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RF Calculators
Conversion Calculators:
A collection of tools for antenna and electrical parameter conversions.
Frequency to Wavelength
Frequency:
Formulas:
$\displaystyle \lambda \,=\, \frac{c}{f}$
$\lambda$ = Free space wavelength in meters [m].
$c$ = Speed of light in a vacuum (free space), in meters per second [m/s].
$f$ = Frequency in Hertz [Hz].
Wavelength to Frequency
Free-Space Wavelength:
Formulas:
$\displaystyle f \,=\, \frac{c}{\lambda}$
$f$ = Frequency in Hertz [Hz].
$c$ = Speed of light in a vacuum (free space), in meters per second [m/s].
$\lambda$ = Free space wavelength in meters [m].
Reactance to Inductance/Capacitance
Reactance (X) in Ohms:
Frequency in MHz:
Inductance Unit (if X ≥ 0):
Capacitance Unit (if X < 0):
Formulas:
$\displaystyle L \,=\, \frac{X}{2\pi f}\ \text{,} \quad X \ge 0$
$\displaystyle C \,=\, -\,\frac{1}{2\pi f \, X}\ \text{,} \quad X < 0$
$L$ = Inductance in Henries [H].
$C$ = Capacitance in Farads [F].
$f$ = Frequency in Hertz [Hz].
$X$ = Reactance in Ohms [$\Omega$].
Inductance to Reactance
Inductance (L):
Frequency in MHz:
Formulas:
$\displaystyle X \,=\, 2\pi f \, L$
$X$ = Reactance in Ohms [$\Omega$].
$f$ = Frequency in Hertz [Hz].
$L$ = Inductance in Henries [H].
Capacitance to Reactance
Capacitance (C):
Frequency in MHz:
Formulas:
$\displaystyle X \,=\, -\,\frac{1}{2\pi f \, C}$
$X$ = Reactance in Ohms [$\Omega$].
$f$ = Frequency in Hertz [Hz].
$C$ = Capacitance in Farads [F].
Power to dBW and dBm
Power:
Formulas:
$\displaystyle P \, \text{[dBW]} \,=\, 10 \, \log_{10} P$
$\displaystyle P \, \text{[dBm]} \,=\, P \, \text{[dBW]} \,+\, 30$
$P$ = Power in Watts [W].
dBm to Watts
Power in dBm:
Formulas:
$\displaystyle P \, \text{[W]} \,=\, 10^{ (P \,-\, 30) /10 }$
$P$ = Power in [dBm].
VSWR to Reflection Coefficient
VSWR:
Formulas:
$\displaystyle |\Gamma| \,=\, \frac{\text{VSWR} \,-\, 1}{\text{VSWR} \,+\, 1}$
$\displaystyle \text{RL} \,=\, -\,20 \, \log_{10} |\Gamma|$
$\displaystyle \text{ML} \,=\, -\,10 \, \log_{10} (1 \,-\, |\Gamma|^2)$
$\text{VSWR}$ = Voltage Standing Wave Ratio.
$|\Gamma|$ = Magnitude of the reflection coefficient.
$\text{RL}$ = Return loss in [dB].
$\text{ML}$ = Mismatch loss in [dB].
Reflection Coefficient to VSWR
Reflection Coefficient |Γ|:
Formulas:
$\displaystyle \text{VSWR} \,=\, \frac{1 \,+\, |\Gamma|}{1 \,-\, |\Gamma|}$
$\text{VSWR}$ = Voltage Standing Wave Ratio.
$|\Gamma|$ = Magnitude of the reflection coefficient.
Return Loss to VSWR
Return Loss in dB:
Formulas:
$\displaystyle |\Gamma| \,=\, 10^{- \text{RL} / 20}$
$\displaystyle \text{VSWR} \,=\, \frac{1 \,+\, |\Gamma|}{1 \,-\, |\Gamma|}$
$\text{RL}$ = Return loss in [dB].
$|\Gamma|$ = Magnitude of the reflection coefficient.
$\text{VSWR}$ = Voltage Standing Wave Ratio.
American Wire Gauge (AWG) to mm and Inches
Formulas:
$\displaystyle d \, \text{[in]} \,=\, 0.005 \times 92^{(36 \,-\, n) / 39}$
$d$ = Wire diameter in inches [in].
$n$ = Gauge number.
Antenna Propagation Calculators:
A set of tools for calculating antenna characteristics and propagation metrics.
Antenna Power Density
Antenna Input Power in Watts:
Antenna Gain in dBi:
Distance to the Antenna in Meters:
Formulas:
$\displaystyle S \,=\, G \; \frac{P}{4\pi R^2}$
$S$ = Power density in Watts per square meter [W/m2].
$G$ = Antenna gain (dimensionless).
$P$ = Antenna Input Power in Watts [W].
$R$ = Distance to the antenna in meters [m].
Antenna Near – Far Field Boundary
Antenna Maximum Dimension:
Frequency in MHz:
Formulas:
$\displaystyle \text{Near-Field – Fresnel} \,=\, 0.62 \, \sqrt{ \frac{D^3}{\lambda} }$
$\displaystyle \text{Fresnel – Far-Field} \,=\, \frac{2 D^2}{\lambda}$
$D$ = Antenna maximum dimension.
