  Constants and Formulas

A Few Constants of Interest
Note: Values in bold are exact.
 Name Symbol Value Unit Astronomical Unit 1.49598E+11 meter Base of natural logs e 2.71828182845904 - - Degree of longitude at equator - - 68.703 miles (statute) Degree of latitude @ 40 degrees - - 69 miles (statute) Pi p 3.141592653589879 - - Radius of the Earth, Equatorial - - 6,378.388 kilometers Radius of the Earth, Equatorial - - 3,963.34 miles (statute) Radius of the Earth, Polar - - 6,356.912 kilometer Radius of the Earth, Polar - - 3,949.99 miles (statute) Sound Velocity in Dry Air @ 0 Deg.C - - 1,087.1 feet/second Sound Velocity in Dry Air @ 0 Deg.C - - 331.36 meters/second Speed of light in a vacuum c 299,792,458 meters/second

Note: Information on all constants in numerous categories is available at the NIST Reference on Constants, Units and Uncertainty. (NIST = the National Institute of Science and Technology.)

Ohm's Law
 Formula Notes: E = I x R Where: I = E / R E = EMF in Volts R = E / I I = Current in Amperes P = I2R R = Resistance in Ohms P = V2/R P = Power in Watts

Power Conversions
 Description Formula Notes Watts to dBm: dBm = 10 x Log10 [Watts x 103] Where: dBm to milliWatts: mW = 10(dBm/10) dBm = Decibels referenced one milliwatt dBm to Watts: W =10(dBm/10)/100 W = Watts; mW = milliWatts
dB Correction Factor
To correct the dB reading when the measured impedance is different from the meter's basis of calibration:
1.) dBCF = 10log(Calibration Ω / load  Ω)
2.) dBActual = dBMeter + dBCF

Where:
dBCF = Correction factor
Ω = Impedance in ohms

Frequency and Wavelength Conversions

 Formula Notes: λm = 299,792.458 / fkHz λm = 299.792458 / fmHz Where: λft = 983,571.056430446 / fkHz λm = Wavelength in meters λft = 983.571056430446 / fmHz λft = Wavelength in feet fkHz = 299,792.458 / λm fkHz = Frequency in kiloHertz fmHz = 299.792458 / λm fmHz = Frequency in megaHertz fkHz = 983,571.056430446 / λft fmHz = 983.571056430446 / λft

Free Space Attenuation
 Formula Notes: a = 96.6 + 20log10 FGHz + 20log10 Dmi Where: a = 36.6 + 20log10 FMHz + 20log10 Dmi a = Attenuation in dB a = 32.45 + 20log10 FMHz + 20log10 Dkm FGHz = Frequency in GHz FMHz = Frequency in MHz Dmi= Path distance in miles Dkm = Path distance in kilometers

Line-Of-Sight
 Description Formula Notes: Optical Line of Sight D = 0.866(v2hTX + v2hRX ) Where: D = Distance in miles Radio Line of Sight (4/3 Earth) D = v2hTX + v2hRX hTX = Height of the Transmitting Antenna in Feet hRX = Height of the Receiving Antenna in Feet

Temperature Conversion

0F = 9/50C + 320
0C = 5/9 (0F - 320)