Electronics Formulas
316 formulas across 28 categories. Click any formula to use the interactive calculator.
Basic Electronics
Ohm's Law
V = I × R
Electrical Power
P = V × I
Voltage Divider
Vout = Vin × R2 / (R1 + R2)
Current Divider
I1 = Itotal × R2 / (R1 + R2)
Thévenin Equivalent
Rth = Voc / Isc
Norton Equivalent
Rn = Voc / Isc
Temperature Coefficient of Resistance
R(T) = Rref × (1 + α × ΔT)
Kirchhoff's Voltage Law (KVL)
ΣV = V₁ + V₂ + V₃ + ... = 0
Kirchhoff's Current Law (KCL)
ΣI = I₁ + I₂ + I₃ + ... = 0
Parallel Plate Capacitor
C = ε₀ × εr × A / d
Resistors
Series Resistance
Rtotal = R1 + R2 + ... + Rn
Parallel Resistance
1/Rtotal = 1/R1 + 1/R2 + ... + 1/Rn
LED Resistor
R = (Vs − Vled) / Iled
Resistor Power Derating
Pmax = Prated × (Tmax−Tamb)/(Tmax−Trated)
Resistive Attenuator
Atten = 20 × log10(R2 / (R1 + R2))
Resistor Tolerance Range
R_max = R × (1 + tol)
Resistor Thermal Noise (Johnson–Nyquist)
Vn = √(4 × k × T × R × BW)
Potentiometer Output
Vout = Vin × Rpos / Rtotal
Delta-to-Wye (Δ→Y) Transform
R_Y = (Ra × Rb) / (Ra + Rb + Rc)
Nearest E24 Resistor Value
Round to nearest standard E24 value
Capacitors
Capacitive Reactance
Xc = 1 / (2πfC)
RC Time Constant
τ = R × C
Capacitor Energy
E = ½CV²
Capacitor Charge
Q = C × V
Series Capacitance
1/Ctotal = 1/C1 + 1/C2 + ... + 1/Cn
Parallel Capacitance
Ctotal = C1 + C2 + ... + Cn
Capacitor Impedance with ESR
Z = √(ESR² + Xc²)
Capacitor Ripple Voltage
ΔV = I / (2 × f × C)
Capacitor Self-Resonant Frequency
f_SRF = 1 / (2π × √(ESL × C))
Constant-Current Capacitor Charge Time
t = C × ΔV / I
Dielectric Dissipation Factor
DF = ESR × 2πfC
Ceramic Capacitor Voltage Derating
C_eff = C_rated × factor
Inductors
Inductive Reactance
XL = 2πfL
RL Time Constant
τ = L / R
Inductor Energy
E = ½LI²
Series Inductance
Ltotal = L1 + L2 + ... + Ln
Parallel Inductance
1/Ltotal = 1/L1 + 1/L2 + ... + 1/Ln
Inductor Quality Factor
Q = 2πfL / Rdc
Inductor Peak Current Check
Ipeak = Idc + V × Δt / (2 × L)
Mutual Inductance
M = k × √(L1 × L2)
Inductor DCR Power Loss
P = I² × DCR
Toroid Core Inductance
L = AL × N²
Transformer Turns Ratio
N = V1 / V2
AC Circuits
Resonant Frequency
f = 1 / (2π√(LC))
Impedance (RLC Series)
Z = √(R² + (XL − XC)²)
Quality Factor (Bandwidth)
Q = f₀ / BW
Quality Factor (RLC)
Q = (1/R) × √(L/C)
Power Factor
PF = P / S = cos(φ)
Apparent Power
S = √(P² + Q²)
Reactive Power
Q = S × sin(φ)
RLC Circuit Bandwidth
BW = f0 / Q
AC RMS / Peak Conversion
V_rms = V_peak / √2
Transformer Turns Ratio
N = V1 / V2
Average Rectified Voltage
V_avg = 0.637 × Vpeak
Three-Phase Line vs Phase Voltage
V_line = √3 × V_phase
Power Factor Correction Capacitor
C = Qc / (ω × V²)
Transformer Efficiency
η = Pout / (Pout + Piron + Pcopper)
Inrush Current
I_inrush = Vpeak / Zsource
Complex Impedance Magnitude (RLC)
|Z| = √(R² + (ωL − 1/(ωC))²)
AC Phase Angle
φ = arctan((XL − XC) / R)
