The short answer
A scientific calculator extends basic arithmetic with trigonometry, logarithms, exponents, roots, and constants like π and e. Expressions follow standard order of operations, and functions like sin(), log(), and sqrt() take their argument in parentheses immediately after the function name. Trigonometric results depend on whether angles are read in degrees or radians, so checking that mode first prevents a very common class of wrong answers.
Key takeaways
- log() computes base-10 logarithm; ln() computes natural logarithm (base e) — two different functions on the same keypad, not two names for the same thing.
- Trig functions (sin, cos, tan) need the correct angle mode selected before evaluating, or the result will be numerically correct for the wrong angle unit.
- Parentheses override the default order of operations and can be nested to force a specific evaluation order.
- Constants like π and e are irrational — the calculator substitutes a high-precision decimal approximation, so results involving them are technically approximations, not exact values.
Degrees vs. radians
| Mode | Full circle | sin(30) |
|---|---|---|
| Degrees | 360° | 0.5 |
| Radians | 2π | ≈ −0.988 |
The same input, sin(30), produces two completely different — but each individually correct — answers depending on the angle mode. Neither result is wrong; they're answers to two different questions.
log vs. ln
log(100) = 2, since 10² = 100
ln(100) ≈ 4.605, since e^4.605 ≈ 100
log always means base 10 on this calculator; ln always means base e. If a problem specifies a different base entirely, use the change-of-base formula to convert.
Worked example: a multi-function expression
2 + 3 × √16 − log(1000)
= 2 + 3 × 4 − 3 (√16 = 4, log(1000) = 3)
= 2 + 12 − 3 = 11
Functions like √ and log are evaluated first (innermost to outermost), then the result feeds into ordinary order of operations — multiplication before addition and subtraction, left to right.
Common mistakes to avoid
- Forgetting to switch between degree and radian mode before a trig calculation — the same input gives very different, both "valid-looking" outputs.
- Using log() when a problem actually calls for ln(), or vice versa — always check which base the problem intends.
- Missing a closing parenthesis after a function call, which either produces an error or silently evaluates something unintended.
- Treating π and e as exact values — they're irrational, so any result derived from them is a rounded approximation, not an exact number.
Related calculators
- Log Calculator — focus specifically on logarithms and antilogarithms with steps shown.
- Exponent Calculator — work with powers, including negative and fractional exponents.
- Root Calculator — compute square, cube, and nth roots with exact and decimal results.
- Basic Calculator — handle everyday arithmetic without the scientific functions.