Scientific Notation Calculator
Convert numbers to/from scientific notation and perform arithmetic on them.
| Quantity | Decimal Form | Scientific Notation |
|---|---|---|
| Speed of Light | 299,792,458 | 2.99792458 × 10⁸ |
| Avogadro's Number | 602,214,076,000,000,000,000,000 | 6.02214076 × 10²³ |
| Electron Mass (kg) | 0.000000000000000000000000000000910938 | 9.10938 × 10⁻³¹ |
| Planck's Constant (J·s) | 0.000000000000000000000000000000000662607 | 6.62607 × 10⁻³⁴ |
| Earth's Mass (kg) | 5,972,000,000,000,000,000,000,000 | 5.972 × 10²⁴ |
| Proton Mass (kg) | 0.000000000000000000000000001672622 | 1.672622 × 10⁻²⁷ |
| Gravitational Constant | 0.0000000000667430 | 6.6743 × 10⁻¹¹ |
Convert any decimal number to and from scientific notation, and add, subtract, multiply, or divide two numbers that are already written in scientific notation.
How Scientific Notation Calculator Works
The Convert tab takes a decimal number and finds its exponent as n = floor(log₁₀(|number|)), then divides the number by 10ⁿ to get the coefficient a, so the result is always written as a × 10ⁿ with 1 ≤ |a| < 10. It also counts the significant figures in whatever you typed.
The Arithmetic tab expands each entered number back into its full value (coefficient × 10^exponent) before combining them. Addition and subtraction work on those expanded values directly; multiplication multiplies the two coefficients and adds the exponents; division divides the coefficients and subtracts the exponents. The raw result is then renormalized so the final answer still has a coefficient between 1 and 10.
Significant figures for an arithmetic result are reported as the smaller of the two operands' sig-fig counts — a common classroom shortcut, since the least-precise input limits how precise the answer can honestly be.
See It In Action
Who Uses Scientific Notation Calculator and Why
- Converting a very small measurement, like an atomic radius, into a compact coefficient-and-exponent form.
- Adding or comparing astronomical or scientific values, such as distances in kilometers or Avogadro's number, that are naturally expressed in scientific notation.
- Multiplying or dividing two scientific-notation values without manually expanding them to full decimal form first.
- Checking how many significant figures a scientific measurement retains after being converted or combined with another value.
Mistakes to Avoid
- Adding or subtracting the coefficients of two scientific-notation numbers directly without first matching their exponents — the calculator expands both to full values before combining them for exactly this reason.
- Forgetting that a multiplication or division result needs renormalizing so its coefficient falls back between 1 and 10, rather than assuming multiplying coefficients and adding exponents is the final answer as-is.
- Expecting an arithmetic result to keep more significant figures than the least-precise input — the calculator reports the smaller of the two operands' sig-fig counts, not the larger.
Tips for Best Results
- For a quick sanity check on any conversion, mentally expand the coefficient × 10ⁿ back to a full decimal and compare it to your original number.
- When multiplying or dividing, remember the exponents combine by addition or subtraction while the coefficients combine by ordinary multiplication or division — treating them the same way is a common source of errors.
Fixing Common Problems
My converted number's coefficient isn't between 1 and 10. — That would indicate the exponent wasn't computed correctly for that magnitude — proper scientific notation always keeps exactly one non-zero digit before the decimal point; re-enter the original decimal value and let the calculator recompute both parts together.
My arithmetic result has fewer significant figures than I expected. — This is intentional — the result keeps only as many significant figures as the less-precise of the two inputs, since a calculation can't be more precise than its least-precise operand.
Terms Explained
Coefficient: The leading number (kept between 1 and 10) in scientific notation, such as the 4.52 in 4.52 × 10⁻⁵.
Significant figures: The meaningful digits in a measured or calculated value, which limit how precisely an arithmetic result can honestly be reported.