Scientific Calculator
Scientific Calculator — Guide & Functions
This free online scientific calculator supports trigonometric functions, logarithms, powers, roots, and the mathematical constants π and e. Use the on-screen keypad or type your expression directly.
Supported functions
| Function | Syntax | Example | Result |
|---|---|---|---|
| Sine | sin(x) | sin(30°) | 0.5 (in degrees) |
| Cosine | cos(x) | cos(0) | 1 |
| Tangent | tan(x) | tan(45°) | 1 |
| Square root | sqrt(x) | sqrt(16) | 4 |
| Cube root | cbrt(x) | cbrt(27) | 3 |
| Power | x^n | 2^10 | 1024 |
| Log base 10 | log(x) | log(100) | 2 |
| Natural log | ln(x) | ln(e) | 1 |
| Absolute value | abs(x) | abs(-7) | 7 |
| Pi constant | pi | 2*pi | 6.2832… |
| Euler's number | e | e^2 | 7.389… |
Common scientific formulas
Quadratic formula
x = (−b ± √(b² − 4ac)) / (2a) — enter as: sqrt(b^2 - 4*a*c)
Pythagorean theorem
c = √(a² + b²) — enter as: sqrt(a^2 + b^2)
Euler's identity
eiπ + 1 = 0 — one of the most beautiful equations in mathematics, linking e, π, i, 1, and 0.
References
- Abramowitz, M. & Stegun, I.A. (1964). Handbook of Mathematical Functions. National Bureau of Standards.
- Stewart, J. (2015). Calculus: Early Transcendentals (8th ed.). Cengage Learning.
Scientific Notation and Order of Magnitude
Scientific notation expresses numbers as a × 10ⁿ where 1 ≤ a < 10. It compresses vast ranges: the mass of a proton (1.673 × 10⁻²⁷ kg) and the mass of the Sun (1.989 × 10³⁰ kg) span 57 orders of magnitude. To multiply in scientific notation: multiply the coefficients and add the exponents. To divide: divide coefficients and subtract exponents. To add or subtract: first convert to the same exponent. Most scientific calculators display results in scientific notation when numbers exceed 10 digits or fall below 0.001, using 'E notation' (1.5E10 means 1.5 × 10¹⁰).
Common scientific constants: speed of light c = 2.998 × 10⁸ m/s; Avogadro's number Nₐ = 6.022 × 10²³ mol⁻¹; Planck's constant h = 6.626 × 10⁻³⁴ J·s; gravitational constant G = 6.674 × 10⁻¹¹ N·m²/kg².
Order of Magnitude Reference
| Power | Value | Example |
|---|---|---|
| 10⁻⁹ | 0.000000001 | 1 nanometre (nm) |
| 10⁻⁶ | 0.000001 | 1 micrometre (μm) |
| 10⁻³ | 0.001 | 1 millimetre |
| 10⁰ | 1 | One unit |
| 10³ | 1,000 | One kilometre (metres) |
| 10⁶ | 1,000,000 | One megabyte (bytes) |
| 10⁹ | 1,000,000,000 | One nanometre⁻¹ (frequency) |
| 10¹² | 1,000,000,000,000 | One terawatt (watts) |