$\lambda$ = Free-space wavelength.
Antenna Downtilt and Coverage
Transmitter Height:
Receiver Height:
Unit for Heights:
Distance between Antennas in km:
Transmitter Beamwidth in degrees:
Formulas:
$\displaystyle \theta \,=\, \arctan\left( \frac{H_t \,-\, H_r}{d} \right)$
$\displaystyle R_i \,=\, \frac{H_t \,-\, H_r}{ \tan(\theta \,+\, \text{BW}/2) }$
$\displaystyle R_o \,=\, \frac{H_t \,-\, H_r}{ \tan(\theta \,-\, \text{BW}/2) }$
$\theta$ = Downtilt angle.
$R_i$ = Inner coverage radius.
$R_o$ = Outer coverage radius.
$H_t$ = Transmitter height.
$H_r$ = Receiver height.
$d$ = Distance between transmitting and receiving antennas.
$\text{BW}$ = Transmitter half-power beamwidth (HPBW).
Line of Sight and Radio Horizon
Transmitter Height:
Receiver Height:
Unit for Heights:
Formulas:
$\displaystyle \text{LoS} \,=\, 3.57 \, \sqrt{H}$
$\displaystyle R_H \,=\, 4.12 \, \sqrt{H}$
$H$ = Antenna height in meters [m].
$\text{LoS}$ = Line of Sight in kilometers [km].
$R_H$ = Radio horizon in kilometers [km].
Friis Transmission
Frequency in MHz:
Transmitter Power:
Transmitter Gain in dBi:
Receiver Gain in dBi:
Antenna Separation:
Formulas:
$\displaystyle P_r \,=\, P_t \, G_t \, G_r \left( \frac{c}{4 \pi R \, f} \right)^2$
$P_r$ = Received power in Watts [W].
$G_r$ = Receiver gain (dimensionless).
$P_t$ = Transmitter power in Watts [W].
$G_t$ = Transmitter gain (dimensionless).
$R$ = Antenna separation in meters [m].
$f$ = Operating frequency in Hertz [Hz].
$c$ = Speed of light in a vacuum (free space), in meters per second [m/s].
Free Space Path Loss
Frequency in MHz:
Transmitter Gain in dBi:
Receiver Gain in dBi:
Antenna Separation:
Formulas:
$\displaystyle \text{FSPL} \,=\, 20 \, \log_{10}(R) \,+\, 20 \, \log_{10}(f) \,+\, 20 \, \log_{10}\left(\frac{4\pi}{c}\right) \,-\, G_t \,-\, G_r$
$\text{FSPL}$ = Free Space Path Loss in [dB].
$R$ = Antenna separation in meters [m].
$f$ = Operating frequency in Hertz [Hz].
$G_t$ = Transmitter gain in [dBi].
$G_r$ = Receiver gain in [dBi].
$c$ = Speed of light in a vacuum (free space), in meters per second [m/s].
Effective Isotropic Radiated Power (EIRP)
Transmitter Output Power:
Cable and Connector Losses in dB:
Antenna Gain in dBi:
Formulas:
$\displaystyle \text{EIRP [dBm]} \,=\, P_t \,-\, C_L \,+\, G$
$\text{EIRP [dBm]}$ = Effective Isotropic Radiated Power in [dBm].
$P_t$ = Transmitter output power in [dBm].
$C_L$ = Cable and connector losses in [dB].
$G$ = Antenna gain in [dBi].
Specific Absorption Rate (SAR)
Electric Field Strength (rms) in V/m:
Conductivity of Material in S/m:
Mass Density in kg/m³:
Formulas:
$\displaystyle \text{SAR} \,=\, \frac{\sigma \, E^2}{\rho}$
$\displaystyle S \,=\, \frac{E^2}{376.73}$
$\text{SAR}$ = Specific Absorption Rate in Watts per kilogram [W/kg].
$\sigma$ = Conductivity of material in Siemens per meter [S/m].
$E$ = Electric field strength (rms) in Volts per meter [V/m].
$\rho$ = Mass density in kilograms per cubic meter [kg/m3].
$S$ = Power density in Watts per square meter [W/m2].
Skin Depth for Metals
Frequency in MHz:
Material:
Resistivity in Ohm meters (Ω.m):
Formulas:
$\displaystyle \delta \,=\, \frac{1}{\pi} \, \sqrt{ \frac{\rho}{4 \times 10^{-7} \, f} }$
$\delta$ = Skin depth in meters [m].
$\rho$ = Resistivity in Ohm meters [Ω m].
$f$ = Frequency in Hertz [Hz].
Antenna Component Calculators
These calculators help design and optimize the components that antennas rely on for efficient operation.
