Scientific Calculator
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Scientific calculations using AddUp 2
Scientific calculations with AddUp are performed by entering complex series of numbers and operators to form the expression to evaluate, as well as various math functions. The expression can be typed in and edited at will, then pressing the Enter key causes it to be evaluated. There is no need to use buttons with this calculator, everything that needs to be evaluated can be directly entered in the work area.
The available mathematical operators are: addition (+), subtraction (-), multiplication (*), division (/), exponent (^ or **), percent (%), factorial(!). These can be used alone or in combination to form complex expressions. Parentheses can also be used to nest sub-expressions. For example:
(123 + 456) * 78 = 45,162
901 - (23 / 45) ^ 6 = 900.98217
7! * 8% = 403.2
Functions are numerous. The more basic arithmetic ones include: absolute value, inverse, modulo and remainder functions, percent and signum. Scientific functions include mathematical functions that are normally found on a scientific calculator: square root, cubic root, power, exponent, logarithm (in various bases), factorial, etc.
ln(123) = 4.8121844
sqrt(81) = 9
Faithful to commonly used scientific notation, multiplications are implied when there is no operator between a value and a function. The same goes for constants and parenthesized expressions. This means that we can use expressions like this:
5 ln(pi + 3) = 9.0754205
5 pi + 3 = 18.707963
5 (pi + 3) = 30.707963
(4 + 1) (pi + 3) = 30.707963
Trigonometric functions are available of course: sine, cosine, tangent, cotangent, secant and cosecant. These functions take parameter values that can be expressed in radians (the default when no unit is specified), in degrees or in gradients.
sin(pi/4 rad) = 0.7071068
sin(pi/4) = 0.7071068
sin(45 deg) = 0.7071068
sin(50 grad) = 0.7071068
As well, inverse trigonometric functions are included: arc-sine, arc-cosine, arc-tangent, arc-cotangent, arc-secant and arc-cosecant.
Akin to trigonometric functions, hyperbolic functions are also provided: hyperbolic sine, hyperbolic cosine, hyperbolic tangent, hyperbolic cotangent, hyperbolic secant and hyperbolic cosecant. As well, inverse hyperbolic functions are included: hyperbolic arc-sine, hyperbolic arc-cosine, hyperbolic arc-tangent, hyperbolic arc-cotangent, hyperbolic arc-secant and hyperbolic arc-cosecant.
For more advanced math and engineering, complex numbers are natively supported. Complex number functions include: real and imaginary extractors, polar conversion, argument (or phase angle), complex conjugate, norm (or magnitude) and square of the norm. Complex numbers can be used directly in most operations where they would normally apply.
(1; 2) / (3; 4) = (0.44; 0.08)
sqrt(-9) = (0; -3)
A good deal of scientific work involves reference to constant values defined in physics, electronics and other scientific fields of study. AddUp defines a large set of scientific constants that are accessible either from the menu or from a button panel for selected fields of study.
| Atomic Units | ||
|---|---|---|
| au1H | Atomic unit of 1st hyperpolarizability (coulomb^3 meter^3 / joule^2) | 3.20636151e-53 |
| au2H | Atomic unit of 2nd hyperpolarizability (coulomb^4 meter^4 / joule^3) | 6.2353808e-65 |
| auAct | Atomic unit of action (joule s) | 1.05457168e-34 |
| auCharge | Atomic unit of charge (coulomb) | 1.60217653e-19 |
| auChDen | Atomic unit of charge density (coulomb / meter^3) | 1.081202317e+12 |
| auE | Atomic unit of energy (joule) | 4.35974417e-18 |
| auECurr | Atomic unit of electric current (amp) | 6.62361782e-3 |
| auEDM | Atomic unit of electric field (volt / meter) | 8.47835309e-30 |
| auEF | Atomic unit of electric field (volt / meter) | 5.14220642e+11 |
| auEFG | Atomic unit of electric field gradient (volt / meter^2) | 9.71736182e+21 |
| auEPerm | Atomic unit of electric permitivity (auEPerm) | 1.112650056e-10 |
| auEPolar | Atomic unit of electric polarizability (coulomb^2 meter^2 / joule) | 1.648777274e-41 |
| auEPot | Atomic unit of electric potential (volt) | 27.2113845 |
| auEQM | Atomic unit of electric quadrupole moment (coulomb meter^2) | 4.48655124e-40 |
