EE Calculators

220 formulas across 17 topics

220 formulas found

Ohm's Law

Relates voltage, current and resistance in a DC circuit.

V = I × R

📝 Worked Example

A circuit has 2A flowing through a 10Ω resistor. Find the voltage.

V = I × R

V = 2 × 10

V = 20V

💡 Good to know

Ohm's Law only holds for ohmic (linear) components like standard resistors. It breaks down for non-linear devices like diodes or transistors.

DC Power

Power dissipated or delivered in a DC circuit.

P = V × I = I²R = V²/R

📝 Worked Example

A device draws 3A at 12V. Find the power consumed.

P = V × I

P = 12 × 3

P = 36W

💡 Good to know

All three power formulas (P=VI, P=I²R, P=V²/R) give the same answer for a resistive load — pick whichever one uses the variables you already know.

Voltage Divider

Output voltage of a resistive voltage divider.

Vout = Vin × R2 / (R1 + R2)

📝 Worked Example

Vin = 12V, R1 = 1kΩ, R2 = 2kΩ. Find Vout.

Vout = Vin × R2 / (R1 + R2)

Vout = 12 × 2000 / (1000 + 2000)

Vout = 24000 / 3000 = 8V

💡 Good to know

Voltage dividers only stay accurate when the load resistance is much larger than R2. If the load draws significant current, it changes the actual output voltage — this is called the 'loading effect'.

Resistors in Series

Total resistance of resistors connected in series.

R_total = R1 + R2 + R3 + ...

Resistors in Parallel

Total resistance of resistors connected in parallel.

1/R_total = 1/R1 + 1/R2

📝 Worked Example

Two resistors, 100Ω and 200Ω, are in parallel. Find the equivalent resistance.

R_total = (R1 × R2) / (R1 + R2)

R_total = (100 × 200) / (100 + 200)

R_total = 20000 / 300 ≈ 66.7Ω

💡 Good to know

The equivalent resistance of resistors in parallel is always smaller than the smallest individual resistor — adding more parallel paths always reduces total resistance, never increases it.

Capacitor Energy

Energy stored in a capacitor.

E = ½ × C × V²

📝 Worked Example

A 100µF capacitor is charged to 50V. Find the energy stored.

E = ½ × C × V²

E = 0.5 × 0.0001 × 50²

E = 0.5 × 0.0001 × 2500 = 0.125 J

💡 Good to know

Capacitor energy increases with the square of voltage, not linearly. Doubling the voltage quadruples the stored energy, not just doubles it.

Inductor Energy

Energy stored in an inductor.

E = ½ × L × I²

Capacitive Reactance

Opposition of a capacitor to AC current.

Xc = 1 / (2π × f × C)

Inductive Reactance

Opposition of an inductor to AC current.

XL = 2π × f × L

Series RLC Impedance

Total impedance of a series RLC circuit.

Z = √(R² + (XL - Xc)²)

AC Real Power

Real (active) power in an AC circuit.

P = V × I × cos(φ)

RC Filter Cutoff Frequency

Cutoff frequency of a first-order RC low-pass or high-pass filter.

fc = 1 / (2π × R × C)

📝 Worked Example

R = 1kΩ, C = 1µF. Find the cutoff frequency.

fc = 1 / (2π × R × C)

fc = 1 / (2π × 1000 × 0.000001)

fc = 1 / 0.00628 ≈ 159 Hz

💡 Good to know

At the cutoff frequency, the output signal drops to 70.7% (-3dB) of its input amplitude — this is the standard point engineers use to define a filter's bandwidth.

RL Filter Cutoff Frequency

Cutoff frequency of a first-order RL filter.

fc = R / (2π × L)

RLC Resonant Frequency

Resonant frequency of an LC or RLC circuit.

f0 = 1 / (2π × √(LC))

Q Factor

Quality factor — sharpness of resonance.

Q = f0 / BW = (1/R) × √(L/C)

Inverting Amplifier Gain

Closed-loop voltage gain of an inverting op-amp configuration.

Av = -Rf / Rin

📝 Worked Example

An inverting amplifier has Rf = 10kΩ and Rin = 2kΩ. Find the voltage gain.

Av = -Rf / Rin

Av = -10000 / 2000

Av = -5 (signal inverted and amplified 5×)

💡 Good to know

The negative sign means the output is flipped 180° in phase compared to the input — the magnitude is amplified, but the polarity is reversed.

