568938e+6. Many programming languages and calculators use this format.

Why does the result show a different number of digits than I entered?

The precision field controls display rounding. The calculator keeps more internal precision during the calculation and rounds the displayed result to the requested number of decimal places.

Can I use negative exponents?

Yes. Enter a negative exponent for values smaller than one. For example, 1.23 × 10⁻³ is 0.00123.

Reference tables

Decimal and scientific notation

Scientific and E-notation

Source

Reference: Calculator.net — Scientific Notation Calculator.