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)

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