Scientific calculator
Trig, logs, powers and memory, typed or tapped.
- Degrees or radians
- Memory and calculation history
- Type directly or use the keypad
How to use the scientific calculator
- Type an expression or tap the keypad.
- Press 2nd for inverse trig, and pick DEG or RAD.
- Press equals, or Enter on your keyboard, for the result.
Degrees vs radians
A full circle is 360 degrees or 2 x pi radians, about 6.2832 radians. Degrees are what most people learn in school and use for compass headings and everyday angles, while radians are the default in physics, calculus and most programming math libraries.
This calculator starts in DEG mode, so sin(30) reads as 30 degrees and returns 0.5. Switch to RAD and the same input, sin(30), is read as 30 radians instead, about 4.77 full turns past zero, which comes out to about negative 0.99, nowhere near 0.5. Always check the mode before trusting a trig result.
Order of operations
Parentheses are worked out first, then powers, then unary minus signs, then multiplication and division, then addition and subtraction, the same left-to-right order taught as PEMDAS.
Powers chain right to left: 2^3^2 evaluates the top power first (3^2 = 9), then 2^9, for 512, not (2^3)^2, which would be 64.
A number placed directly against a constant, function or parenthesis is read as multiplication, so 2pi equals 6.2832 and 3sin(90) equals 3, without needing a x sign.
One expression can use several of these rules at once. Take 3 + 2 x 4^2 - sqrt(9): the power comes first (4^2 = 16), then the multiplication (2 x 16 = 32), then sqrt(9) resolves to 3, and addition and subtraction run left to right last (3 + 32 - 3), for a final answer of 32.
Trig values worth memorizing
| Angle | sin | cos | tan |
|---|---|---|---|
| 0 degrees | 0 | 1 | 0 |
| 30 degrees | 0.5 | 0.87 | 0.58 |
| 45 degrees | 0.71 | 0.71 | 1 |
| 60 degrees | 0.87 | 0.5 | 1.73 |
| 90 degrees | 1 | 0 | undefined |
Tangent has no defined value at 90 degrees, since it is sine divided by cosine and cosine is 0 there. The calculator shows a very large number instead of an error at that point.
Factorial, log and ln
Factorial, written n!, counts the number of ways to arrange n items in order. 5! is 5 x 4 x 3 x 2 x 1, or 120, the number of ways to line up 5 people, and it is the basis of permutation and combination formulas.
log is base 10, useful for orders of magnitude and scales like pH or the Richter scale. ln is the natural log, base e, used for continuous growth and decay, like compound interest or radioactive decay. These are worth knowing without reaching for the keypad.
| Expression | Result |
|---|---|
| log(10) | 1 |
| log(100) | 2 |
| ln(1) | 0 |
| ln(e) | 1 |
log(10) is 1 because 10 to the power of 1 is 10. log(100) is 2 because 10 squared is 100. ln(1) is 0 because e to the power of 0 is 1, and ln(e) is 1 because e to the power of 1 is e.
Scientific calculator FAQ
What is sin(30) in degrees?
0.5. Make sure DEG is selected, since sin(30) in radians gives a different answer.
How do I use inverse trig functions?
Press 2nd to swap sin, cos and tan for asin, acos and atan, then press it again to swap back.
What is the difference between log and ln?
log is base 10, so log(100) is 2. ln is the natural log, base e, so ln(e) is 1.
Does it follow order of operations?
Yes. Multiplication and division happen before addition and subtraction, powers happen before both, and parentheses always come first.
Can I type 2pi or 3sin(90) without a multiplication sign?
Yes, a number followed directly by a constant, function or parenthesis is read as multiplication.
What is 2^3^2?
512. Powers evaluate right to left, so 3^2 is worked out first (9), then 2^9, which is 512.
What does tan(90) show?
A very large number rather than a clean error, since tangent has a vertical asymptote at 90 degrees where the true value is undefined. Treat a huge tan result near 90 or 270 degrees as undefined.
What is factorial used for?
n! counts the number of ways to arrange n items in order. 5! is 5 x 4 x 3 x 2 x 1, or 120, the number of ways to line up 5 people.