Scientific Calculator: Powers, Logarithms, Trigonometry & More
Powers & Roots (ISO 80000-2)
Exponentiation (xⁿ) is x multiplied by itself n times for positive integers. For fractional exponents, x^(m/n) = ⁿ√(xᵐ). Key identities: (x·y)ⁿ = xⁿ·yⁿ; (xⁿ)ᵐ = xⁿᵐ; x⁰ = 1 for all x ≠ 0. Negative bases with fractional exponents produce complex numbers.
Logarithms (ISO 80000-2)
log_b(x) answers: "to what power must b be raised to get x?" Three standard bases: log₁₀ (engineering), ln (calculus/science), log₂ (computer science). Change-of-base: log_b(x) = ln(x)/ln(b). Identities: log(a·b) = log(a) + log(b); log(aⁿ) = n·log(a). Undefined for x ≤ 0.
Trigonometry (ISO 80000-2)
Six functions from the unit circle: sin(θ), cos(θ), tan(θ) = sin/cos, csc = 1/sin, sec = 1/cos, cot = cos/sin. Supports degrees, radians, and gradians. Inverse functions (asin, acos, atan) return angles. Pythagorean identity: sin²(θ) + cos²(θ) = 1.
Scientific Notation (ISO 80000-1)
Any number as coefficient × 10^exponent (1 ≤ |coefficient| < 10). Compact for extremes: 6.022 × 10²³, 1.602 × 10⁻¹⁹. Engineering notation constrains exponent to multiples of 3 to match SI prefixes. Multiply: (a × 10ᵐ)(b × 10ⁿ) = (a·b) × 10^(m+n).
Significant Figures (NIST SP 330)
Sig figs communicate measurement precision. NIST rules: (1) Non-zero digits significant. (2) Zeros between non-zero significant. (3) Leading zeros not significant. (4) Trailing zeros after decimal significant. When multiplying/dividing, round to the least sig figs.
SI Unit Conversion (NIST SP 330)
Converts: Length (m, km, cm, mm, ft, in, mi, yd), Mass (kg, g, lb, oz), Temperature (°C, °F, K), Pressure (Pa, kPa, bar, psi, atm), Energy (J, kJ, cal, kcal, Wh, kWh), Speed (m/s, km/h, mph, kn). Temperature is the only non-linear conversion. All other conversions use multiplicative factors per NIST SP 330 (2019).
FAQs
What is the difference between log₁₀, ln, and log₂?
log₁₀ (common log) is the power of 10 needed to reach x. ln (natural log) uses base e ≈ 2.71828. log₂ (binary log) uses base 2. They relate: ln(x) = log₁₀(x) × ln(10) ≈ log₁₀(x) × 2.3026.
How do I convert degrees to radians?
Multiply degrees by π/180. For example, 180° = π radians ≈ 3.14159 rad, 90° = π/2 ≈ 1.5708 rad. Our calculator accepts degrees, radians, or gradians.
What are significant figures and how do I count them?
Significant figures (sig figs) are meaningful digits. NIST rules: (1) all non-zero digits count; (2) zeros between non-zero digits count; (3) leading zeros do NOT count; (4) trailing zeros after a decimal DO count. Example: 0.00430 has 3 sig figs.
What is scientific notation and when is it used?
Scientific notation expresses numbers as coefficient × 10^exponent, where 1 ≤ |coefficient| < 10. Per ISO 80000-1, it is used for very large numbers (6.022 × 10²³) or very small numbers (1.6 × 10⁻¹⁹). Engineering notation uses exponents that are multiples of 3 to match SI prefixes.
Why is tan(90°) undefined?
tan(θ) = sin(θ)/cos(θ). At 90°, cos(90°) = 0, so tan(90°) = 1/0, which is undefined. The tangent is also undefined at 270°, 450°, and all angles where cos = 0.
How do I convert Celsius to Fahrenheit?
Use our unit conversion mode (Temperature). °F = (°C × 9/5) + 32 and °C = (°F − 32) × 5/9. Unlike other unit conversions, temperature requires an offset. Kelvin: K = °C + 273.15.
What SI prefixes should I know?
Key SI prefixes per ISO 80000: kilo (k) = 10³, mega (M) = 10⁶, giga (G) = 10⁹, tera (T) = 10¹², milli (m) = 10⁻³, micro (μ) = 10⁻⁶, nano (n) = 10⁻⁹, pico (p) = 10⁻¹². Our Reference Table shows all 20 standard SI prefixes.