| auForce | Atomic unit of force (newton) | 8.2387225e-08 |
| auLength | Atomic unit of length (meter) | 0.5291772108e-10 |
| auM | Atomic unit of magnetizability (joule / tesla^2) | 7.89103660e-29 |
| auMass | Atomic unit of mass (kg) | 9.1093826e-31 |
| auMDM | Atomic unit of magnetic dipole moment (joule / tesla) | 1.85480190e-23 |
| auMFD | Atomic unit of magnetic flux density (tesla) | 2.35051742e+5 |
| auMom | Atomic unit of momentum (kg meter / s) | 1.99285166e-24 |
| auSpeed | Atomic unit of speed or velocity (meter / s) | 2.1876912633e+6 |
| auTime | Atomic unit of time (s) | 2.418884326505e-17 |
| Chemo-Physical | ||
|---|---|---|
| amc | Atomic mass constant (kg) | 1.66053886e-27 |
| amcEE | Atomic mass constant energy equivalent (joule) | 1.49241790e-10 |
| avogadro | Avogadro constant (1 / mol) | 6.0221415e+23 |
| boltzmann | Boltzmann constant (joule / Kelvin) | 1.3806505e-23 |
| c1 | First radiation constant (weber meter^2) | 3.74177138e-16 |
| c1SR | First radiation constant for spectral radiance (weber meter^2 / steradian) | 1.19104282e-16 |
| c2 | Second radiation constant (meter Kelvin) | 1.4387752e-2 |
| fConst | Faraday constant (coulomb / mol) | 96485.3383 |
| loschmidt | Loschmidt constant, 273.15 K, 101.325 kPa (1 / meter^3) | 2.6867773e+25 |
| mol [also: mole] | Amount of substance unit (mol) | 1 |
| molGC | Molar gas constant (joule / mol Kelvin) | 8.314472 |
| molMassC | Molar mass constant (kg / mol) | 1e-3 |
| molMC12 | Molar mass of carbon-12 (kg / mol) | 12e-3 |
| molPlk | Molar Planck constant (joule s / mol) | 3.990312716e-10 |
| molVolGas | Molar volume of ideal gas, 273.15 K, 101.325 kPa (meter^3 / mol) | 22.413996e-3 |
| sactet | Sackur-Tetrode constant, 1 K, 101.325 kPa | -1.1648677 |
| stefBolt | Stefan-Boltzmann constant (weber / meter^2 Kelvin^4) | 5.670400e-8 |
| wien | Wien displacement law constant (meter Kelvin) | 2.8977685e-3 |
| Electromagnetic | ||
|---|---|---|
| bohrMag | Bohr magneton (joule / tesla) | 927.400949e-26 |
| condQ | Conductance quantum (s) | 7.748091733e-5 |
| josephson | Josephson constant (hertz / volt) | 4.83597879e+4 |
| magFluxQ | Magnetic flux quantum (weber) | 2.06783372e-15 |
| nucMag | Nuclear magneton (joule / tesla) | 5.05078343e-27 |
| vonKlitzing | Von Klitzing constant (ohm) | 25812.807449 |
Hidden Values
Hidden constants are values that are not normally used in calculations but that may be reported in results, usually because of an invalid expression or similar error condition. These values do not appear in menus or button panels since they are not intended to be used as input.
| Hidden Values | ||
|---|---|---|
| inf | Infinity. This value cannot normally be used in expression since it represents a greater value than what can be represented by computer hardware. However it may be displayed in certain cases along with error messages to indicate excessively large results. | inf |
| NaN | Not-a-number. This value cannot normally be used in expression since it represents a non-numeric value. However it may be displayed in certain cases along with error messages to indicate impossible calculations. | NaN |
| Mathematics | ||
|---|---|---|
| e | Euler number | 2.718281828459045... |
| i | Imaginary number (square root of -1) | (0; -1) |
| pi | Ratio of a circle's periphery to its diameter | 3.141592653589793... |
| Natural Units | ||
|---|---|---|
| naAct | Natural unit of action | 1.05457168e-34 |
| naE | Natural unit of energy (joule) | 8.1871047e-14 |
| naLength | Natural unit of length (meter) | 386.1592678e-15 |
| naMass | Natural unit of mass (kg) | 9.1093826e-31 |
| naMom | Natural unit of momemtum (kg meter / s) | 2.73092419e-22 |
| naTime | Natural unit of time (s) | 1.2880886677e-21 |
Prefix Multipliers
Prefix multipliers are special constant values that can be used either alone or as prefixes. Used alone, they simply generate their constant value. Used as a prefix of another constant or measurement unit, they modify the value of the quantity they are attached to, multiplying it by their own value. All prefixes defined in the international SI system of measurements (kilo, micro, etc.) are included in this set. A few commonly used non-SI terms (half, double, etc.) are also included here and perform the same functions.
