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RF Calculations & RF Unit Conversions

Note: The decimal point "." is used as decimal separator for both input and output:

Calculate wavelength from frequency:

Formula:
λ = c/f
λ: Wavelength in meters
c: Speed of light (299792458 m/s)
f: Frequency in Hz

Input frequency in Hz:

Calculate frequency from wavelength:

Formula:

λ = c/f
λ: Wavelength in meters
c: Speed of light (299792458 m/s)
f: Frequency in Hz

Input wavelength in m:

Conversion between different units of Power Flux Density:

Power Flux Density in W/m2:

Power Flux Density in mW/m2:

Power Flux Density in uW/m2:

Power Flux Density in W/cm2:

Power Flux Density in mW/cm2:

Power Flux Density in uW/cm2:

Calculate 3-axis Field Intensity from 1-axis Mesurement:

Formula:
Field Intensity = √ (x2 + y2 + z2)
E: 3-axis Field intensity, measured in V/m
X, Y, Z: Single axis field intensity, measured in V/m.

Note:
Some instruments only measure single axis field intensity. This calculation is used to calculate the 3-axis field intensity from 3 single axis measurements.

Single axis Field Intensity (x-axis) in V/m:

Single axis Field Intensity (y-axis) in V/m:

Single axis Field Intensity (z-axis) in V/m:

Calculate Field Intensity from Power Flux Density:

Formula:
Pd = E2/Z0 = Z0*H2
Pd: Power Flux Density, measured in W/m2
E: Field Intensity for the electric field, measured in V/m.
H: Magnetic field, measured in A/m.
Z0: Impedance of free air = 120π = 377Ω

Note:
I far-field conditions Field intensity and Power Flux Density is related by free air impedance. This calculation is therefore only valid for far-field conditions.

Power Flux Density in W/m2:

Calculate Power Flux Density from Electric Field Intensity:

Formula:
Pd = E2/Z0 = Z0*H2
Pd: Power Flux Density, measured in W/m2
E: Field Intensity for the electric field, measured in V/m.
H: Magnetic field, measured in A/m.
Z0: Impedance of free air = 120π = 377Ω

Note:
I far-field conditions Field intensity and Power Flux Density is related by free air impedance. This calculation is therefore only valid for far-field conditions.

Electric Field Intensity in v/m:

Calculate Power Flux Density from an Isotropic Antenna:

Formula:
Pd = Pt / (4 * π * d2)
Pd: Power Flux Density, measured in W/m2
Pt: Transmitter Output Power, measured in W
d: Distance, measured in meters

Transmitter Output Power in Watts:

Distance in meters from transmitter:

Calculate Power Flux Density from an Directional Antenna:

Formula:
Pd = (Pt * Gt) / (4 * π * R2)
Pd: Power Flux Density, measured in W/m2
Pt: Transmitter Output Power, measured in W
Gt: Transmitter antenna gain (linear)
d: Distance, measured in meters

Transmitter Output Power in Watts:
Distance in meters from transmitter:
Gain (linear, non-dimensional) for transmitter antenna:

Conversion from Gain in dB to linear gain:

Formula:
Glinear = 10(GdB / 10)
Glinear: Gain measured in linear terms (dimensionless)
GdB : Gain measured in dB

Note:
Gain can be measured either as a purely matematical construct - in which case it is referred to as dB.
It can also be measured in decibels referenced to an isotropic antenna - in which case it is referred to as dBi
Since the gain of an isotropic antenna is 1, these units are interchangeable. 1 dB gain is equal to 1 dBi gain, but the term dBi denotes the reference to the isotropic antenna.

An alternative definition compares the antenna to the power received by a lossless half-wave dipole antenna, in which case the units are written as dBd. Since a lossless dipole antenna has a gain of 2.15 dBi, the relation between these units is: gain in dBd = gain in dBi - 2.15 dB

Gain in dB:

Conversion from power in dBm to power in Watt:

Formula:
P(W)Power = 1W * 10(P(dBm)/10) / 1000
P(W) : Electrical Power, measured in W
P(dBm) : Electrical Power, measured in dBm

Note:
dBm denotes a measurement in decibels referenced to a milliWatt

Power in dBm:

Conversion from power in dBW to power in Watt:

Formula:
P(W)Power = 1W * 10(P(dBW)/10)
P(W) : Electrical Power, measured in W
P(dBW) : Electrical Power, measured in dBW

Note:
dBW denotes a measurement in decibels referenced to a Watt

Power in dBW:

Conversion from power in Watt to power in dBm:

Formula:
P(dBm) = 10 * log10(1000 * P(W))
P(W) : Electrical Power, measured in W
P(dBm) : Electrical Power, measured in dBm

Note:
dBm denotes a measurement in decibels referenced to a milliWatt

Input power in Watt:

Conversion from power in Watt to power in dBW:

Formula:
P(dBW) = 10 * log10(1 * P(W))
P(W) : Electrical Power, measured in W
P(dBm) : Electrical Power, measured in dBW

Note:
dBW denotes a measurement in decibels referenced to a Watt

Input power in Watt:

Calculate EIRP from Transmitter Power and Gain:

Formula:
EIRP = Pt * Gt
Pt: Transmitter Power, measured i W
Gt: Transmitter Gain, measured as a linear ratio

Transmitter Power in Watt:
Linear Gain:

Calculate EIRP from Electric Field and Distance:

Formula:
EIRP = (E * d)2 / 30
E: Electrical Field, measured in V/m
d: Distance, measured in meters

Electric Field in V/m:
Distance in m:

Calculate ERP from EIRP:

Formula:
ERP = EIRP / 1.64

EIRP:

Friis Transmission Formula (calculation of received power) solved for wavelength:

Formula:
Pr = (Pt * Gt * Gr * λ2 ) / (4*pi*d)2
Pr : Received Power, measured in W
Pt : Transmittet Power, measured in W
Gt : Transmitter Antenna Gain, linear
Gr : Receiver Antenna Gain, linear
λ : Wavelength, measured in meters
d : Distance, measured in meters

Transmitter Power (W):
Transmitter gain (linear):
Wavelength (m):
Distance (m):

Calculate Safety Distance from a transmitter:

Formula:
Pd = (Pt * Gt) / (4 * π * d2)
Pd: Power Flux Density, measured in W/m2
Pt: Transmitter Power, measured in W
Gt: Transmitter Antenna Gain, linear
d: Distance, measured in meters

Note:
Safety distances are calculated using:
SBM2008 "No Concern"-Limit: 0.0000001 W/m2
BioInitiative 2012 "Precautionary Level": 0.000003 W/m2

Transmitter Output Power in Watts:
Gain (linear, non-dimensional) for transmitter antenna: