Constant | Value | Units | Description |
---|---|---|---|
ALPHAMASS | 6.6446565×10-27 | kg | Alpha particle mass |
APERY | 1.202056903159594 | Apery's Constant: ζ3 = 1 + 1/23 + 1/33 + 1/43 + ... | |
ASTROUNIT | 1.495979×108 | km | au = astronomical unit (mean distance between the Earth and the Sun) ≈ 92.956×106 mi |
ATMOSPHERE | 1.01325×105 | Pa | atm = standard atmosphere |
ATOMICMASS | 1.66053886×10-27 | kg | amu = atomic mass unit |
AVOGADRO | 6.02214153×1023 | /mol | Avogadro constant |
BOHRMAGN | 927.400949×10-26 | J/T | Bohr magneton |
BOHRRADIUS | 0.5291772108×10-10 | m | Bohr radius: size of the ground state hydrogen atom |
BOLTZMANN | 1.3806505×10-23 | J/K | Boltzmann constant |
BTUPKJ | 0.94782 | Conversion factor - BTUs per kJoule | |
c† ⇒ LIGHTSPEED | 2.99792458×108 | m/s | c = Speed of light in a vacuum |
CALORIE | 4.1868 | J | Energy required to raise the temperature of one gram of water by one degree centigrade at atmospheric pressure |
CALPJ | 0.23885 | Conversion factor - calories per Joule | |
CATALAN | 0.915965594177219 | K = Catalan's constant | |
COMPTON | 2.426310238×10-12 | m | Λc = Compton Wavelength |
CONDQ | 7.748091733*10-5 | S | G0 = Conductance Quantum |
CUBERT2 | 1.259921049894873 | ³√2 | |
CUBERT3 | 1.442249570307408 | ³√3 | |
D2RADIANS | 1.745329251994×10-2 | 2π/360 - Angle
conversion factor: D2RADIANS × degrees = radians | |
DAYLENGTH | 86164.09 | s | Seconds per sidereal day (1 day = 23h 56m 4.09s) |
DEUTERONMASS | 3.34358335×10-27 | kg | deuteron mass |
Constant | Value | Units | Description |
e† ⇒ ENATURAL | 2.718281828459045 | e = base of the natural logarithms | |
EINV | 0.367879441171442 | 1.0/e | |
ELECTRIC | 8.854187817×10-12 | F/m | ε0 = 1/(μ0c2) = Electric constant: permittivity of vacuum |
ELECTRONMASS | 9.1093826×10-31 | kg | electron mass |
ELECTRONVOLT | 1.60217653×10-19 | J | eV = electron volt |
ELEMENTARYCHG | 1.60217653×10-19 | C | elementary charge |
ENATURAL (e†) | 2.718281828459045 | e = base of the natural logarithms | |
ESQUARED | 7.389056098930650 | e2 | |
ETOPI | 23.14069263277927 | eπ | |
EULER | 0.577215664901533 | Euler constant | |
FARADAY | 96485.3383 | C/mol | Faraday constant |
FINESTRUCT | 7.297352568×10-3 | Fine-structure constant | |
FIVEK | 3.106856 | mi | 5,000 meters |
FOOT | 0.3048 | m | Unit of length in the British System (12 inches) |
FOURTHPI | 0.785398163397448 | π/4 (45°) | |
FTLBFPJOULE | 1.35581795 | Conversion factor - ft-lbf per joule | |
g† ⇒ GRAVITY | 9.80665 | m/s² | g = standard acceleration of gravity (≈ 32.174 ft/s²) |
GALUKPL | 0.219969 | Conversion factor - UK gallons per liter | |
GALUSPL | 0.264172 | Conversion factor - US gallons per liter | |
GASCONST | 8.314472 | J/mol/K | R = Molar Gas Constant |
GRAM | 2.20462*10-3 | lb | Unit of mass in the Metric System (0.03527 oz) |
GRAVITATIONAL | 6.6742×10-11 | m3/kg/s2 | G = Gravitational constant |
GRAVITY (g†) | 9.80665 | m/s2 | g = standard acceleration of gravity (≈ 32.174 ft/s²) |
h† ⇒ PLANCK | 6.6260693×10-34 | Js | h = Planck constant |
HALFMARATHON | 13.109375 | mi | Half Marathon: 13mi 192.5yds ≈ 21.0975km |
HALFPI | 1.5707963267949 | π/2 (90°) | |
Constant | Value | Units | Description |
HARTREE | 4.35974417×10-18 | J | Hartree constant = 2×(binding energy of the ground state electron in the hydrogen atom) |
INCH | 0.0254 | m | unit of length in British System |
INVFINESTR | 137.03599911 | α-1 = Inverse of the fine-structure constant | |