Non-Inverting Amplifier Gain

Closed-loop voltage gain of a non-inverting op-amp.

Av = 1 + (Rf / R1)

Op-Amp Slew Rate

Maximum rate of change of output voltage.

SR = ΔVout / Δt

BJT Current Gain (β)

DC current gain (hFE) of a BJT transistor.

β = Ic / Ib

BJT Emitter Current

Emitter current equals collector plus base current.

Ie = Ic + Ib

MOSFET Drain Current (Saturation)

PRO

Drain current of an NMOS in saturation region.

Id = (kn/2) × (Vgs - Vth)²

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Propagation Delay

Average propagation delay of a logic gate.

tpd = (tpHL + tpLH) / 2

Maximum Clock Frequency

Maximum clock frequency limited by propagation delay.

fmax = 1 / (tpd_total)

Noise Margin

High and low noise margins of a logic gate.

NMH = VOH - VIH, NML = VIL - VOL

Three-Phase Power

Total real power in a balanced three-phase system.

P = √3 × VL × IL × cos(φ)

📝 Worked Example

A balanced 3-phase load has VL = 400V, IL = 10A, and power factor 0.8. Find the real power.

P = √3 × VL × IL × cos(φ)

P = 1.732 × 400 × 10 × 0.8

P ≈ 5546 W

💡 Good to know

The √3 factor appears because of the phase relationship between the three lines in a balanced three-phase system — it accounts for the geometric relationship between line and phase quantities.

Power Factor

Ratio of real power to apparent power.

PF = P / S = cos(φ)

Transformer Turns Ratio

Relationship between turns ratio, voltage and current.

Vs/Vp = Ns/Np = Is/Ip (inverted)

📝 Worked Example

A transformer has 1000 primary turns and 100 secondary turns, with 230V on the primary. Find the secondary voltage.

Vs = Vp × (Ns / Np)

Vs = 230 × (100 / 1000)

Vs = 230 × 0.1 = 23V

💡 Good to know

This is a step-down transformer because Ns < Np, meaning secondary voltage is lower than primary. If Ns > Np instead, it would be a step-up transformer.

Decibel (Voltage)

Voltage gain expressed in decibels.

dB = 20 × log₁₀(Vout / Vin)

📝 Worked Example

An amplifier has Vin = 0.1V and Vout = 1V. Find the gain in dB.

dB = 20 × log₁₀(Vout / Vin)

dB = 20 × log₁₀(1 / 0.1)

dB = 20 × log₁₀(10) = 20 dB

💡 Good to know

Every 20dB increase represents a 10× increase in voltage gain. So 40dB means 100× gain, and 60dB means 1000× — the scale is logarithmic, not linear.

Decibel (Power)

Power gain expressed in decibels.

dB = 10 × log₁₀(Pout / Pin)

Nyquist Sampling Rate

Minimum sampling frequency to avoid aliasing.

fs ≥ 2 × fmax

RC Time Constant

Time for RC circuit to charge to 63.2% of final voltage.

τ = R × C

Skin Depth

PRO

Depth at which current density falls to 1/e of surface value.

δ = √(2ρ / (ωμ))

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Wavelength

Wavelength of an electromagnetic wave in free space.

λ = c / f

PCB Trace Width (IPC-2221)

PRO

Minimum trace width for a given current — simplified IPC-2221 external layer.

W = I / (k × ΔT^0.44 × A^0.725)

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PCB Trace Resistance

PRO

DC resistance of a PCB trace.

R = ρ × L / A

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Kirchhoff's Current Law (KCL)

Sum of currents entering a node equals sum of currents leaving.

∑i_entering = ∑i_leaving

Thévenin Voltage

Thévenin equivalent voltage equals the open-circuit voltage at terminals.

Vth = Voc (open circuit voltage)

Maximum Power Transfer

Maximum power delivered to load when RL = Rth.

Pmax = Vth² / (4 × Rth)

Current Divider

Current through a parallel branch.

Ix = Itotal × Rother / Rtotal

Star to Delta Conversion

Convert star (Y) resistor network to delta (Δ).

Rdelta = (R1×R2 + R2×R3 + R3×R1) / Rstar

Reactive Power

Reactive power stored and released by inductors and capacitors.

Q = Vrms × Irms × sin(φ)

Apparent Power

Total power supplied to an AC circuit.

