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