JOSEPHSON | 483597.879×109 | hz/V | Kj = Josephson constant |
JOULEPCAL | 4.1868 | Conversion factor - Joules per calorie | |
JOULEPFTLBF | 0.73756215 | Conversion factor - joules per ft-lbf | |
KGPLB | 0.45359237 | Conversion factor - kilograms per pound. Same value as POUND | |
KJOULEPBTU | 1.05506 | Conversion factor - kJoules per BTU | |
KM | 0.6213712 | mi | 1 kilometer |
KMPMI | 1.609344 | Conversion factor - kilometers per mile. Same value as MILE | |
KNOT | 1.15078 | mi/hr | 1 knot (international) |
LBPKG | 2.2046226 | Conversion factor - pounds per kilogram | |
LIGHTSPEED (c†) | 2.99792458×108 | m/s | c = Speed of light in a vacuum |
LIGHTYEAR | 9.46053×1012 | km | Distance light travels in a year ≈ 5.8785×1012 mi |
LITERPGALUK | 4.54609 | Conversion factor - liters per UK gallon | |
LITERPGALUS | 3.7854118 | Conversion factor - liters per US gallon | |
LN10 | 2.302585092994046 | ln(10) = natural logarithm of 10 | |
LN2 | 0.693147180559945 | ln(2) = natural logarithm of 2 | |
LN3 | 1.098612288668110 | ln(3) = natural logarithm of 3 | |
LOG102 | 0.301029995663981 | log10(2) | |
LOG103 | 0.477121254719662 | log10(3) | |
LOG10E | 0.444294481903252 | log10(e) | |
LUNARMONTH | 29.5306 | days | Days per lunar month |
Constant | Value | Units | Description |
MAGNETIC | 12.566370614×10-7 | N/A2 | μ0 = Magnetic constant: permeability of vacuum |
MAGNFLUXQ | 2.06783372*10-15 | Wb | Φ0 = Magnetic flux quantum |
MARATHON | 26.21875 | mi | The Marathon: 26mi 385yds ≈ 42.195km |
METER | 39.37008 | in | Unit of length in the Metric System (3.28084 ft) |
METERPYD | 0.9144002 | Meters per yard | |
METRICMILE | 0.9320568 | mi | 1500 meters |
MILE | 1.609344 | km | 1 mile (5,280 ft) |
MILEPKM | 0.6213712 | Conversion factor - miles per kilometer. Same value as KM | |
MUONMASS | 1.8835314×10-28 | kg | Muon mass |
NAUTMILE | 1.15078 | mi | 1 nautical mile |
NEUTRONMASS | 1.67492728×10-27 | kg | Neutron mass |
NUCLMAGN | 5.05078343×10-27 | J/T | Nuclear magneton |
OUNCE | 0.028349523125 | kg | Unit of mass in the British System |
PARSEC | 3.262 | ly | Distance from the Sun resulting in a parallax of 1 second of arc as seen from Earth (3.086×1013 km ≈ 1.9176×1013 mi) |
PERATIO | 1836.15267261 | Proton-electron mass ratio | |
PHI | 1.618033988749895 | Golden Ratio: Φ =
½(1+√5
)
Note: (1/Φ) = (Φ-1) | |
PHIINV | 0.6180339887498948 | 1/Φ Note: PHIINV = (1/Φ) = (Φ−1) | |
PI | 3.141592653589793 | π = circumference/diameter for a circle | |
PIINV | 0.318309886183791 | 1.0/π | |
PIINVSQRT | 0.5641895835477563 | 1.0/√π | |
PISQUARED | 9.869604401089359 | π2 | |
PITOE | 22.45915771836105 | πe | |
Constant | Value | Units | Description |
PLANCK (h†) | 6.6260693×10-34 | Js | h = Planck constant |
PLANCK2PI | 1.05457168×10-34 | Js | h(bar) = Planck constant(h)/(2π) (a.k.a. Dirac's Constant) |
POUND | 0.45359237 | kg | Unit of mass in the British System (16 ounces) |
PROTONMASS | 1.67262171×10-27 | kg | Proton mass |
RADIANS2D | 57.295779513082 | 360/(2π) - Angle
conversion factor: RADIANS2D × radians = degrees | |
RADIUSEARTH | 3956.6 | mi | Radius of the Earth (≈ 6367.5 km) |
RADIUSMARS | 2104.1 | mi | Radius of Mars (≈ 3386.2 km) |
RADIUSMOON | 1079.6 | mi | Radius of the Moon (≈ 1737.5 km) |
RYDBERG | 10973731.568525 | /m | Rydberg constant |
SIXTHPI | 0.523598775598299 | π/6 (30°) | |
SOUNDSPEED | 331.36 | m/s | Speed of sound in dry air at 0° C. (Approximations: 1193km/hr ≈ 741mph ≈ 1087ft/sec). See SpeedOfSound() for impact of temperature. |
