What is a scientific calculator?
A scientific calculator adds functions such as sine, cosine, logarithms, square roots and exponentials to ordinary arithmetic. This one evaluates a typed expression, so you can write sin(30) + sqrt(16) and get 4.5 in one step. Trigonometric functions take angles in degrees, and the constants pi and e are built in.
How to use it
- Type an expression. Functions need their argument in brackets:
sin(30), notsin 30. - Click Calculate.
- Read the result, shown to up to 10 decimal places with trailing zeros removed.
Arithmetic follows the usual order: brackets, then powers (^), then multiplication and division, then addition and subtraction. Multiplication always needs a *, so write 2 * pi, not 2pi. The basic calculator guide covers the arithmetic rules in more detail, since both calculators share the same parser.
Supported functions and constants
| Typed as | What it does | Example | Result |
|---|---|---|---|
sin(x) |
Sine, x in degrees | sin(30) |
0.5 |
cos(x) |
Cosine, x in degrees | cos(60) |
0.5 |
tan(x) |
Tangent, x in degrees | tan(45) |
1 |
sqrt(x) |
Square root, x ≥ 0 | sqrt(2) |
1.4142135624 |
log(x) |
Base-10 logarithm, x > 0 | log(1000) |
3 |
ln(x) |
Natural logarithm, x > 0 | ln(10) |
2.302585093 |
exp(x) |
e raised to the power x | exp(1) |
2.7182818285 |
abs(x) |
Absolute value | abs(-7.5) |
7.5 |
x ^ y |
Power | 2^10 |
1024 |
pi |
3.14159265… | pi |
3.1415926536 |
e |
2.71828182… | e |
2.7182818285 |
Function names aren't case-sensitive, and functions can be nested: sqrt(3^2 + 4^2) returns 5, the length of the hypotenuse of a 3-4-5 triangle.
Degrees vs radians
There are two common units for angles. Degrees split a full turn into 360 parts. Radians measure the angle by arc length, so a full turn is 2π radians, and the radian is the angle unit of the International System of Units (BIPM SI Brochure). Spreadsheets and programming languages usually expect radians; school maths and most handheld calculators default to degrees.
This calculator always uses degrees. That matters when you copy a formula written in radians:
| You want | Type | Result |
|---|---|---|
| sin of 30° | sin(30) |
0.5 |
| sin of π/6 radians (also 30°) | sin(pi/6 * 180/pi) |
0.5 |
| sin of 1 radian | sin(1 * 180 / pi) |
0.8414709848 |
What sin(pi/6) actually computes |
sin of 0.5236° | 0.0091383954 |
The last row is the mistake to watch for: the expression is valid, so you get a number, but it's the sine of half a degree.
Worked examples
Mixing trig and logs. 5 * cos(60) + log(100)^2
- cos(60) = 0.5, so 5 * 0.5 = 2.5.
- log(100) = 2, and 2^2 = 4. The power applies to the result of the function.
- 2.5 + 4 = 6.5.
Continuous growth. £1,000 growing at a continuous rate of 5% a year for 3 years is 1000 × e^(0.05 × 3). Typed as 1000 * exp(0.05 * 3), it returns 1161.8342427283.
Power before sign. -sin(30)^2 returns -0.25: the power is applied first, then the minus sign.
Errors and edge cases
sqrt(-1)returns "Cannot take the square root of a negative number." Complex numbers aren't supported.log(0)andln(-5)return "Cannot take the logarithm of a non-positive number."tan(90)andtan(270)are mathematically undefined, but return very large numbers (16331239353195370 and 5443746451065123) because of floating-point rounding in the degree-to-radian conversion.sin(180)andcos(90)return exactly 0. The true floating-point results are tiny numbers around 10^-16, which the 10-decimal rounding removes.- Results too large to store, such as
exp(1000), show as inf.
The NIST Digital Library of Mathematical Functions is a good reference for the exact definitions and identities of the trigonometric functions.
Related calculators
- Basic calculator: the same expression syntax without the functions.
- Algebra solver: solve ax + b = c for x.
- Fraction calculator: exact answers as simplified fractions.
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