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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 |
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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 |
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digits |
used to enter mantissa and exponent figures |
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< |
used to delete the last character entered |
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. |
The decimal point (.) used in the mantissa |
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E and E- |
used
to start writing the exponent (E for positive exponents, |
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+/- |
changes the sign of the floating-point number in x |
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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 |
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drop |
removes the content of the x register, and pulls the stack down |
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There
are five basic arithmetic operators |
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+ |
add the content of register x and register y, store the result in register x and remove y |
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- |
substract the content of register x from register y, store the result in register x and remove y |
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* |
multiply the content of register x and register y, store the result in register x and remove y |
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/ |
divide the content of register y by the content of register x, store the result in register x and remove y |
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y**x |
elevate register y to the power in x, store the result in register x and remove y |
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Stack management commands allows some reordering of the floating-point numbers in the arithmetic stack: |
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dup |
duplicate (enter a copy of) register x |
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drop |
delete register x |
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swap |
interchange register x and register y |
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over |
duplicate (enter a copy of) register y |
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up |
roll up the content of the stack by bringing the oldest element in register x |
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down |
roll down the content of the stack by bringing register x to the top of the stack |
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Clear Stack |
remove the whole content of the floating-point stack |
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A few keys activates functions applied to the content of the x register: |
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^2 |
replace x by x2 |
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sqr |
replace x by the square root of x |
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1/x |
replace x by its multiplicative inverse 1/x |
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x! |
replace x by its factorial x!. If x is not an integer, the gamma function gamma(x-1) is computed |
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abs |
replace x by its positive absolute value |
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exp |
replace x by ex |
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ln |
replace x by its Napier logarithm log(x) |
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rnd |
round x to the nearest integer value |
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int |
remove from x the digits after the decimal point, to leave its integer part |
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frac |
remove from x the digits before the decimal point, to leave the fractional part |
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The following functions compute basic trigonometric functions: |
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mode |
switch from radians to degrees and back when using circular trigonometric functions |
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sin |
replace x by sin(x) |
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asin |
replace x by inverse sine function asin(x) |
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cos |
replace x by cos(x) |
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acos |
replace x by inverse cosine function acos(x) |
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tan |
replace x by tan(x) |
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atan |
replace x by inverse tangent function atan(x) |
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sinh |
replace x by the hyperbolic sine sh(x) |
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asinh |
replace x by the inverse hyperbolic sine function ash(x) |
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cosh |
replace x by the hyperbolic cosine ch(x) |
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acosh |
replace x by the inverse hyperbolic cosine function ach(x) |
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tanh |
replace x by the hyperbolic tangent th(x) |
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atanh |
replace x by the inverse hyperbolic tangent function ath(x) |
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The following keys are used to introduce physics constants, all expressed in the SI system : |
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h |
Planck
Constant (ratio of the |
6.62660755 x 10-34 J.s |
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hbar |
Planck Constant/(2*pi) |
1.05457267 x 10-34 J.s |
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c |
speed of light in vacuum |
299792458 ms-1 |
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N |
Avogadro number |
6.02213674 x 1023 |
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k |
Boltzmann constant |
1.3806581 x 10-23J.K-1 |
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R |
Perfect gas constant |
8.314511869 J.K-1 |
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1/(4*pi*eps0) |
Constant in Coulomb law |
8.987551760 x 109 Nm2C-2 |
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G |
Gravitational constant |
6.6725985 x 10-11 Nm2kg-2 |
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eps0 |
vacuum permittivity |
8.85418782 x 10-12 Fm-1 |
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mu0 |
vacuum permeability |
4 x pi x 10-7 Hm-1 |
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e |
absolute value of electron charge |
1.60217733 x 10-19 C |
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m |
electron mass |
9.10938975 x 10-31 kg |
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muB |
Bohr magneton |
9.27401543 x 10-24 JT-1 |
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a0 |
Bohr radius |
5.29177249 x 10-11 m |
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Rd |
Rydberg (13.6 eV) |
2.17987411 x 10-18 J |
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Hr |
Hartree (27.2 eV) |
4.35974822 x 10-18 J |
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alpha |
fine-structure constant |
0.00729735308 |
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Compton |
Compton wavelength of electron |
2.42631058 x 10-12 m |
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amu |
atomic mass unit |
1.66054021 x 10-27 kg |
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mp |
proton rest mass |
1.672614 x 10-27 kg |
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mn |
neutron rest mass |
1.67492 x 10-27 kg |
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Stefan |
Stefan constant |
5.66914 x 10-08 Jm-2s-1K-4 |
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c1 |
first radiation constant (8*pi*hc) |
5.66914 x 10-08 Jm-2s-1K-4 |
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c2 |
Second radiation constant |
0.01438833 m.K |
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A few important unit conversions are possible with this calculators: |
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mode |
switch from radians to degrees and back when using circular trigonometric functions |
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A/m |
A length, in register x, expressed in units of m (meters) is converted into angstr&oulm;ms |
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m/A |
A length, in register x, expressed in units of angstr&oulm;ms is converted into meters |
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eV/J |
An energy, in register x, expressed in units of J (joules) is converted into electron-volts |
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J/eV |
An energy, in register x, given in units of electron-volts is converted into SI joules |
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cal/J |
An energy, in register x, expressed in units of J (joules) is converted into calories |
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J/cal |
An energy, in register x, given in units of calories is converted into SI joules |
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deg |
Specifies that the number just entered is expressed in degree, and make the appropriate conversion according to the mode selected (deg or rad) |
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min |
Specifies that the number just entered is expressed in minutes, and make the appropriate conversion according to the mode selected (deg or rad) |
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sec |
Specifies that the number just entered is expressed in seconds, and make the appropriate conversion according to the mode selected (deg or rad) |