GUTCalc understands integers and floating point numbers. You can use 'exponential notation' like 1e3 for 1000 (though exponents have to be integers). Include units and constants by typing their abbreviations. SI prefixes are supported (from femto- to peta-).
GUTCalc also knows about parentheses and the usual operations (+,-,*,/,^). Multiplication is implied where necessary. The standard order of operations is enforced and operators (including implied multiplication) are left-associative. For example, 1/10s is one tenth of a second, not one tenth of a Hertz. If that's what you want, use parentheses (like 1/(10 s)) or 'greedy division' //: 1//10 s = .1 Hz. (Greedy division has higher precedence than ordinary division and multiplication, but lower precedence than exponentiation. In other words, it works like a big fraction bar.)
You can apply functions as well. GUTCalc knows sqrt, exp, ln, log, and trig functions (regular and hyperbolic). Functions act directly to the right with the precedence of exponentiation (as of version >0.3), so (e.g.) log 10^3 = 1^3 = 1. Of course you probably want to use parentheses most of the time.
Finally, you can convert your answer into other units using the in keyword. You can only use 'in' once, at the very top level of your expression (not inside parentheses). Even though it's probably a bad idea, GUTCalc will let you use addition, subtraction, and functions on the right-hand side of in.
Examples:
5 kg in lb (converts 5 kilograms to (U.S.) pounds)
1/sqrt(8 pi G) in GeV (calculate the reduced Plank mass in GeV. This works in Natural mode, because it will add factors of c for us!)
qe (just print out the charge of an electron. In SI mode, you get the answer in Coulombs; in Natural mode, you get about 0.3, since charge is dimensionless in Natural units. GUTCalc uses the rationalized Heaviside-Lorentz convention, where α=qe^2/(4pi).)
arctan(5 m) (doesn't work, since you can't take the arctangent of a dimensionful number)
arctan(qe) (only works in Natural mode where charge is dimensionless)
About Gaussian CGS Units:
Gaussian CGS mode makes assumptions (c = 4 pi eps0 = 1) that are inconsistent with Natural mode. Some calculations and conversions will have different results between these modes, even if you specify the final units explicitly. GUTCalc assumes that CGS electrostatic units (esu and statV) refer to specific physical amounts of charge and electric potential, respectively. Their conversions to mechanical units are different in the two modes. In particular, esu in C will always return the correct value, but esu in sqrt(dyn)cm will correctly return 1 in Gaussian CGS mode, but will return 3.54491 in Natural mode and fail in SI mode. (Note: This behavior was changed in v0.5 to favor the electrostatic interpretation rather than the mechanical interpretation.)