Single-Layer Circular Coil Inductance
Lundin Handbook Formula
Coil Diameter:
Coil Length:
Unit for Diameter and Length:
Number of Turns:
Core Relative Permeability:
Unit for Displaying Inductance:
Formulas:
$\displaystyle L_i = 10^{-7} \; \pi^2 \, \mu_r \, N^2 \, \frac{D^2}{L} \, \left[ F_1\left( \frac{D^2}{L^2} \right) \,-\, \frac{4 D}{3 \pi L} \right]\ \ \text{for} \ D \ \le L$
$\displaystyle L_i = 2 \times 10^{-7} \, \pi \, \mu_r \, N^2 \, D \left[ \left(\ln\left(\frac{4 D}{L}\right) \,-\, 0.5\right) \, F_1\left(\frac{L^2}{D^2}\right) \,+\, F_2\left(\frac{L^2}{D^2}\right) \right] \ \ \text{for} \ \ D > L$
$\displaystyle F_1(x) \,=\, \frac{1 \,+\, 0.383901 \, x \,+\, 0.017108 \, x^2}{1 \,+\, 0.258952 \, x}$
$\displaystyle F_2(x) \,=\, 0.093842 \, x \,+\, 0.002029 \, x^2 \,-\, 0.000801 \, x^3$
$L_i$ = Coil inductance in Henries [H].
$\mu_r$ = Core relative permeability.
$N$ = Number of turns.
$D$ = Coil diameter in meters [m].
$L$ = Coil length in meters [m].
Inductor Quality Factor (Q)
Frequency:
Inductance:
Internal Resistance in Ohms:
Formulas:
$\displaystyle Q \,=\, \frac{2 \pi f \, L}{R}$
$Q$ = Inductor quality factor.
$f$ = Frequency in Hertz [Hz].
$L$ = Inductance in Henries [H].
$R$ = Internal resistance in Ohms [$\Omega$].
Inductor Internal Resistance
Formulas:
$\displaystyle R \,=\, \frac{2 \pi f \, L}{Q}$
$R$ = Internal resistance in Ohms [$\Omega$].
$f$ = Frequency in Hertz [Hz].
$L$ = Inductance in Henries [H].
$Q$ = Inductor quality factor.
Insertion Loss
Select Calculation Type:
Enter Power (in Watts):
Formulas:
$\displaystyle \text{IL} \,=\, 10 \, \log_{10}\left( \frac{P_1}{P_2} \right)$
$\displaystyle \text{IL} \,=\, 20 \, \log_{10}\left( \frac{V_1}{V_2} \right)$
$\text{IL}$ = Insertion loss in [dB].
$P_1$ = Power before insertion.
$P_2$ = Power after insertion.
$V_1$ = Voltage before insertion.
$V_2$ = Voltage after insertion.
Bifilar Transmission Line
Select Calculation Type:
Enter the following parameters (same unit of length):
Formulas:
$\displaystyle Z_0 \,=\, \frac{376.73}{ \pi \, \sqrt{\varepsilon_r} } \; \cosh^{-1}\left( \frac{s}{d}\right)$
$\displaystyle S \,=\, s \,-\, d$
$Z_0$ = Characteristic impedance in Ohms [$\Omega$].
$\varepsilon_r$ = Relative dielectric constant.
$s$ = Center-to-center conductor spacing.
$d$ = Conductor diameter.
$S$ = Space between conductors.
Coaxial Transmission Line
Formulas:
$\displaystyle Z_0 \,=\, \frac{376.73}{ 2 \pi \, \sqrt{\varepsilon_r} } \; \ln\left( \frac{D}{d} \right)$
$\displaystyle L \,=\, 2 \times 10^{-7} \; \ln\left( \frac{D}{d} \right)$
$\displaystyle C \,=\, \frac{ 2 \pi \, \varepsilon_r \varepsilon_0 }{\ln\left( \frac{D}{d} \right)}$
$\displaystyle f_c \,=\, \frac{2 \, c}{ \pi \sqrt{\varepsilon_r} \, (D \,+\, d) }$
$Z_0$ = Characteristic impedance in Ohms [$\Omega$].
$\varepsilon_r$ = Relative dielectric constant.
$D$ = Outer diameter.
$d$ = Inner diameter.
$L$ = Inductance per unit length in Henries per meter [H/m].
$C$ = Capacitance per unit length in Farads per meter [F/m].
$f_c$ = Cutoff frequency in Hertz [Hz] ($D$ and $d$ in meters).
$\varepsilon_0$ = Free-space absolute dielectric constant in [F/m].
$c$ = Speed of light in a vacuum (free-space) in [m/s].
Quarter Wave Transformer
Formulas:
$\displaystyle Z_c \,=\, \sqrt{Z_L \, Z_{in}}$
$Z_c$ = Characteristic impedance of the λ/4 stub in Ohms [$\Omega$].
$Z_L$ = Load impedance in Ohms [$\Omega$].
$Z_{in}$ = Input impedance in Ohms [$\Omega$].
Transformer Turn Ratio
Formulas:
$\displaystyle \frac{N_p}{N_s} \,=\, \sqrt{ \frac{Z_p}{Z_s} }$
$N_p / N_s$ = Primary to secondary turn ratio.
$Z_p$ = Primary impedance in Ohms [$\Omega$].
$Z_s$ = Secondary impedance in Ohms [$\Omega$].