S = Vrms × Irms = √(P² + Q²)

Power Factor Correction Capacitor

Capacitor needed to correct lagging power factor.

C = Qc / (ω × V²)

RMS Voltage (Sinusoidal)

RMS value of a sinusoidal voltage waveform.

Vrms = Vm / √2 = 0.707 × Vm

Angular Frequency

Angular frequency of a sinusoidal signal.

ω = 2π × f

RC Circuit Transient Response

Voltage response of RC circuit during charging or discharging.

v(t) = Vf + (Vi - Vf) × e^(-t/τ)

RL Time Constant

Time constant of an RL circuit.

τ = L / R

RLC Damping Ratio

Damping ratio determines RLC transient response type.

ζ = R / (2 × √(L/C))

Damped Natural Frequency

Actual oscillation frequency of underdamped RLC circuit.

ωd = ω0 × √(1 - ζ²)

Inductor Impedance (s-domain)

PRO

Impedance of inductor in Laplace s-domain.

Z(s) = sL

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Capacitor Impedance (s-domain)

PRO

Impedance of capacitor in Laplace s-domain.

Z(s) = 1 / (sC)

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Fundamental Frequency

PRO

Fundamental frequency and angular frequency of a periodic signal.

f0 = 1/T, ω0 = 2π/T

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Star Connection Line Voltage

Line voltage in a balanced star (Y) connected system.

VL = √3 × Vph

Delta Connection Line Current

Line current in a balanced delta (Δ) connected system.

IL = √3 × Iph

Three-Phase Reactive Power

Total reactive power in a balanced three-phase system.

Q = √3 × VL × IL × sin(φ)

Three-Phase Apparent Power

Total apparent power in a balanced three-phase system.

S = √3 × VL × IL

Mutual Inductance

Mutual inductance between two magnetically coupled coils.

M = k × √(L1 × L2)

Bode Plot Magnitude

Convert transfer function magnitude to decibels for Bode plot.

Magnitude (dB) = 20 × log₁₀|H(jω)|

DC Gain of Transfer Function

PRO

DC gain of a transfer function found by setting s=0.

K = lim(s→0) G(s)

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PID Controller Output

PRO

Output of a PID controller based on error signal.

u(t) = Kp×e + Ki×∫e dt + Kd×de/dt

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Settling Time (2%)

PRO

Time for response to settle within 2% of final value.

ts = 4 / (ζ × ωn)

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Peak Overshoot

PRO

Maximum percentage overshoot in underdamped step response.

Mp = e^(-πζ / √(1-ζ²)) × 100%

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Gain Margin

PRO

How much gain can increase before system becomes unstable.

GM = 1 / |G(jω_pc)|

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Rise Time

PRO

Time for response to rise from 10% to 90% of final value.

tr = (1.8) / ωn

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DC Motor Speed

Speed of a DC motor in terms of supply voltage and back EMF.

N = (V - Ia×Ra) / (K×φ)

DC Motor Torque

Electromagnetic torque developed by a DC motor.

T = K × φ × Ia

Back EMF of DC Motor

Back EMF generated in armature of DC motor.

Eb = V - Ia × Ra

DC Generator EMF

Generated EMF in a DC generator.

E = V + Ia × Ra

DC Machine Efficiency

Efficiency of a DC motor or generator.

η = (Pout / Pin) × 100%

Transformer Efficiency

Efficiency of a transformer accounting for core and copper losses.

η = Pout / (Pout + Pcore + Pcu) × 100%

Voltage Regulation

Percentage voltage regulation of a transformer.

VR = (Vno_load - Vfull_load) / Vfull_load × 100%

Transformer Copper Loss

Copper (I²R) loss in transformer windings.

Pcu = Ia² × Ra

Synchronous Speed

Synchronous speed of an AC induction motor.

Ns = 120 × f / P

📝 Worked Example

A motor runs on a 50Hz supply with 4 poles. Find the synchronous speed.

Ns = 120 × f / P

Ns = 120 × 50 / 4

Ns = 1500 RPM

💡 Good to know

Synchronous speed depends only on supply frequency and pole count — it has nothing to do with motor load. Increasing the load changes the rotor's actual speed, not the synchronous speed itself.

