Degrees or radians
A full turn is 360 degrees or 2π radians, so 1 radian is about 57.2958°. The DEG/RAD key switches how sin, cos and tan read their input, and how the inverse functions report their answer. The most common mistake on any scientific calculator is being in the wrong mode: sin(30) is 0.5 in degrees but −0.988 in radians. School geometry mostly uses degrees; calculus and physics formulas use radians.
| Degrees | Radians | sin | cos | tan |
|---|---|---|---|---|
| 0° | 0 | 0 | 1 | 0 |
| 30° | π/6 | 1/2 | √3/2 | √3/3 |
| 45° | π/4 | √2/2 | √2/2 | 1 |
| 60° | π/3 | √3/2 | 1/2 | √3 |
| 90° | π/2 | 1 | 0 | undefined |
| 180° | π | 0 | −1 | 0 |
Logarithms
A logarithm answers "what power gives this number?": log(1000) = 3 because 10³ = 1000, and ln(e) = 1 because e¹ = e, with e ≈ 2.71828. Logs turn multiplication into addition, which is why they were the main calculating tool for 350 years before electronic calculators, through log tables and slide rules.
They are also how money doubling times are worked out. At interest rate r, money doubles in ln(2) ÷ ln(1 + r) years: at 7%, type ln(2)/ln(1.07) to get 10.24 years. The "rule of 72" (72 ÷ 7 ≈ 10.3) is a shortcut for the same thing. The compound interest calculator does it with a chart.
Powers, roots and factorials
xʸ raises x to the power y, and powers are worked right to left: 2^3^2 = 2^9 = 512. A root is a fractional power, so the cube root of 27 is 27^(1/3) = 3. The factorial n! multiplies every whole number from 1 to n: 5! = 120, and 0! = 1 by definition. Factorials grow fast: 20! is about 2.4 quintillion, and 171! is too large for this or any standard calculator. For non-whole numbers the calculator uses the gamma function, so 0.5! = √π ÷ 2 ≈ 0.8862.
Scientific notation
Very large and very small results are shown in scientific notation: 6.02214076e23 means 6.02214076 × 10²³ (Avogadro's number). You can type numbers the same way, for example 3e8 for the speed of light in metres per second. Results are rounded to 14 significant digits.