The most common use of prefixes is to form the extended names of various SI units such as kilogram, centilitre and megatonne. But AddUp does not restrict their usage to SI units alone: they can be added to non-SI units and to other constants. For example halfMeter, quarterPound, megaMiles and triplePi will all be recognized as proper unit or constant values.
| Non-SI Prefix Multipliers | ||
|---|---|---|
| double | 2 | 2 |
| half | 1/2 | 1/2 |
| mono | 1 (placeholder, no effect) | 1 |
| quarter | 1/4 | 1/4 |
| tetra (1) [also: quadri] | 4 | 4 |
| third | 1/3 | 1/3 |
| triple | 3 | 3 |
| SI Prefix Multipliers | ||
|---|---|---|
| atto | 0.000 000 000 000 000 001 | 1e-18 |
| centi | 0.01 | 1e-2 |
| deca | 10 | 1e+1 |
| deci | 0.1 | 1e-1 |
| exa | 1 000 000 000 000 000 000 | 1e+18 |
| femto | 0.000 000 000 000 001 | 1e-15 |
| giga | 1 000 000 000 | 1e+9 |
| hecto | 100 | 1e+2 |
| kilo | 1000 | 1e+3 |
| mega | 1 000 000 | 1e+6 |
| micro | 0.000 001 | 1e-6 |
| milli | 0.001 | 1e-3 |
| nano | 0.000 000 001 | 1e-9 |
| peta | 1 000 000 000 000 000 | 1e+15 |
| pico | 0.000 000 000 001 | 1e-12 |
| tera (1) | 1 000 000 000 000 | 1e+12 |
| yocto | 0.000 000 000 000 000 000 000 001 | 1e-24 |
| yotta | 1 000 000 000 000 000 000 000 000 | 1e+24 |
| zepto | 0.000 000 000 000 000 000 001 | 1e-21 |
| zetta | 1 000 000 000 000 000 000 000 | 1e+21 |
Sub-Atomic
Sub-atomic constants include measurements of sub-atomic particles and other values that best apply at the sub-atomic level. These constants are sub-divided into panels that refer to individual sub-atomic aspect, plus a general panel for miscellaneous constant values at this scale.
| Sub-Atomic, Alpha Particle | ||
|---|---|---|
| aMass | Alpha particle mass (kg) | 6.6446565e-27L |
| aMassEE | Alpha particle mass energy equivalent (joule) | 5.9719194e-10 |
| aMassMol | Alpha particle molar mass (kg / mol) | 4.001506179149e-3 |
| Sub-Atomic, Deuteron | ||
|---|---|---|
| dMagMom | Deuteron magnetic moment (joule / tesla) | 0.433073482e-26 |
| dMass | Deuteron mass (kg) | 3.34358335e-27 |
| dMassEE | Deuteron mass energy equivalent (joule) | 3.00506285e-10 |
| dMassMol | Deuteron molar mass (kg / mol) | 2.01355321270e-3 |
| dRMSCR | Deuteron rms charge radius (meter) | 2.1394e-15 |
| Sub-Atomic, General | ||
|---|---|---|
| eCharge | Electron charge, elementary charge (coulomb) | 1.60217653e-19 |
| eGFact | Electron g factor | -2.0023193043718 |
| eGyrMag | Electron gyromagnetic ratio (1 / s tesla) | 1.76085974e+11 |
| eMagMom | Electron magnetic moment (joule / tesla) | -928.476412e-26 |
| eMagMomAnom | Electron magnetic moment anomaly | 1.1596521859e-3 |
| eMass | Electron mass (kg) | 9.1093826e-31 |
| eMassEE | Electron mass energy equivalent (joule) | 8.1871047e-14 |
| eMassMol | Electron molar mass (kg / mol) | 5.4857990945e-7 |
| eRad | Classical electron radius (meter) | 2.817940325e-15 |
| Sub-Atomic, Electron | ||
|---|---|---|
| bohrRad | Bohr radius (meter) | 0.5291772108e-10 |
| circQ | Quantum of circulation (m^2 / s) | 3.636947550e-4 |
| comptonW | Compton wavelength (meter) | 2.426310238e-12 |
| fermiCC | Fermi coupling constant (1 / GeV^2) | 1.16639e-5 |
| fsc | Fine-structure constant | 7.297352568e-3 |
| hartree | Atomic unit of energy (J) | 4.35974417e-18 |
| rydberg | Rydberg constant (1 / meter) | 10973731.568525 |
| thomsonCS | Thomson cross section (meter^2) | 0.665245873e-28 |