Motor Slip

Slip of an induction motor — difference between sync and rotor speed.

s = (Ns - Nr) / Ns

📝 Worked Example

An induction motor has a synchronous speed of 1500 RPM and runs at 1450 RPM. Find the slip.

s = (Ns - Nr) / Ns

s = (1500 - 1450) / 1500

s = 50 / 1500 = 0.033 = 3.3%

💡 Good to know

Slip can never be zero in a running induction motor. Without relative motion between the rotor and the magnetic field, no current is induced in the rotor, so no torque is produced.

Rotor Frequency

Frequency of currents in the rotor of an induction motor.

fr = s × f

Motor Mechanical Output Power

Mechanical power output from induction motor.

Pmech = (1 - s) × Pair_gap

Half Wave Rectifier (DC output)

Average DC output voltage of a half-wave rectifier.

Vdc = Vm / π

Full Wave Rectifier (DC output)

Average DC output voltage of a full-wave rectifier.

Vdc = 2Vm / π

Ripple Factor

Measure of AC ripple in DC output of a rectifier.

RF = Vac_rms / Vdc

Duty Cycle

Duty cycle of a switching converter or PWM signal.

D = ton / T = ton × f

Buck Converter Output Voltage

Output voltage of an ideal buck (step-down) DC-DC converter.

Vout = D × Vin

Boost Converter Output Voltage

Output voltage of an ideal boost (step-up) DC-DC converter.

Vout = Vin / (1 - D)

Buck-Boost Converter Output

Output voltage of an ideal buck-boost DC-DC converter (inverted).

Vout = -Vin × D / (1 - D)

Diode Current (Shockley)

Current through a diode using the Shockley diode equation.

Id = Is × (e^(Vd/nVt) - 1)

Thermal Voltage

Thermal voltage at a given temperature (≈26mV at 300K).

Vt = kT / q

BJT Alpha (α)

Common-base current gain of a BJT transistor.

α = Ic / Ie = β / (β + 1)

BJT Transconductance

PRO

Small-signal transconductance of a BJT at operating point.

gm = Ic / Vt

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Wheatstone Bridge Balance

Balance condition for a Wheatstone bridge circuit.

R1/R2 = R3/R4

Voltmeter Sensitivity

Sensitivity of a voltmeter in ohms per volt.

S = 1 / Ifs

AM Modulation Index

PRO

Amplitude modulation index ratio of message to carrier amplitude.

ma = Am / Ac

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FM Modulation Index

PRO

Frequency modulation index ratio of frequency deviation to message frequency.

mf = Δf / fm

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Shannon Channel Capacity

PRO

Maximum data rate of a noisy channel (Shannon-Hartley theorem).

C = B × log₂(1 + SNR)

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Signal-to-Noise Ratio (dB)

Signal-to-noise ratio expressed in decibels.

SNR_dB = 10 × log₁₀(Ps / Pn)

Battery Capacity

Battery capacity in ampere-hours.

C = I × t

Battery Energy

Total energy stored in a battery.

E = V × C = V × I × t

Half-Wave Dipole Length

PRO

Physical length of a half-wave dipole antenna.

L = λ/2 = c / (2f)

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Free Space Path Loss

PRO

Signal attenuation in free space between transmitter and receiver.

FSPL = (4πd/λ)² = (4πdf/c)²

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Norton Current

Norton equivalent current equals short-circuit current at terminals.

In = Vth / Rth

Capacitors in Series

Total capacitance of capacitors in series.

1/C_total = 1/C1 + 1/C2

Capacitors in Parallel

Total capacitance of capacitors in parallel.

C_total = C1 + C2 + C3

Inductors in Series

Total inductance of inductors in series.

L_total = L1 + L2 + L3

Inductors in Parallel

Total inductance of inductors in parallel.

1/L_total = 1/L1 + 1/L2

Electric Charge

Electric charge transferred by current over time.

Q = I × t

Conductance

Electrical conductance is the reciprocal of resistance.

G = 1 / R

Resistance from Resistivity

Resistance of a conductor based on material and dimensions.

R = ρ × L / A

Resistance vs Temperature

Change in resistance due to temperature change.

R2 = R1 × (1 + α × ΔT)

Period and Frequency

Relationship between period and frequency of a signal.

T = 1 / f

Impedance Magnitude

Magnitude of complex impedance.

|Z| = √(R² + X²)

Phase Angle

Phase angle between voltage and current in AC circuit.

φ = tan⁻¹(X / R)

Filter Bandwidth

Bandwidth of a bandpass filter.