Power Triangle (S, P, Q)
S² = P² + Q²
Signal & dB
dB (Power)
dB = 10 × log₁₀(P2/P1)
dB (Voltage)
dB = 20 × log₁₀(V2/V1)
dBm to Watts
P = 10^((dBm − 30) / 10)
dBV (Voltage Level)
dBV = 20 × log10(V / 1V)
dBu (Voltage Level)
dBu = 20 × log10(V / 0.7746V)
dBm to dBW Conversion
dBW = dBm − 30
Receiver Noise Floor
NF_floor = −174 + NF + 10×log10(BW)
Effective Number of Bits
ENOB = (SINAD − 1.76) / 6.02
SINAD from ADC Bits
SINAD = 6.02 × N + 1.76
Octave & Decade Frequency Spans
octaves = log2(f2/f1), decades = log10(f2/f1)
Battery
Battery Runtime
t = Capacity / Current
Battery Energy
E = V × Capacity
Battery Loaded Voltage
Vload = Voc − I × Rint
Battery Charge Time
t = Capacity / Icharge
Battery Self-Discharge
Crem = C0 × (1 − rate)^days
Battery Temperature Derating
Ceff = Cnom × factor
Cell Balancing Current
Ibal = ΔV / Rbal
State of Charge (Coulomb Counting)
SoC = SoC_init + (I × t / Q) × 100
Battery Internal Resistance
Rint = (Voc − Vload) / I
Battery Pack Series-Parallel
Vpack = Ns × Vcell, Qpack = Np × Qcell
Battery Cycle Life Capacity Fade
Qn = Q0 × (1 − fade)^n
C-Rate to Current
I = C_rate × Q
Battery Voltage Sag
Vsag = Voc − Crate × Q × Rint
Power & Efficiency
Linear Regulator Dissipation
P = (Vin − Vout) × I
Efficiency
η = Pout / Pin
Buck Converter
Vout = Vin × D
Boost Converter
Vout = Vin / (1 − D)
Peukert Effect
t = C / I^k
Energy After Losses
Eout = Ein × η
Solar Charge Time
t = (Cap × V) / (P × η)
LDO Minimum Output
Vout_min = Vin − Vdrop
Buck Converter Input Current
Iin = Iout × Vout / (Vin × η)
SMPS Output Voltage Ripple
ΔV = Iout × D × (1−D) / (f × C)
SMPS Inductor Current Ripple
ΔI = Vin × D / (f × L)
Three-Phase Power
P = √3 × VLL × IL × cos(φ)
Flyback Converter Turns Ratio
Np/Ns = Vin×D / (Vout×(1−D))
Charge Pump Output Voltage
Vout = N × Vin − N × Vf
Buck-Boost Duty Cycle
D = Vout / (Vin + Vout)
Forward Converter Output
Vout = Vin × D × N2/N1
SMPS Input Filter Inductor
L = Vin / (ΔI × f)
Half-Bridge Dead Time
t_dead = Qgd / Igate
PFC Boost Inductor
L = Vin² × (Vout − Vin) / (Vout × ΔI × f × Pout)
Hold-Up Time Capacitor
t = C × (Vmax² − Vmin²) / (2 × P)
Switching Loss (Power Context)
Psw = 0.5 × V × I × (tr + tf) × f
Thermal
Junction Temperature
Tj = Ta + P × Rθja
Full Thermal Chain
Tj = Ta + P × (Rθjc + Rθcs + Rθsa)
Required Heatsink
Rθsa = (Tj,max − Ta) / P − Rθjc − Rθcs
Maximum Power (Junction to Case)
Pmax = (Tj − Tc) / θjc
Thermal Time Constant
τ = Cth × Rth
Forced Convection Heat Transfer
Q = h × A × ΔT
Power Derating (Temperature)
Pmax = Prated × (Tmax−T) / (Tmax−Tknee)
Natural Convection Thermal Resistance
Rsa = 1 / (h × A)
Thermal Runaway Stability Check
Stable if dP/dT < 1/Rth_ja
PCB Copper Thermal Resistance
Rth = d / (k × A)
Cooling Fan Airflow Requirement
CFM = P / (1.08 × ΔT)
Semiconductors
MOSFET Conduction Loss
P = I² × Rds(on)
MOSFET Switching Loss