| weakMA | Weak mixing angle | 0.22215 |
| Sub-Atomic, Helion | ||
|---|---|---|
| hGyrMagSh | Shielded helion gyromagnetic ratio (1 / s tesla) | 2.03789470e+8 |
| hMagMomSh | Shielded helion magnetic moment (joule / tesla) | -1.074553024e-26 |
| hMass | Helion mass (kg) | 5.00641214e-27 |
| hMassEE | Helion mass energy equivalent (joule) | 4.49953884e-10 |
| hMassMol | Helion molar mass (kg / mol) | 3.0149322434e-3 |
| Sub-Atomic, Muon | ||
|---|---|---|
| mCompW | Muon Compton wavelength (meter) | 11.73444105e-15 |
| mGFact | Muon g factor | -2.0023318396 |
| mMagMom | Muon magnetic moment (joule / tesla) | -4.49044799e-26 |
| mMagMomAnom | Muon magnetic moment anomaly | 1.16591981e-3 |
| mMass | Muon mass (kg) | 1.88353140e-28 |
| mMassEE | Muon mass energy equivalent (joule) | 1.69283360e-11 |
| mMassMol | Muon molar mass (kg / mol) | 0.1134289264e-3 |
| Sub-Atomic, Neutron | ||
|---|---|---|
| nCompW | Neutron Compton wavelength (meter) | 1.3195909067e-15 |
| nGFact | Neutron g factor | -3.82608546 |
| nGyrMag | Neutron gyromagnetic ratio (1 / s tesla) | 1.83247183e+8 |
| nMagMom | Neutron magnetic moment (joule / tesla) | -0.96623645e-26 |
| nMass | Neutron mass (kg) | 1.67492728e-27 |
| nMassEE | Neutron mass energy equivalent (joule) | 1.50534957e-10 |
| nMassMol | Neutron molar mass (kg / mol) | 1.00866491560e-3 |
| Sub-Atomic, Proton | ||
|---|---|---|
| pCompW | Proton Compton wavelength (meter) | 1.3214098555e-15 |
| pGFact | Proton g factor | 5.585694701 |
| pGyrMag | Proton gyromagnetic ratio (1 / s tesla) | 2.67522205e+8 |
| pMagMom | Proton magnetic moment (joule / tesla) | 1.41060671e-26 |
| pMagMomSh | Shielded proton magnetic moment (joule / tesla) | 1.41057047e-26 |
| pMagSh | Proton magnetic shielding correction | 25.689e-6 |
| pMass | Proton mass (kg) | 1.67262171e-27 |
| pMassEE | Proton mass energy equivalent (joule) | 1.50327743e-10 |
| pMassMol | Proton molar mass (kg / mol) | 1.00727646688e-3 |
| pRMSCR | Proton rms charge radius (meter) | 0.8750e-15 |
| Sub-Atomic, Tau | ||
|---|---|---|
| tCompW | Tau Compton wavelength (meter) | 0.69772e-15 |
| tMass | Tau mass (kg) | 3.16777e-27 |
| tMassEE | Tau mass energy equivalent (joule) | 2.84705e-10 |
| tMassMol | Tau molar mass (kg / mol) | 1.90768e-3 |
| Universal | ||
|---|---|---|
| chImpVac | Characteristic impedence of vacuum (ohm) | 376.730313461 |
| dirac | Dirac constant (joule s) | 1.05457168e-34 |
| eConst | Electric constant (farad / meter) | 8.854187817 |
| hBar [also: auAct, dirac] | Dirac constant (joule s) | 1.05457168e-34 |
| lightSpeed | Speed of light in a vacuum (mps) | 299792458 |
| magc | Magnetic constant (newton / meter^2) | 4e-7 PI |
| newtonG | Newtonian constant of gravitation (meter^3 / kg s^2) | 6.6742e-11 |
| plk | Plank constant (joule s) | 6.6260693e-34 |
| plkLength | Plank length (meter) | 1.61624e-35 |
| plkMass | Plank mass (kg) | 2.17645e-8 |
| plkTemp | Plank temperature (Kelvin) | 1.41679e+32 |
| plkTime | Plank time (s) | 5.39121e-44 |
| X-Ray | ||
|---|---|---|
| angStar | Angstrom star (meter) | 1.00001509e-10 |
| cuXU | Cu x unit (meter) | 1.00207710e-13 |
| moXU | Mo x unit (meter) | 1.00209966e-13 |
| siLP | Lattice parameter of silicon (meter) | 543.102122e-12 |
| siLS | {220} lattice spacing of silicon (meter) | 192.0155965e-12 |
| siMV | Molar volume of silicon (meter^3 / mol) | 12.0588382e-6 |