Scientific calculator
The same expression engine as the basic one, with trigonometry, logarithms, powers and constants.
History
Work something out and it collects here.
How it works
Functions are written as sin(30) or sqrt(16). The brackets may be left out when the argument is a single number, so sqrt9 works too.
The angle mode decides how trigonometry is calculated. In degrees, sin(90) gives 1; in radians, sin(pi/2) gives the same answer.
The inv button swaps sine, cosine and tangent for their inverses. In degrees, asin(1) gives 90.
The available functions are sin, cos, tan and their inverses, sinh, cosh, tanh, ln, log, log2, sqrt, cbrt, abs, exp, round, floor, ceil and sign.
The constants pi, tau and e can be typed directly, and 2pi is read as two times pi.
A leading minus binds more weakly than a power, so −2^2 is −4. Write (−2)^2 if you mean 4.
Factorials are written with an exclamation mark after the number and apply only to whole numbers that are not negative.
Functions with two or more arguments
log(2, 8) gives 3: the first argument is the base and the second the number, so log(8, 2) gives 0.333333333333. root(−8, 3) gives −2, because an odd root of a negative number is real, whereas (−8)^(1/3) gives no answer. mod(−7, 3) gives 2: the remainder takes the sign of the number you divide by. Modulo can also be written between the numbers, as in 7 mod 2.
ncr(35, 7) gives 6,724,520, the number of ways to choose 7 things from 35 regardless of order, and npr(10, 3) gives 720, where order counts. Beyond the keys there are gcd and lcm for the greatest common divisor and least common multiple, hypot, min, max, the inverse hyperbolic functions asinh, acosh and atanh, and atan2(y, x), which gives the angle in the right quadrant: atan2(−1, −1) is −135 in degrees.
The comma in functions with several arguments
Inside a function that takes several arguments, the comma separates them. max(2,5) therefore gives 5, not 2.5, and max(1,500) gives 500, not 1,500. Write decimals with a full stop there, as in max(2.5, 3). A semicolon also works as a separator, and once semicolons separate the arguments, a comma is read as it is outside such functions: a comma that separates thousands in the usual way is a thousands separator, and any other comma is a decimal mark. max(2,5; 3) therefore gives 3, and max(1,500; 3) gives 1,500.
The letter e after a number means a power of ten only when a digit follows: 2e3 is 2,000, while 2e is two times the number e, 5.43656365692.
Limits and ranges
The inverse functions give principal values: asin and atan lie between −90 and 90 degrees, and acos between 0 and 180. asin(2) gives no answer, because sine never exceeds 1. One degree is π / 180 radians. Because π / 180 cannot be stored exactly, the tool treats whole multiples of 30 and 45 degrees separately: sin(180) gives 0 rather than a tiny leftover, and tan(90) gives no answer, because the tangent has no value there.
The largest number the browser can store is about 1.8 × 10³⁰⁸. 170! is about 7.26 × 10³⁰⁶ and is therefore the largest factorial that can be worked out; 171! gives no answer.
round follows the JavaScript rule and sends halves towards plus infinity: round(2.5) is 3 but round(−2.5) is −2. That differs from the rounding tool, which rounds −2.5 to −3.