P = ½ × V × I × (tr + tf) × f
BJT Total Dissipation
P = VCE × IC + VBE × IB
Diode Power Loss
P = Vf × If
Zener Regulation Resistor
R = (Vin − Vz) / (Iz + Iload)
Transistor Current Gain (β)
β = IC / IB
MOSFET Gate Drive Power
Pd = Qg × Vgs × f
MOSFET Rds(on) vs Temperature
RDS(T) = RDS_ref × (1 + tc × ΔT)
Op-Amp Slew Rate Limit
fmax = SR / (2π × Vpk)
BJT Vbe vs Temperature
Vbe(T) = Vbe_ref − 0.002 × ΔT
Diode Vf vs Temperature
Vf(T) = Vf_ref − 0.002 × ΔT
Op-Amp Input Offset Error
Vos_total = Vos + drift × ΔT
MOSFET Gate Drive Headroom
Vmargin = Vgs − Vth
BJT Emitter Bias Current
Ic ≈ (VB − 0.7) / RE
Shockley Diode Equation
I = Is × (e^(V/(n×Vt)) − 1)
IGBT Total Loss
P = Vce × Ic × D + Esw × f
MOSFET Body Diode Loss
P = Vf × If × (1 − D)
MOSFET Avalanche Energy
Eas = 0.5 × L × I² × Vbr/(Vbr − Vcc)
Varactor Diode Capacitance
C = Cj0 / (1 + V/Vbi)^m
Signal & RF
Wavelength
λ = c / f
Free Space Path Loss
FSPL = 20log(d) + 20log(f) + const
Signal-to-Noise Ratio
SNR = 10 × log₁₀(Ps/Pn)
Nyquist Sampling Rate
fs_min = 2 × fmax
Link Budget
Prx = Ptx + Gtx − Ltx − FSPL + Grx − Lrx
Antenna Gain
G = 10 × log₁₀(4πAe/λ²)
Skin Depth
δ = 1 / √(πfμσ)
Friis Noise Figure (3-stage)
NFtotal = NF1 + (NF2−1)/G1 + (NF3−1)/(G1×G2)
Thermal Noise Power
Pn = k × T × BW
VSWR
VSWR = (1 + |Γ|) / (1 − |Γ|)
Return Loss
RL = −20 × log10(|Γ|)
Effective Radiated Power
ERP = Ptx × Gt
Third-Order Intercept Point
OIP3 = Pout + (IIP3 − Pin) / 2
Equivalent Noise Temperature
Te = T0 × (NF − 1)
Group Delay (Approximation)
τg ≈ 1 / (2π × BW)
Reflection Coefficient
Γ = (ZL − Z0) / (ZL + Z0)
Insertion Loss from S21
IL = −20 × log10(|S21|)
Doppler Frequency Shift
Δf = fc × v / c
Radar Range Equation
Rmax = (Pt×Gt×Gr×λ²×σ / ((4π)³×Smin))^0.25
Carson's Rule FM Bandwidth
BW = 2 × (Δf + fm)
Filters
RC Low-Pass Filter
fc = 1 / (2πRC)
RC High-Pass Filter
fc = 1 / (2πRC)
Bandpass Bandwidth
BW = f2 − f1
Filter Rolloff Rate
Rolloff = N × 20 dB/decade
Notch Frequency
f = 1 / (2π√(LC))
Butterworth Q Factor
Q = 1 / (2 × sin(π/(2N)))
Sallen-Key Cutoff Frequency
fc = 1 / (2π × √(R1×R2×C1×C2))
Chebyshev Filter Order
N = acosh(√(ε²s/ε²p)) / acosh(fs/fp)
Bessel Filter Group Delay
τ = R × C
Active Filter Gain (MFB)
Gain = −Rf / Ri
Filter Q to Damping Ratio
Q = 1 / (2 × ζ)
LC Filter Cutoff Frequency
fc = 1 / (2π × √(L × C))
First-Order Bode Phase
φ = −arctan(f/fc)
Moving Average Filter Bandwidth
f3dB ≈ 0.443 × fs / N
Switched-Capacitor Filter Cutoff
fc = fclk / ratio
Pi-Filter Attenuation
A = 20 × log10(1/(ω² × L × C))
PCB & Traces
Trace Current Capacity (IPC-2221)
I = k × ΔT^0.44 × A^0.725
Trace Resistance
R = ρ × L / A (copper)
Trace Voltage Drop
Vdrop = I × R
Via Current Capacity (IPC-2221)
I = k × ΔT^0.44 × A^0.725
Microstrip Impedance
Z₀ ≈ (87/√(εr+1.41)) × ln(5.98h/(0.8w+t))
Stripline Impedance
Z0 = (60/√εr) × ln(4h/(0.67π×(0.8w+t)))
Differential Pair Impedance