BW = f2 - f1 = f0 / Q

LC Filter Resonant Frequency

Resonant frequency of an LC filter circuit.

f0 = 1 / (2π√(LC))

-3dB Cutoff Point

At cutoff frequency, output is 70.7% of maximum (−3dB).

|H(fc)| = 0.707 × |H|max

Summing Amplifier

Output of an inverting summing op-amp amplifier.

Vout = -Rf × (V1/R1 + V2/R2)

Op-Amp Differentiator Gain

PRO

Output of an op-amp differentiator circuit.

Vout = -Rf × C × dVin/dt

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Op-Amp Integrator Gain

PRO

Gain of op-amp integrator at a given frequency.

Vout = -1/(RC) × ∫Vin dt

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Op-Amp Gain-Bandwidth Product

Gain-bandwidth product is constant for an op-amp.

GBW = Av × f

Binary to Decimal

Convert binary number to decimal.

D = Σ(bit × 2^position)

Fan-Out

Maximum number of gates a logic gate output can drive.

Fan-out = IOH / IIH

CMOS Dynamic Power

PRO

Dynamic power dissipation in CMOS logic gates.

P = α × C × V² × f

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Steady State Error (Step)

PRO

Steady state error for step input with position constant Kp.

ess = 1 / (1 + Kp)

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Phase Margin

PRO

Phase margin indicates stability — positive PM means stable.

PM = 180° + ∠G(jωgc)

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Natural Frequency from Char. Eq.

PRO

Natural frequency of a second order system.

ωn = √(K / (LC))

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Transmission Line Losses

Power lost in transmission line resistance.

Ploss = I² × R_line

Per Unit Value

Per unit system normalizes power system quantities.

PU = Actual Value / Base Value

Base Impedance

PRO

Base impedance for per unit calculations in power systems.

Zbase = Vbase² / Sbase

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DC Motor Input Power

Electrical input power to a DC motor armature.

Pin = V × Ia

DC Motor Mechanical Power

Mechanical power developed in DC motor armature.

Pmech = Eb × Ia

Shunt Field Current

Field current in a shunt DC machine.

If = V / Rf

Induction Motor Efficiency

Efficiency of an induction motor.

η = Pmech / Pin × 100%

Synchronous Motor Speed

Synchronous motors run exactly at synchronous speed.

N = Ns = 120f / P

Rotor Copper Loss

Power lost in rotor resistance of induction motor.

Protor = s × Pair_gap

SCR Average Output Voltage

PRO

Average output voltage of half-wave SCR rectifier with firing angle α.

Vdc = Vm/2π × (1 + cos α)

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Single Phase Inverter Output

PRO

RMS output voltage of single phase PWM inverter.

Vout_rms = Vdc × √(2D - 1)

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Switching Losses

PRO

Power lost during switching transitions in power converters.

Psw = Vdc × Io × (tr + tf) × f / 2

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Magnetic Flux

Magnetic flux through a surface.

Φ = B × A × cos(θ)

Faraday's Law

Induced EMF is proportional to rate of change of magnetic flux.

EMF = -N × dΦ/dt

Ampere's Law (MMF)

Magnetomotive force in a magnetic circuit.

MMF = N × I = H × l

Magnetic Reluctance

Opposition to magnetic flux in a magnetic circuit.

R = l / (μ × A)

Magnetic Field in Solenoid

Magnetic flux density inside a solenoid.

B = μ × N × I / l

Solar Panel Power

Power output of a solar panel.

P = η × A × G

Wind Turbine Power

Power extracted from wind by a turbine.

P = ½ × ρ × A × v³ × Cp

Solar Cell Fill Factor

Fill factor measures quality of a solar cell.

FF = Pmax / (Voc × Isc)

Transformer Current Ratio

Current ratio is inverse of turns ratio in ideal transformer.

I1/I2 = N2/N1

Transformer KVA Rating

Apparent power rating of a transformer.

S = V1 × I1 = V2 × I2

Reflected Impedance

Impedance seen at primary when load is connected to secondary.

Z1 = (N1/N2)² × Z2

Transformer Max Efficiency Condition

Maximum efficiency occurs when core loss equals copper loss.

Pcore = x² × Pcu_fl

All Day Efficiency

Energy efficiency of transformer over 24 hours.

η_allday = Energy_out / Energy_in × 100%

Auto-Transformer Ratio

Voltage ratio of an auto-transformer.

V2/V1 = N2/N1

Short Circuit Voltage %

Percentage short circuit voltage of transformer.

