Standard Form Calculator — Scientific Notation Converter
Enter any number — however large or small — and get its standard form a × 10ⁿ (scientific notation) with the mantissa (1 ≤ |a| < 10), exponent n, and step-by-step working.
Find the exponent
Compute the mantissa
Write in standard form
- 1
Exponent n = floor(log₁₀|x|)
floor(log₁₀(|0.00045|)) = -4The exponent is the floor of the base-10 logarithm of the absolute value of the input. - 2
Mantissa a = x ÷ 10ⁿ
0.00045 ÷ 10^-4 = 4.50000000
How does this calculator work?
Standard form = a × 10ⁿ where 1 ≤ |a| < 10. Exponent n = floor(log₁₀(|x|)); mantissa a = x ÷ 10ⁿ. Example: 0.00045 → 4.5 × 10⁻⁴; 4,500,000 → 4.5 × 10⁶. Used in science to express very large or very small quantities without trailing/leading zeros.
Formula
How this is calculated
Standard form (called scientific notation in North America) expresses any non-zero number as a × 10ⁿ, where a is the mantissa — a number with exactly one non-zero digit before the decimal point, so 1 ≤ |a| < 10 — and n is an integer exponent. The exponent tells you how many places to move the decimal point to recover the original number: positive n moves it right, negative n moves it left.
To find n, take the floor of log₁₀ of the absolute value of the number. For example, log₁₀(0.00045) ≈ −3.35, so n = −4 (the floor). Then a = 0.00045 ÷ 10⁻⁴ = 4.5, giving 4.5 × 10⁻⁴. For a large number like 4,500,000, log₁₀(4.5 × 10⁶) ≈ 6.65, so n = 6 and a = 4,500,000 ÷ 10⁶ = 4.5, giving 4.5 × 10⁶.
Standard form is used throughout science and engineering to write values that span many orders of magnitude — from atomic radii (~10⁻¹⁰ m) to astronomical distances (~10²⁶ m) — without leading or trailing zeros obscuring the significant figures.
Frequently asked questions
They are the same thing. In the UK and Australian curricula the convention a × 10ⁿ (1 ≤ |a| < 10) is usually called "standard form"; in the US and Canada it is called "scientific notation". Some UK textbooks also refer to it as "standard index form".
The mantissa a must satisfy 1 ≤ |a| < 10 — it has exactly one non-zero digit to the left of the decimal point. So 4.5 is valid; 45 or 0.45 are not (they would need a different exponent to compensate). The calculator always produces a mantissa in this range.
Multiply the mantissa by the power of ten: 4.5 × 10⁻⁴ = 0.00045 (move decimal 4 places left). For positive exponents move right: 4.5 × 10⁶ = 4,500,000. The "Standard Notation Calculator" companion does this reverse conversion.
Also known as
TG we-Calculate Editorial Team. (2026). Standard Form Calculator — Scientific Notation Converter [Online calculator]. TG we-Calculate. https://we-calculate.com/calculator/standard-form-calculator
TG we-Calculate Editorial Team. "Standard Form Calculator — Scientific Notation Converter." TG we-Calculate. 2026. https://we-calculate.com/calculator/standard-form-calculator.
TG we-Calculate Editorial Team, "Standard Form Calculator — Scientific Notation Converter," TG we-Calculate, 2026. [Online]. Available: https://we-calculate.com/calculator/standard-form-calculator
@misc{wecalculate_standard_form_calculator, title = {Standard Form Calculator — Scientific Notation Converter}, author = {{TG we-Calculate Editorial Team}}, howpublished = {\url{https://we-calculate.com/calculator/standard-form-calculator}}, year = {2026}, note = {TG we-Calculate} }
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