Exponential Form Calculator — Scientific Notation Converter
Convert any non-zero number to scientific notation (m × 10^e) instantly. Enter the number and see the mantissa, exponent, log₁₀, natural log, and a step-by-step breakdown of the conversion. Optionally express the number in any alternate base.
Find the order of magnitude: floor of log₁₀(|N|)
Compute the mantissa: N ÷ 10^exponent (result must satisfy 1 ≤ |m| < 10)
Write in scientific notation
How does this calculator work?
Scientific notation: N = m × 10^e where e = ⌊log₁₀|N|⌋ and m = N/10^e. Enter any non-zero number to get the mantissa (1 ≤ |m| < 10), the integer exponent (order of magnitude), log₁₀, and ln — plus a step-by-step conversion walkthrough.
Formula
How this is calculated
Scientific notation (also called standard form or exponential form) expresses any number as a product of a mantissa m (with 1 ≤ |m| < 10) and a power of ten: N = m × 10^e. To find the exponent, take the base-10 logarithm of |N| and round down to the nearest integer (floor). To find the mantissa, divide N by 10^e — the result always falls in [1, 10) for positive numbers. For negative N, the mantissa carries the sign.
The exponent e tells you the order of magnitude: the rough power of ten closest to the number. This is why scientific notation is invaluable in science and engineering — it makes very large numbers (atomic distances, astronomical lengths) and very small numbers (electron mass, wavelengths) compact and comparable at a glance without trailing or leading zeros.
The alternate-base form expresses |N| as b^x, where x = log_b(|N|) = ln(|N|) / ln(b). This is useful when working in binary (base 2), natural base e, or any domain-specific base. Note that non-integer exponents in arbitrary bases are exact as real numbers but may be irrational — the displayed value is rounded to 6 significant figures.
Frequently asked questions
Scientific notation writes a number as m × 10^e, where the mantissa m satisfies 1 ≤ |m| < 10 and e is an integer. For example, 6,370,000 m (Earth's radius) = 6.37 × 10^6 m. It makes very large and very small numbers easy to read and compare.
Multiply the mantissa by 10^e. If e is positive, shift the decimal point e places to the right; if e is negative, shift it |e| places to the left. For example, 3.2 × 10^−4 = 0.00032.
Engineering notation restricts the exponent to multiples of 3 (so prefixes like kilo = 10³, mega = 10⁶, milli = 10⁻³ align naturally), meaning the mantissa can range from 1 to 999. Scientific notation always forces |m| < 10. This calculator uses scientific notation.
TG we-Calculate Editorial Team. (2026). Exponential Form Calculator — Scientific Notation Converter [Online calculator]. TG we-Calculate. https://we-calculate.com/calculator/exponential-form-calculator
TG we-Calculate Editorial Team. "Exponential Form Calculator — Scientific Notation Converter." TG we-Calculate. 2026. https://we-calculate.com/calculator/exponential-form-calculator.
TG we-Calculate Editorial Team, "Exponential Form Calculator — Scientific Notation Converter," TG we-Calculate, 2026. [Online]. Available: https://we-calculate.com/calculator/exponential-form-calculator
@misc{wecalculate_exponential_form_calculator, title = {Exponential Form Calculator — Scientific Notation Converter}, author = {{TG we-Calculate Editorial Team}}, howpublished = {\url{https://we-calculate.com/calculator/exponential-form-calculator}}, year = {2026}, note = {TG we-Calculate} }
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