SQRT10 | 3.162277660168379 | √10 | |
SQRT2 | 1.414213562373095 | √2 | |
SQRT3 | 1.732050807568877 | √3 | |
SQRT5 | 2.236067977499790 | √5 | |
SQRT6 | 2.449489742783178 | √6 | |
SQRT7 | 2.645751311064591 | √7 | |
SQRT8 | 2.828427124746190 | √8 = 2 √2 | |
SQRTE | 1.64872127070013 | √e | |
SQRTPI | 1.77245385090552 | √π | |
STEFANBOLTZ | 5.670400×10-8 | W/m2/K4 | Stefan-Boltzmann constant |
TAUMASS | 3.16777×10-27 | kg | Tau mass |
TENK | 6.213712 | mi | 10,000 meters |
THIRDPI | 1.0471975511966 | π/3 (60°) | |
TWOPI | 6.28318530717959 | 2π | |
YARDPM | 1.093613 | Yards per meter | |
YEAR | 365.2425 | days | Days per year |
Constant | Value | Units | Description |
AEROBICDANCE | PINGPONG | SQUASH |
AEROBICSHI | RACKETBALL | STEPCOUNT |
AEROBICSLO | ROLLERBLADING | SWIMMINGFM |
BASKETBALL | ROLLERSKATING | SWIMMINGFY |
CYCLING | ROWING | SWIMMINGMM |
GOLFCARRY | RUNNING | SWIMMINGMY |
GOLFWALK | SKIINGCC | TAICHI |
HANDBALL | SKIINGDH | TENNISD |
HOCKEY | SKIINGWATER | TENNISS |
ICESKATING | SKIPROPE | VOLLEYBALL |
JUDO | SNOWSHOEING | WALKING |
KARATE | SNOWSHOVELING | WATERAEROBICS |
LACROSSE | SOCCER |
|
|
AUTUMN | EASTER | HANUKKAH | LINCOLN | SPRING | VETERANS |
CHANUKKAH | FALL | IDES | MEMORIAL | STPATS | WASHINGTON |
CHRISTMAS | FATHERS | JULY4 | MLK | SUMMER | WINTER |
CINCODEMAYO | GOODFRIDAY | KWANZAA | MOTHERS | THANKSGIVING | XMAS |
COLUMBUS | HALLOWEEN | LABOR | PRESIDENTS | VALENTINES |
1) | A simple equation with a constant, two functions, and two variables |
2) | Calculate race times and race paces |
3) | Calculate calories consumed during a bike ride and other actvities |
4) | Investigate mortgage payoff strategies (various extra payments each month) |
5) | Calculate the implications of refinancing a mortgage |
x | |
---|---|
omega | |
tr | x | omega | ||
---|---|---|---|---|
------ | --- | --------- | ||
Max | 1) | 1.6864589 | 5 | 5.18 |
2) | -0.9853364 | 5 | 9.1 | |
3) | 1.534163 | 5 | 17.104 | |
4) | -0.500223 | 7 | 5.18 | |
5) | -1.0239357 | 7 | 9.1 | |
Min | 6) | -1.5780752 | 7 | 17.104 |
Mdn | 7) | 0.2603652 | 10 | 5.18 |
8) | 1.5068937 | 10 | 9.1 | |
9) | 1.6523817 | 10 | 17.104 |
xmin | |
---|---|
Dist (mi) | Time | Pace | ||
---|---|---|---|---|
The Marathon: | 26.21875 | 3:00:00 | 6:52/mi | (8.74 mph) |
The Marathon: | 26.21875 | 3:10:00 | 7:15/mi | (8.28 mph) |
The Marathon: | 26.21875 | 3:20:00 | 7:38/mi | (7.87 mph) |
The Marathon: | 26.21875 | 3:30:00 | 8:01/mi | (7.49 mph) |
The Marathon: | 26.21875 | 3:40:00 | 8:23/mi | (7.15 mph) |
The Marathon: | 26.21875 | 3:50:00 | 8:46/mi | (6.84 mph) |
Function | Args | Results | Prototype/Description | Expr Use? | |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
Calories | 5 | text | Calories( activity, weight, dist,
min, sec ): Approximate calories consumed by
various activities. Arguments as in the table
below. For example: "Calories( running, 165, 3.25, 25,
20 )" yields "408 calories -- Running (165 lbs, 3.25mi
in 25:20 => 7:48/mi = 7.70 mph)". See also
Fitness(), HeartRate(), Karvonen(), Points(), Bmi()
|
No |
Function | Args | Results | Prototype/Description | Expr Use? |
---|---|---|---|---|
Payoff2 | 4 | table | Payoff2( payment, rate,
balance, extra ): Show impact of extra amount
submitted with each future mortgage payment when the loan is