Vsc% = (Vsc / V1) × 100

AM Signal Bandwidth

Bandwidth of an amplitude modulated signal.

BW = 2 × fm

FM Signal Bandwidth (Carson)

Bandwidth of FM signal using Carson's rule.

BW = 2 × (Δf + fm)

AM Total Power

Total power of an AM signal including sidebands.

Pt = Pc × (1 + ma²/2)

Bit Rate

Bit rate based on sampling frequency and modulation order.

Rb = fs × log₂(M)

Friis Transmission Equation

PRO

Received power in a wireless link.

Pr = Pt × Gt × Gr × (λ/4πd)²

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Noise Figure

Degradation of SNR through a component.

NF = SNRin / SNRout (dB)

Wavelength from Frequency

Wavelength of electromagnetic wave at given frequency.

λ = c / f

PCB Via Current Capacity

Maximum current a PCB via can carry.

I = A × J

Microstrip Impedance

PRO

Characteristic impedance of a PCB microstrip trace.

Z0 ≈ 87/√(εr+1.41) × ln(5.98h / (0.8w + t))

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PCB Crosstalk (3W Rule)

3W rule to minimize crosstalk between PCB traces.

Spacing ≥ 3 × trace width

Decoupling Capacitor Value

Decoupling capacitor needed for transient current demand.

C = I × Δt / ΔV

PCB Component Power Dissipation

Junction temperature of component on PCB.

Tj = Ta + (Rθja × P)

PCB Trace Voltage Drop

Voltage drop across a PCB trace carrying current.

Vdrop = I × R_trace

Convolution (Length)

Output length of convolution of two discrete signals.

L_out = L1 + L2 - 1

Signal Energy

Total energy of a discrete time signal.

E = Σ|x(n)|²

Signal Power

Average power of a periodic signal.

P = E / T = A²

Z-Transform Time Delay

PRO

Time delay property of Z-transform.

Z{x(n-k)} = z^(-k) × X(z)

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DFT Frequency Resolution

Frequency resolution of a Discrete Fourier Transform.

Δf = fs / N

Aliasing Frequency

Apparent frequency when signal is undersampled.

fa = |f - n × fs|

Kirchhoff's Voltage Law (KVL)

Sum of all voltages around any closed loop equals zero.

∑V = 0 (around any closed loop)

Joule Heating

Heat generated by current flowing through resistance.

H = I² × R × t

Electric Field Strength

Electric field between two parallel plates.

E = V / d

Q Factor (Series RLC)

Quality factor of a series RLC circuit at resonance.

Q = ω0L / R = 1 / (ω0RC)

Q Factor (Parallel RLC)

Quality factor of a parallel RLC circuit at resonance.

Q = R / (ω0L) = ω0RC

Zener Voltage Regulator

Series resistor for zener diode voltage regulator.

Rs = (Vin - Vz) / (Iz + IL)

MOSFET Triode Region Current

PRO

Drain current of NMOS in triode (linear) region.

Id = kn × [(Vgs-Vth)Vds - Vds²/2]

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BJT Voltage Divider Bias

Base voltage in voltage divider bias circuit.

VB = Vcc × R2 / (R1 + R2)

Short Circuit Current

Short circuit current in a power system.

Isc = V / Zsc

Transmission Line Voltage Regulation

Percentage voltage regulation of a transmission line.

VR% = (Vs - Vr) / Vr × 100

Closed Loop Transfer Function

PRO

Closed loop transfer function with feedback.

T(s) = G(s) / (1 + G(s)H(s))

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Delay Time

PRO

Time for response to reach 50% of final value.

td = 1 + 0.7ζ / ωn

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Coulomb's Law

Force between two point charges.

F = k × Q1 × Q2 / r²

Gauss's Law

Total charge enclosed equals permittivity times electric flux.

Q_enc = ε0 × ΦE

Lorentz Force

Force on a charged particle in electric and magnetic fields.

F = q × (E + v × B)

Parallel Plate Capacitance

Capacitance of a parallel plate capacitor.

C = ε0 × εr × A / d

Signal Bandwidth

Bandwidth is difference between highest and lowest frequencies.

BW = fH - fL

Power Gain in dB

Power gain of an amplifier expressed in decibels.

G_dB = 10 × log₁₀(Pout/Pin)

Maximum Power Dissipation (Resistor)

Maximum power a resistor can safely dissipate.

