The Toolbox

Formula Reference

Essential electrical, RF, and communications formulas for exam prep and field use.

Ohm's Law & Power

V = I × RVoltage equals current times resistance

I = V / RCurrent equals voltage divided by resistance

R = V / IResistance equals voltage divided by current

P = V × IPower equals voltage times current

P = I² × RPower equals current squared times resistance

P = V² / RPower equals voltage squared divided by resistance

V = √(P × R)Voltage equals square root of power times resistance

I = √(P / R)Current equals square root of power divided by resistance

Wavelength & Antenna Length

λ = c / fWavelength (meters) = speed of light (300,000,000 m/s) divided by frequency (Hz)

λ = 300 / f(MHz)Wavelength in meters when frequency is in MHz

λ/2 = 150 / f(MHz)Half-wave antenna length in meters

λ/4 = 75 / f(MHz)Quarter-wave antenna length in meters

λ/2 (feet) = 492 / f(MHz)Half-wave antenna length in feet

λ/4 (feet) = 246 / f(MHz)Quarter-wave antenna length in feet

Reactance & Impedance

XL = 2πfLInductive reactance (Ω) — f in Hz, L in henries

XC = 1 / (2πfC)Capacitive reactance (Ω) — f in Hz, C in farads

f = 1 / (2π√LC)Resonant frequency — L in henries, C in farads

Z = √(R² + X²)Series impedance magnitude

Z = √(R² + (XL - XC)²)Series RLC impedance magnitude

θ = arctan(X / R)Phase angle between voltage and current

Decibels & Power Ratios

dB = 10 × log(P1 / P2)Power ratio to decibels

dB = 20 × log(V1 / V2)Voltage ratio to decibels

P1/P2 = 10^(dB/10)Decibels to power ratio

V1/V2 = 10^(dB/20)Decibels to voltage ratio

ERP = P × 10^(net dB/10)Effective Radiated Power — net dB = antenna gain minus all losses

Time Constants

τ = R × CRC time constant in seconds — R in ohms, C in farads

τ = L / RRL time constant in seconds — L in henries, R in ohms

V(t) = Vs × (1 - e^(-t/τ))Capacitor charging voltage at time t

V(t) = Vs × e^(-t/τ)Capacitor discharging voltage at time t

63.2%Voltage reached after 1 time constant (charging)

86.5%Voltage reached after 2 time constants (charging)

36.8%Voltage remaining after 1 time constant (discharging)

Power Factor & True Power

PF = cos(θ)Power factor equals cosine of the phase angle

True Power = VA × PFTrue power (watts) = apparent power × power factor

PF at 30° = 0.866Power factor at 30 degree phase angle

PF at 45° = 0.707Power factor at 45 degree phase angle

PF at 60° = 0.500Power factor at 60 degree phase angle

RADAR

R(max) = c / (2 × PRF)Maximum unambiguous range — c = 300,000,000 m/s

R(min) = (PW × c) / 2Minimum range — PW = pulse width in seconds

PRI = 1 / PRFPulse Repetition Interval = 1 divided by Pulse Repetition Frequency

Batteries & Motors

t = Ah / ABattery runtime (hours) = capacity (Ah) divided by load current (A)

I = P / VDC current = power divided by voltage

I = P / (V × η)DC motor current — η = efficiency as decimal (e.g. 0.85)

I = P / (V × PF × η)AC motor current — includes power factor and efficiency

1 HP = 746 WOne horsepower equals 746 watts

FM Modulation

MI = Δf / fmModulation index = frequency deviation divided by modulating frequency

DR = Δf(max) / fm(max)Deviation ratio = maximum deviation divided by maximum modulating frequency

BW = 2 × (Δf + fm)FM bandwidth (Carson's Rule) = 2 × (deviation + modulating frequency)

SSB Power

PEP = Vpeak² / (2 × R)Peak Envelope Power from peak voltage and load resistance

PEP = Vp-p² / (8 × R)Peak Envelope Power from peak-to-peak voltage

Vrms = √(P × R)RMS voltage from power and resistance

AC Voltage Conversions

Vpeak = Vrms × 1.414Peak voltage from RMS voltage (sine wave)

Vrms = Vpeak × 0.707RMS voltage from peak voltage (sine wave)

Vavg = Vrms × 0.9Average voltage from RMS voltage (sine wave)

Vp-p = Vpeak × 2Peak-to-peak voltage from peak voltage

Transformer Turns Ratio

Vs/Vp = Ns/NpSecondary voltage / Primary voltage = Secondary turns / Primary turns

Turns ratio = √(Zp / Zs)Turns ratio for impedance matching

Zs/Zp = (Ns/Np)²Impedance ratio equals turns ratio squared