partly paid off: payment = Monthly payment (principal + interest only: no escrow) rate = Annual interest rate (percent - e.g., 5.85) balance = Current balance (principal) extra = Extra amount with each payment Same as PayoffExtra2(). See also Refinance(), Mortgage(), and the other Payoff*() functions. |
No |
Standard | $200 extra | |
---|---|---|
--------------- | -------------- | |
Balance | $204,237 | $204,237 |
Payment | $1,331.76 | $1,531.76 |
Last payment | $447.13 | $47.65 |
Months | 334 | 240 |
Interest | $239,687 | $161,902 |
% Interest | 54.0% | 44.2% |
--------------- | -------------- | |
Total | $443,923 | $366,138 |
--------------- | -------------- | |
Savings | — | $77,785 |
add | |
---|---|
Monthly | Monthly | /-------------- Saves ------------\ | Final | Total | Total | |||
---|---|---|---|---|---|---|---|---|
Extra | Payment | $ | % | Months | Payment | Interest | Payments | |
----------- | ------------- | ----------------------------------------- | ------------ | ------------------------ | -------------- | |||
0 | $1,331.76 | — | $447.13 | $239,687 | 54.0% | $443,923 | ||
$50 | $1,381.76 | $26,619 | 6.0% | 31 | $12.80 | $213,068 | 51.1% | $417,304 |
$100 | $1,431.76 | $47,323 | 10.7% | 56 | $3.15 | $192,364 | 48.5% | $396,601 |
$168.24 | $1,500 | $69,318 | 15.6% | 84 | $1,105.15 | $170,368 | 45.5% | $374,605 |
$200 | $1,531.76 | $77,785 | 17.5% | 94 | $47.65 | $161,902 | 44.2% | $366,138 |
$250 | $1,581.76 | $89,408 | 20.1% | 109 | $201.20 | $150,279 | 42.4% | $354,515 |
$300 | $1,631.76 | $99,364 | 22.4% | 122 | $257.47 | $140,322 | 40.7% | $344,559 |
$400 | $1,731.76 | $115,583 | 26.0% | 144 | $1,037.17 | $124,103 | 37.8% | $328,340 |
$500 | $1,831.76 | $128,280 | 28.9% | 161 | $580.17 | $111,406 | 35.3% | $315,643 |
Function | Args | Results | Prototype/Description | Expr Use? |
---|---|---|---|---|
Refinance | 7 | table | Refinance( currBalance,
currPayment, currRate, newRate, loanCharge, loanLoan,
newDuration ): Impact (total cost, breakeven, %
interest, et cetera) of refinancing a loan: currBalance – Current loan balance (principal) currPayment – Current loan payment (principal and interest components only) currRate – Current loan annual interest rate (percent - e.g., 7.125) newRate – New loan annual interest rate (percent - e.g., 5.75) loanCharge – Addition to principal (loan charge - e.g., closing costs, points) loanLoan – Addition to principal ("equity" payout - may be 0) newDuration – New loan duration (years) Notes: (1) Do not include escrow payments (typically taxes and insurance) with currPayment, (2) See also Mortgage() and the Payoff*() functions |
No |
Current Mortgage | New Mortgage (w/out Equity) | New Mortgage (w/ Equity) | New Mortgage (Old Payment) | |
---|---|---|---|---|
------------ | --------------- | --------------- | ---------------- | |
Interest Rate | 7.375% | 5.125% | 5.125% | 5.125% |
Equity "Loan" | 0.00 | $5,000.00 | $5,000.00 | |
Balance | $210,420.00 | $213,170.00 | $218,170.00 | $218,170.00 |
Payment | $1,885.66 | $1,699.65 | $1,739.51 | $1,885.66 |
Last Payment | $1,809.77 | $1,699.65 | $1,739.51 | $1,710.84 |
Months | 189 | 180 | 180 | 160 |
Breakeven | 15 | 37 | 22 | |
Interest | $145,893.85 | $92,767.00 | $94,941.80 | $83,360.78 |
% Interest | 40.9 | 30.3 | 30.8 | 28.1 |
------------ | --------------- | --------------- | ---------------- | |
Total To Pay | $356,313.85 | $305,937.00 | $308,111.80 | $296,530.78 |
------------ | --------------- | --------------- | ---------------- | |
Savings | — | $50,376.85 | $48,202.05 | $59,783.06 |