How the Scientific Calculator Works
A scientific calculator does more than add and subtract. It handles brackets, powers, roots, logarithms, factorials and the trigonometric functions sin, cos and tan. This one works like the calculator you may know from school: you type a whole expression, press =, and it works out the answer using the normal order of operations.
How to use it
- Press the keys to build an expression, such as
2+3*4orsin(30). The expression shows on the screen. - Press = to see the result. To keep going from the answer, press an operator such as + or x right away.
- AC clears everything, and the back key removes the last character.
- The DEG / RAD switch decides if sin, cos and tan use degrees or radians.
The keys
| Key | What it does |
|---|---|
| sin, cos, tan | Trigonometric functions |
| ln | Natural logarithm (base e) |
| log | Logarithm base 10 |
| x^y | Power: x to the power of y |
| √ | Square root |
| x! | Factorial |
| π and e | The constants 3.14159... and 2.71828... |
| ( and ) | Brackets |
Order of operations
The calculator follows the same rules as maths class, from the strongest to the weakest:
| Order | Operation |
|---|---|
| 1 | Brackets and functions: sin( ), sqrt( ) |
| 2 | Factorials (!) |
| 3 | Powers (^), worked from right to left |
| 4 | Minus sign in front of a number |
| 5 | Multiply and divide |
| 6 | Add and subtract |
A number next to a bracket or a constant is multiplied, so 2π means 2 x π, and 3(4) means 3 x 4.
Worked examples
| You type | Result |
|---|---|
| 2+3*4 | 14 (multiplying comes first) |
| (2+3)*4 | 20 |
| -2^2 | -4 |
| 2^3^2 | 512 (that is 2^9) |
| 5! | 120 |
| sqrt(144) | 12 |
| log(1000) | 3 |
| ln(e) | 1 |
| sin(30) in DEG mode | 0.5 |
| 2π | 6.28318531 |
Degrees or radians
Angles can be measured in degrees (a full turn is 360) or in radians (a full turn is 2π). In DEG mode, sin(30) is 0.5. In RAD mode, sin(30) means 30 radians, which is about -0.988. If an answer looks wrong, check this switch first. 180 degrees is π radians.
Chart: sine and cosine
The blue bar is sin and the green bar is cos for the same angle (in DEG mode). When one gets longer, the other gets shorter:
0 deg sin ▏ 0 cos ████████████████████████████████████████ 1 30 deg sin ████████████████████ 0.5 cos ███████████████████████████████████ 0.866 45 deg sin ████████████████████████████ 0.707 cos ████████████████████████████ 0.707 60 deg sin ███████████████████████████████████ 0.866 cos ████████████████████ 0.5 90 deg sin ████████████████████████████████████████ 1 cos ▏ 0
Tips
- Close your brackets. A missing bracket at the very end is closed for you, but a stray closing bracket shows Error.
- tan(90) in DEG mode shows Error, because it is undefined.
- Factorials work for whole numbers 0 and up. 3.5! or (-2)! shows Error. Very large factorials show Infinity.
- log is base 10 and ln is base e. The log of 0 or of a negative number is not a real number.
- Tiny values such as 1e-16 (from rounding) are shown as 0, so sin(180) gives 0.
This tool gives an estimate for general information only. Results are rounded to 8 decimal places. For exams, check that your calculator is allowed.