Pmax = Vmax² / R

Electron Drift Velocity

PRO

Average velocity of electrons in a conductor.

vd = I / (n × q × A)

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RMS of Triangle Wave

RMS value of a triangular waveform.

Vrms = Vm / √3

Crest Factor

Ratio of peak value to RMS value of a waveform.

CF = Vpeak / Vrms

Form Factor

Ratio of RMS value to average value of a waveform.

FF = Vrms / Vavg

RC Charging Current

Current during capacitor charging in an RC circuit.

i(t) = (V/R) × e^(-t/RC)

Second Order Filter Passband Gain

PRO

Passband gain of a Sallen-Key second order active filter.

Av = 1 + Rf/R1

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Op-Amp CMRR

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Common Mode Rejection Ratio of an op-amp.

CMRR = Ad / Acm (dB)

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JFET Drain Current

PRO

Drain current of a JFET in saturation region.

Id = Idss × (1 - Vgs/Vp)²

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Half Adder Sum & Carry

Boolean expressions for half adder circuit.

Sum = A⊕B, Carry = A·B

Transformer No-Load Current

No-load current of a transformer combining core loss and magnetizing components.

Io = √(Ic² + Im²)

SVC Reactive Power Compensation

PRO

Reactive power provided by a Static VAR Compensator.

Qsvc = V² / Xc - V² / XL

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Root Locus Gain at Point

PRO

Gain value at a specific point on the root locus.

K = 1 / |G(s)H(s)|

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Speed of Light

Speed of light in vacuum — exact defined value.

c = 299,792,458 m/s

Elementary Charge

Charge of a single electron or proton.

e = 1.602176634 × 10⁻¹⁹ C

Vacuum Permittivity

Electric constant — permittivity of free space.

ε0 = 8.8541878128 × 10⁻¹² F/m

Vacuum Permeability

Magnetic constant — permeability of free space.

μ0 = 4π × 10⁻⁷ H/m

Characteristic Impedance of Vacuum

Free space impedance for electromagnetic waves.

Z0 = √(μ0/ε0) ≈ 376.730 Ω

Planck Constant

PRO

Fundamental constant relating energy and frequency.

h = 6.62607015 × 10⁻³⁴ J·s

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Boltzmann Constant

Relates energy at the particle level to temperature.

kB = 1.380649 × 10⁻²³ J/K

Avogadro Constant

PRO

Number of particles in one mole of substance.

NA = 6.02214076 × 10²³ /mol

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Electron Mass

PRO

Rest mass of an electron.

me = 9.10938370 × 10⁻³¹ kg

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Proton Mass

PRO

Rest mass of a proton.

mp = 1.672621924 × 10⁻²⁷ kg

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Thermal Voltage (300K)

Thermal voltage at room temperature, used in diode equations.

VT = kBT/e ≈ 25.85 mV

Silicon Bandgap Energy

Energy gap of silicon at room temperature.

Eg(Si) = 1.12 eV at 300K

Intrinsic Carrier Concentration (Si)

Intrinsic carrier concentration of silicon at room temperature.

ni ≈ 1.5 × 10¹⁰ cm⁻³ at 300K

Copper Resistivity

Electrical resistivity of copper at room temperature.

ρ(Cu) = 1.68 × 10⁻⁸ Ω·m at 20°C

Aluminum Resistivity

Electrical resistivity of aluminum at room temperature.

ρ(Al) = 2.65 × 10⁻⁸ Ω·m at 20°C

Silver Resistivity

Electrical resistivity of silver — best conductor.

ρ(Ag) = 1.59 × 10⁻⁸ Ω·m at 20°C

Standard PCB Copper Thickness (1oz)

Standard 1oz copper thickness used in PCB manufacturing.

t = 35 μm (1.4 mil)

Fine-Structure Constant

PRO

Dimensionless constant characterizing electromagnetic interaction strength.

α = e²/(4πε0ℏc) ≈ 1/137.036

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Bohr Radius

PRO

Most probable distance between proton and electron in hydrogen atom.

a0 = 5.291772109 × 10⁻¹¹ m

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GaAs Bandgap Energy

PRO

Energy gap of Gallium Arsenide — used in high frequency devices.

Eg(GaAs) = 1.42 eV

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GaN Bandgap Energy

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Energy gap of Gallium Nitride — used in power electronics.

Eg(GaN) = 3.4 eV

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