Zdiff ≈ 2 × Z0 × (1 − 0.48 × e^(−0.96s/h))
Near-End Crosstalk
NEXT = Kb × length
Via Inductance
L = 5.08 × h × (ln(4h/d) + 1) nH
EMI Shielding Effectiveness
SE = 20 × log10(Ei / Et)
Plane Spreading Resistance
Rspread = ρ / (π × r)
Transmission Line Propagation Delay
td = length × √(LC)
Creepage/Clearance Estimate
clearance ≈ Vpeak / 500 mm
PCB Signal Propagation Velocity
vp = c / √(εr_eff)
Thermal Via Array Resistance
Rarray = Rsingle / n
Copper Weight to Thickness
t = oz × 35 µm
Annular Ring Width
AR = (Dpad − Ddrill) / 2
PCB Trace Signal Delay
td = length / vp
Controlled Impedance Tolerance
ΔZ/Z = √((Δh/h)² + (Δw/w)² + (Δεr/εr)²)
Timing & Oscillators
555 Timer Astable
f = 1.44 / ((R1 + 2×R2) × C)
555 Timer Monostable
t = 1.1 × R × C
Crystal Load Capacitance
CL = (C1×C2)/(C1+C2) + Cstray
RC Oscillator Frequency
f = 1 / (2πRC)
Crystal Frequency Stability
Δf = f0 × ppm × 1e-6
PLL Lock Time
t ≈ 2π / (ωn × ζ)
VCO Tuning Sensitivity
KVCO = Δf / ΔV
Jitter from Phase Noise
Tj = √(2 × ∫L(f)df) / (2πf0)
SPI Maximum Clock Frequency
fmax = 1 / (tsetup + thold + tprop)
CAN Bus Termination Resistor
Rterm = Z0 / 2
PLL Output Frequency
fout = fref × N / R
Delay-Matched Trace Length
Δl = vp × Δt
PWM Resolution (Bits)
bits = log2(fclk / fpwm)
Motors & Mechanical
Motor Mechanical Power
P = τ × ω
Motor Torque
τ = Kt × I
Motor Speed
n = (V − I×R) / Ke
Gear Ratio Output Torque
τout = τin × N × η
Back-EMF Voltage
Vemf = Ke × ω
Motor Efficiency
η = Pmech / Pelec
Rotational Dynamics
τ = J × α
Stepper Motor Step Angle
θ = 360 / (steps × microstep)
BLDC Motor Kv to Kt Conversion
Kt = 9.549 / Kv
Shaft (Mechanical) Power
P = τ × 2π × n / 60
Servo Load Torque
T = F × d
PWM Motor Effective Voltage
Veff = Vcc × D
Sensors & ADC
ADC Resolution (LSB)
LSB = Vref / 2^N
ADC Theoretical SNR
SNR = 6.02 × N + 1.76 dB
Steinhart-Hart Temperature
1/T = A + B×ln(R) + C×(ln(R))³
Wheatstone Bridge
Vout = Vin × (R3/(R3+R4) − R2/(R1+R2))
Linear Sensor Transfer Function
Vout = S × value + offset
Oversampling SNR Improvement
SNR_eff = SNR + 10 × log10(N)
RTD Callendar-Van Dusen
R(T) = R0 × (1 + A×T + B×T²)
Strain Gauge Resistance Change
ΔR = R × GF × ε
Hall Effect Voltage
Vh = Rh × I × B / t
NTC Thermistor Divider
Vout = Vcc × Rntc / (Rntc + Rfixed)
Capacitive Sensor Change
ΔC = ε0 × A / d
Photodiode Current
Iph = S × E × A
Thermocouple Seebeck Voltage
V = S × ΔT
Current Shunt Measurement
I = Vshunt / Rshunt
Ultrasonic Distance Measurement
d = v × t / 2
Optical Encoder Speed
n = (count / PPR) × 60 / t
Wire & Cable
Wire Resistance
R = ρ × L / A
AWG to Cross-Section Area
A = 0.012668 × 92^((36−AWG)/19.5)
Cable Voltage Drop
Vdrop = 2 × I × R/m × L
Maximum Cable Length
L = Vdrop / (2 × I × R/m)
Skin Effect AC Resistance
Rac = Rdc × (1 + (d/(2δ))²)
Coaxial Cable Impedance
Z0 = (138/√εr) × log10(D/d)
Connector Contact Resistance
