About this calculator
Free online scientific calculator with trigonometric functions, logarithms, exponents, and more. Perfect for students, engineers, and professionals. No.
How to use
Type a math expression into the Expression field, choose whether angles should be read in Degrees or Radians, and click Calculate. Use + - * / ^ % ! for arithmetic, exponents, modulo, and factorial; parentheses to group terms; pi and e for the built-in constants; and functions like sin(), cos(), tan(), asin(), acos(), atan(), sinh(), cosh(), tanh(), log(), ln(), log2(), sqrt(), cbrt(), exp(), and abs(). For example, sin(45) + sqrt(16) - 2^3 evaluates to -3.2929 in Degrees mode. Click Clear to reset all fields.
Scientific Notation Examples
| Number | Scientific Notation | Power of 10 |
|---|---|---|
| 0.000001 | 1×10⁻⁶ | 10⁻⁶ |
| 0.001 | 1×10⁻³ | 10⁻³ |
| 0.1 | 1×10⁻¹ | 10⁻¹ |
| 1 | 1×10⁰ | 10⁰ |
| 1,000 | 1×10³ | 10³ |
| 1,000,000 | 1×10⁶ | 10⁶ |
| 6,022,000,000,000,000,000,000,000 (Avogadro's number) | 6.022×10²³ | 10²³ |
| 299,792,458 (speed of light, m/s) | 2.998×10⁸ | 10⁸ |
| 0.000000001 (1 nanometer) | 1×10⁻⁹ | 10⁻⁹ |
Scientific Notation Rules
| Operation | Rule | Example |
|---|---|---|
| Multiply | Add exponents | (3×10²)×(2×10³) = 6×10⁵ |
| Divide | Subtract exponents | (6×10⁶)÷(2×10²) = 3×10⁴ |
| Add/Subtract | Convert to same exponent first | 3×10⁴ + 2×10³ = 3.2×10⁴ |
| Raise to power | Multiply exponent | (2×10³)² = 4×10⁶ |
Common Metric Prefixes
| Prefix | Symbol | Power of 10 | Example |
|---|---|---|---|
| pico | p | 10⁻¹² | picosecond |
| nano | n | 10⁻⁹ | nanometer |
| micro | μ | 10⁻⁶ | microgram |
| milli | m | 10⁻³ | milliliter |
| kilo | k | 10³ | kilometer |
| mega | M | 10⁶ | megabyte |
| giga | G | 10⁹ | gigawatt |
| tera | T | 10¹² | terabyte |
Frequently Asked Questions
How do I know if my answer is reasonable?
Always estimate first — round your inputs to nice numbers and calculate mentally or on scratch paper. If your calculator result is orders of magnitude different from your estimate, recheck your inputs for typos or unit errors. For most practical math, a result within 10% of your mental estimate is a good sanity check.
What's the difference between exact and approximate answers?
Exact answers are expressed in simplified form (e.g., √2, π/4, 3/7) without decimal approximation. Approximate answers round to a specified number of decimal places or significant figures. Use exact form when the problem asks for it; decimal approximations when a numerical result is needed for a real-world application.
Why does rounding matter in multi-step calculations?
Rounding intermediate results introduces small errors that compound through each calculation step — this is called rounding error or accumulated error. For best accuracy, keep full precision through all intermediate steps and only round the final answer. Most calculators do this automatically when you chain operations.
When should I use this type of calculation?
Check that your situation matches the assumptions behind the formula. Most mathematical models have specific domains of validity — ranges of input values where the model is accurate. Extrapolating beyond these ranges (e.g., applying a linear model to non-linear data) gives misleading results even when the formula is applied correctly.
How do you write a number in scientific notation?
To write a number in scientific notation, move the decimal point so that only one non-zero digit sits to its left, then multiply by 10 raised to the number of places you moved it. Moving the decimal left gives a positive exponent; moving it right gives a negative exponent. For example, 45,000 becomes 4.5 × 10⁴ (decimal moved 4 places left), and 0.0032 becomes 3.2 × 10⁻³ (decimal moved 3 places right). The coefficient (the number before ×10) must always be between 1 and 10.
How do you multiply numbers in scientific notation?
To multiply two numbers in scientific notation, multiply the coefficients together and add the exponents. For example, (3 × 10⁴) × (2 × 10³) = (3 × 2) × 10⁴⁺³ = 6 × 10⁷. If the resulting coefficient is 10 or greater, adjust it: for example, (5 × 10²) × (4 × 10³) = 20 × 10⁵ = 2 × 10⁶. Division works similarly — divide the coefficients and subtract the exponents.
What is Avogadro's number?
Avogadro's number is approximately 6.022 × 10²³ and represents the number of atoms, molecules, or particles in one mole of a substance. It is a fundamental constant in chemistry named after Italian scientist Amedeo Avogadro. Written out in full it is 602,200,000,000,000,000,000,000 — a 24-digit number that makes scientific notation indispensable in chemistry and physics calculations involving moles, atomic masses, and reaction stoichiometry.
How do you convert scientific notation to standard form?
To convert scientific notation back to standard form, move the decimal point by the number of places indicated by the exponent. A positive exponent means move the decimal to the right (making the number larger), and a negative exponent means move to the left (making the number smaller). For example, 3.7 × 10⁵ = 370,000 (move decimal 5 places right), and 2.5 × 10⁻⁴ = 0.00025 (move decimal 4 places left). Fill any empty places with zeros.