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 9-levels stack of floating-point numbers, with various management commands, arithmetic operations and functions, and predefined physical constants. The following keys will be described

 Input to the stack The operands are stored as floating-point numbers in the floating-point 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 element is lost. digits 0,1,2...9 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, E- for negative exponents) +/- changes the sign of the floating-point 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 floating-point number drop removes the content of the x register, and pulls the stack down

 Basic arithmetic operators There are five basic arithmetic operators in this calculator : + 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 Stack management commands allows some reordering of the floating-point 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 floating-point stack

 Functions applying to x register A few keys activates functions applied to the content of the x register: ^2 replace x by x2 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(x-1) is computed abs replace x by its positive absolute value exp replace x by ex 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

 Trigonometric functions 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)

 Physics predefined constants The following keys are used to introduce physics constants, all expressed in the SI system : h Planck Constant (ratio of the photon energy to its frequency) 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 1023 k Boltzmann constant 1.3806581 x 10-23J.K-1 R Perfect gas constant 8.314511869 J.K-1 1/(4*pi*eps0) Constant in Coulomb law 8.987551760 x 109 Nm2C-2 G Gravitational constant 6.6725985 x 10-11 Nm2kg-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 fine-structure 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-2s-1K-4 c1 first radiation constant (8*pi*hc) 5.66914 x 10-08 Jm-2s-1K-4 c2 Second radiation constant 0.01438833 m.K

 Conversion functions 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 electron-volts J/eV An energy, in register x, given in units of electron-volts 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)