This page provides a simple tool useful for hand computations in the context of basic (classical and quantum) physics The calculator is designed to accept data and operating instructions in reverse polish notation, avoiding the use of parenthesis. It implements a simple 9levels stack of floatingpoint numbers, with various management commands, arithmetic operations and functions, and predefined physical constants. The following keys will be described 


The operands are stored as floatingpoint numbers in the floatingpoint stack of the calculator. The most recent elements are entered in the x register, which lies at the bottom of the stack. New elements are entered there, pushing up the entire stack. If
the stack overflows to 10 numbers, the oldest 

digits 
used to enter mantissa and exponent figures 
< 
used to delete the last character entered 
. 
The decimal point (.) used in the mantissa 
E and E 
used
to start writing the exponent (E for positive exponents, 
+/ 
changes the sign of the floatingpoint number in x 
Enter 
stops the editing of x register and pushes the stack up, so that the x register is free to receive a new floatingpoint number 
drop 
removes the content of the x register, and pulls the stack down 
There
are five basic arithmetic operators 

+ 
add the content of register x and register y, store the result in register x and remove y 
 
substract the content of register x from register y, store the result in register x and remove y 
* 
multiply the content of register x and register y, store the result in register x and remove y 
/ 
divide the content of register y by the content of register x, store the result in register x and remove y 
y**x 
elevate register y to the power in x, store the result in register x and remove y 
Stack management commands allows some reordering of the floatingpoint numbers in the arithmetic stack: 

dup 
duplicate (enter a copy of) register x 
drop 
delete register x 
swap 
interchange register x and register y 
over 
duplicate (enter a copy of) register y 
up 
roll up the content of the stack by bringing the oldest element in register x 
down 
roll down the content of the stack by bringing register x to the top of the stack 
Clear Stack 
remove the whole content of the floatingpoint stack 
A few keys activates functions applied to the content of the x register: 

^2 
replace x by x^{2} 
sqr 
replace x by the square root of x 
1/x 
replace x by its multiplicative inverse 1/x 
x! 
replace x by its factorial x!. If x is not an integer, the gamma function gamma(x1) is computed 
abs 
replace x by its positive absolute value 
exp 
replace x by e^{x} 
ln 
replace x by its Napier logarithm log(x) 
rnd 
round x to the nearest integer value 
int 
remove from x the digits after the decimal point, to leave its integer part 
frac 
remove from x the digits before the decimal point, to leave the fractional part 
The following functions compute basic trigonometric functions: 

mode 
switch from radians to degrees and back when using circular trigonometric functions 
sin 
replace x by sin(x) 
asin 
replace x by inverse sine function asin(x) 
cos 
replace x by cos(x) 
acos 
replace x by inverse cosine function acos(x) 
tan 
replace x by tan(x) 
atan 
replace x by inverse tangent function atan(x) 
sinh 
replace x by the hyperbolic sine sh(x) 
asinh 
replace x by the inverse hyperbolic sine function ash(x) 
cosh 
replace x by the hyperbolic cosine ch(x) 
acosh 
replace x by the inverse hyperbolic cosine function ach(x) 
tanh 
replace x by the hyperbolic tangent th(x) 
atanh 
replace x by the inverse hyperbolic tangent function ath(x) 
The following keys are used to introduce physics constants, all expressed in the SI system : 

h 
Planck
Constant (ratio of the 
6.62660755 x 10^{34} J.s 
hbar 
Planck Constant/(2*pi) 
1.05457267 x 10^{34} J.s 
c 
speed of light in vacuum 
299792458 ms^{1} 
N 
Avogadro number 
6.02213674 x 10^{23} 
k 
Boltzmann constant 
1.3806581 x 10^{23}J.K^{1} 
R 
Perfect gas constant 
8.314511869 J.K^{1} 
1/(4*pi*eps0) 
Constant in Coulomb law 
8.987551760 x 10^{9} Nm^{2}C^{2} 
G 
Gravitational constant 
6.6725985 x 10^{11} Nm^{2}kg^{2} 
eps0 
vacuum permittivity 
8.85418782 x 10^{12} Fm^{1} 
mu0 
vacuum permeability 
4 x pi x 10^{7} Hm^{1} 
e 
absolute value of electron charge 
1.60217733 x 10^{19} C 
m 
electron mass 
9.10938975 x 10^{31} kg 
muB 
Bohr magneton 
9.27401543 x 10^{24} JT^{1} 
a0 
Bohr radius 
5.29177249 x 10^{11} m 
Rd 
Rydberg (13.6 eV) 
2.17987411 x 10^{18} J 
Hr 
Hartree (27.2 eV) 
4.35974822 x 10^{18} J 
alpha 
finestructure constant 
0.00729735308 
Compton 
Compton wavelength of electron 
2.42631058 x 10^{12} m 
amu 
atomic mass unit 
1.66054021 x 10^{27} kg 
mp 
proton rest mass 
1.672614 x 10^{27} kg 
mn 
neutron rest mass 
1.67492 x 10^{27} kg 
Stefan 
Stefan constant 
5.66914 x 10^{08} Jm^{2}s^{1}K^{4} 
c1 
first radiation constant (8*pi*hc) 
5.66914 x 10^{08} Jm^{2}s^{1}K^{4} 
c2 
Second radiation constant 
0.01438833 m.K 
A few important unit conversions are possible with this calculators: 

mode 
switch from radians to degrees and back when using circular trigonometric functions 
A/m 
A length, in register x, expressed in units of m (meters) is converted into angstr&oulm;ms 
m/A 
A length, in register x, expressed in units of angstr&oulm;ms is converted into meters 
eV/J 
An energy, in register x, expressed in units of J (joules) is converted into electronvolts 
J/eV 
An energy, in register x, given in units of electronvolts is converted into SI joules 
cal/J 
An energy, in register x, expressed in units of J (joules) is converted into calories 
J/cal 
An energy, in register x, given in units of calories is converted into SI joules 
deg 
Specifies that the number just entered is expressed in degree, and make the appropriate conversion according to the mode selected (deg or rad) 
min 
Specifies that the number just entered is expressed in minutes, and make the appropriate conversion according to the mode selected (deg or rad) 
sec 
Specifies that the number just entered is expressed in seconds, and make the appropriate conversion according to the mode selected (deg or rad) 