Rc = ρ / (π × a)
Cable Shielding Effectiveness
SE = 20 × log10(1 + 2πfµσt²)
AWG Wire Ampacity Estimate
I_max ≈ 10^((40 − AWG)/15)
Coaxial Cable Loss
α ≈ R / (2 × Z0) dB/m
Coax Electrical vs Physical Length
l_elec = l_phys × VF
AWG to Cross-Section Area
A = 0.012668 × 92^((36−AWG)/19.5)
Op-Amps
Non-Inverting Amplifier
Vout = Vin × (1 + Rf/Ri)
Inverting Amplifier
Vout = −Vin × Rf/Ri
Summing Amplifier
Vout = −Rf × (V1/R1 + V2/R2 + V3/R3)
Difference Amplifier
Vout = (Rf/Ri) × (V2 − V1)
Gain-Bandwidth Product
GBW = Gain × f
Common-Mode Rejection Ratio
CMRR = 20 × log10(Ad / Acm)
Op-Amp Integrator Gain
|Vout| = Vin / (2πfRC)
Op-Amp Differentiator Gain
|Vout| = Vin × 2πfRC
Instrumentation Amplifier Gain
G = (1 + 2R1/Rg) × (R3/R2)
Op-Amp Schmitt Trigger Hysteresis
Vhyst = Vref × R1 / (R1 + R2)
Transimpedance Amplifier Bandwidth
f3dB = √(GBW / (2π × Rf × Cf))
Digital Logic
CMOS Dynamic Power
P = C × V² × f
Rise Time to Bandwidth
BW = 0.35 / tr
Setup Time Margin
Tmargin = Tclk − Tpd − Tsetup
Static Power Dissipation
P = Vdd × Ileakage
Clock Skew Timing Margin
Tmargin = Tclk − Tskew − Tsetup
Logic Noise Margin
NMH = VOH_min − VIH_min
Digital Fanout
N = Isource / Isink_per_gate
Pull-Up Resistor for Logic
R = (Vcc − VOH) / Isink
Resistive Level Shifter Ratio
R1/R2 = (Vin − Vout) / Vout
Power Distribution
Signal Processing
Communications
UART Baud Rate Error
Error% = |actual − target| / target × 100
RS-485 Termination Resistor
R = Z_cable
RS-485 Bias Resistor
R_bias = (Vcc − V_diff_min) / I_bias
Shannon Channel Capacity
C = B × log₂(1 + SNR)
Bit Error Rate (BPSK)
BER = 0.5 × erfc(√(Eb/N0))
Wireless Link Range
d = f(Ptx, Gtx, Grx, sensitivity, freq)
Manchester Encoding Bandwidth
BW = 2 × bitrate
I²C Pull-up Resistor
R_max = t_rise / (0.8473 × C_bus)
EMC / EMI
Harmonic Frequency
f_n = n × f_sw
Differential Mode Filter Inductance
L = Z / (2πf)
Common Mode Choke Impedance
Z = V_noise / I_limit
Shielding Effectiveness
SE = 20 × log₁₀(E_inc / E_trans)
Aperture Leakage Cutoff
f_c = c / (2 × slot_length)
EMI Filter Insertion Loss Required
IL = V_measured − V_limit
ESD Clamping Voltage
V_clamp = V_br + I_esd × R_dyn
Audio Engineering
Audio Crossover Frequency
f_c = 1 / (2π√(LC))
SPL from Power & Sensitivity
SPL = sensitivity + 10 × log₁₀(P)
Audio Cable High-Frequency Rolloff
f_3dB = 1 / (2πRC)
SPL from Pressure
SPL = 20 × log₁₀(p / p_ref)
Crest Factor
CF = V_peak / V_rms
Reverberation Time (RT60)
RT60 = 0.161 × V / (α × S)
Total Harmonic Distortion
THD = √(V₂²+V₃²+V₄²+V₅²) / V₁ × 100%
Solar / Renewable
Solar Panel Power Output
P = G × η × A
Solar Array Sizing
N = E_daily / (G_peak × η × PSH)
Battery Bank Sizing
Q = (E_daily × days) / (DOD × V)
MPPT Buck Converter Duty Cycle
D = 1 − V_mpp / V_oc
Wind Turbine Power
P = 0.5 × ρ × A × v³ × Cp
European Inverter Efficiency
η_EU = weighted average of partial-load efficiencies