Scientific Notation Calculator
Convert numbers among decimal, scientific, E and engineering notation, or calculate with two scientific-notation values.
Scientific notation formulas
A nonzero number in normalized scientific notation has the form a × 10n, where 1 ≤ |a| < 10 and n is an integer. Moving the decimal point left increases n; moving it right decreases n.
Engineering notation uses an exponent divisible by 3, so the coefficient lies from 1 up to but not including 1,000. E notation writes the same value as aEn, such as 1.23e4.
For multiplication, multiply coefficients and add exponents. For division, divide coefficients and subtract exponents. Addition and subtraction first require equivalent powers of ten.
Checked examples
| Input or operation | Scientific notation | Decimal result |
|---|---|---|
| 12,345 | 1.2345 × 10⁴ | 12345 |
| 0.0012 | 1.2 × 10⁻³ | 0.0012 |
| −4,500,000 | −4.5 × 10⁶ | −4500000 |
| 1.23e4 | 1.23 × 10⁴ | 12300 |
| 1.2e3 + 3.4e2 | 1.54 × 10³ | 1540 |
| 1e3 − 1e−3 | 9.99999 × 10² | 999.999 |
| 1.2e3 × 3e−2 | 3.6 × 10¹ | 36 |
| 1 ÷ 3 | 3.3333333333333333333 × 10⁻¹ | Rounded to 20 significant digits |
How to use the calculator
- Select conversion or arithmetic.
- Enter a decimal, E-notation value, or a value such as 1.23 × 10^4.
- For arithmetic, choose the operation and enter the second number.
- Select Calculate notation to compare all four formats.
Limits and precision
- Each input supports up to 100 significant digits and an exponent from −1000 to 1000.
- Do not use commas as thousands separators; enter 12345 rather than 12,345.
- Conversions, addition, subtraction and multiplication use exact decimal integer arithmetic.
- Division is rounded to 20 significant digits when it does not terminate within the calculated precision.
- Zero is reported as 0 × 10⁰ by convention.
- Very large decimal outputs may contain hundreds of zeros; scientific notation remains the compact representation.
Frequently asked questions
Are scientific notation and E notation equivalent?
Yes. For example, 3.2 × 10⁵ and 3.2e5 represent the same value.
What is the difference between scientific and engineering notation?
Scientific notation uses any integer exponent and a coefficient below 10. Engineering notation uses an exponent divisible by 3 and a coefficient below 1,000.
Why must powers of ten match before addition?
The coefficients refer to different place values until their exponents are aligned. After alignment, the coefficients can be added or subtracted.
Does the calculator use floating-point arithmetic?
Conversions and the three exact operations use decimal strings and integers. Only nonterminating division requires rounding, which is shown explicitly.
Related calculators
Use the Percentage Calculator for percentage operations, the Fraction Calculator for exact rational arithmetic, the Quadratic Formula Calculator for equation roots, the Square Root Calculator to simplify radicals, or the GCF and LCM Calculator for integer factors and multiples.