EE Calculators
220 formulas across 17 topics
220 formulas found
Ohm's Law
Relates voltage, current and resistance in a DC circuit.
📝 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.
📝 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.
📝 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.
Resistors in Parallel
Total resistance of resistors connected in parallel.
📝 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.
📝 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.
Capacitive Reactance
Opposition of a capacitor to AC current.
Inductive Reactance
Opposition of an inductor to AC current.
Series RLC Impedance
Total impedance of a series RLC circuit.
AC Real Power
Real (active) power in an AC circuit.
RC Filter Cutoff Frequency
Cutoff frequency of a first-order RC low-pass or high-pass filter.
📝 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.
RLC Resonant Frequency
Resonant frequency of an LC or RLC circuit.
Q Factor
Quality factor — sharpness of resonance.
Inverting Amplifier Gain
Closed-loop voltage gain of an inverting op-amp configuration.
📝 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.
Op-Amp Slew Rate
Maximum rate of change of output voltage.
BJT Current Gain (β)
DC current gain (hFE) of a BJT transistor.
BJT Emitter Current
Emitter current equals collector plus base current.
MOSFET Drain Current (Saturation)
PRODrain current of an NMOS in saturation region.
This calculator is a Pro feature
Upgrade to Pro — $4.99/moPropagation Delay
Average propagation delay of a logic gate.
Maximum Clock Frequency
Maximum clock frequency limited by propagation delay.
Noise Margin
High and low noise margins of a logic gate.
Three-Phase Power
Total real power in a balanced three-phase system.
📝 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.
Transformer Turns Ratio
Relationship between turns ratio, voltage and current.
📝 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.
📝 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.
Nyquist Sampling Rate
Minimum sampling frequency to avoid aliasing.
RC Time Constant
Time for RC circuit to charge to 63.2% of final voltage.
Skin Depth
PRODepth at which current density falls to 1/e of surface value.
This calculator is a Pro feature
Upgrade to Pro — $4.99/moWavelength
Wavelength of an electromagnetic wave in free space.
PCB Trace Width (IPC-2221)
PROMinimum trace width for a given current — simplified IPC-2221 external layer.
This calculator is a Pro feature
Upgrade to Pro — $4.99/moPCB Trace Resistance
PRODC resistance of a PCB trace.
This calculator is a Pro feature
Upgrade to Pro — $4.99/moKirchhoff's Current Law (KCL)
Sum of currents entering a node equals sum of currents leaving.
Thévenin Voltage
Thévenin equivalent voltage equals the open-circuit voltage at terminals.
Maximum Power Transfer
Maximum power delivered to load when RL = Rth.
Current Divider
Current through a parallel branch.
Star to Delta Conversion
Convert star (Y) resistor network to delta (Δ).
Reactive Power
Reactive power stored and released by inductors and capacitors.
Apparent Power
Total power supplied to an AC circuit.
Power Factor Correction Capacitor
Capacitor needed to correct lagging power factor.
RMS Voltage (Sinusoidal)
RMS value of a sinusoidal voltage waveform.
Angular Frequency
Angular frequency of a sinusoidal signal.
RC Circuit Transient Response
Voltage response of RC circuit during charging or discharging.
RL Time Constant
Time constant of an RL circuit.
RLC Damping Ratio
Damping ratio determines RLC transient response type.
Damped Natural Frequency
Actual oscillation frequency of underdamped RLC circuit.
Inductor Impedance (s-domain)
PROImpedance of inductor in Laplace s-domain.
This calculator is a Pro feature
Upgrade to Pro — $4.99/moCapacitor Impedance (s-domain)
PROImpedance of capacitor in Laplace s-domain.
This calculator is a Pro feature
Upgrade to Pro — $4.99/moFundamental Frequency
PROFundamental frequency and angular frequency of a periodic signal.
This calculator is a Pro feature
Upgrade to Pro — $4.99/moStar Connection Line Voltage
Line voltage in a balanced star (Y) connected system.
Delta Connection Line Current
Line current in a balanced delta (Δ) connected system.
Three-Phase Reactive Power
Total reactive power in a balanced three-phase system.
Three-Phase Apparent Power
Total apparent power in a balanced three-phase system.
Mutual Inductance
Mutual inductance between two magnetically coupled coils.
Bode Plot Magnitude
Convert transfer function magnitude to decibels for Bode plot.
DC Gain of Transfer Function
PRODC gain of a transfer function found by setting s=0.
This calculator is a Pro feature
Upgrade to Pro — $4.99/moPID Controller Output
PROOutput of a PID controller based on error signal.
This calculator is a Pro feature
Upgrade to Pro — $4.99/moSettling Time (2%)
PROTime for response to settle within 2% of final value.
This calculator is a Pro feature
Upgrade to Pro — $4.99/moPeak Overshoot
PROMaximum percentage overshoot in underdamped step response.
This calculator is a Pro feature
Upgrade to Pro — $4.99/moGain Margin
PROHow much gain can increase before system becomes unstable.
This calculator is a Pro feature
Upgrade to Pro — $4.99/moRise Time
PROTime for response to rise from 10% to 90% of final value.
This calculator is a Pro feature
Upgrade to Pro — $4.99/moDC Motor Speed
Speed of a DC motor in terms of supply voltage and back EMF.
DC Motor Torque
Electromagnetic torque developed by a DC motor.
Back EMF of DC Motor
Back EMF generated in armature of DC motor.
DC Generator EMF
Generated EMF in a DC generator.
DC Machine Efficiency
Efficiency of a DC motor or generator.
Transformer Efficiency
Efficiency of a transformer accounting for core and copper losses.
Voltage Regulation
Percentage voltage regulation of a transformer.
Transformer Copper Loss
Copper (I²R) loss in transformer windings.
Synchronous Speed
Synchronous speed of an AC induction motor.
📝 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.
📝 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.
Motor Mechanical Output Power
Mechanical power output from induction motor.
Half Wave Rectifier (DC output)
Average DC output voltage of a half-wave rectifier.
Full Wave Rectifier (DC output)
Average DC output voltage of a full-wave rectifier.
Ripple Factor
Measure of AC ripple in DC output of a rectifier.
Duty Cycle
Duty cycle of a switching converter or PWM signal.
Buck Converter Output Voltage
Output voltage of an ideal buck (step-down) DC-DC converter.
Boost Converter Output Voltage
Output voltage of an ideal boost (step-up) DC-DC converter.
Buck-Boost Converter Output
Output voltage of an ideal buck-boost DC-DC converter (inverted).
Diode Current (Shockley)
Current through a diode using the Shockley diode equation.
Thermal Voltage
Thermal voltage at a given temperature (≈26mV at 300K).
BJT Alpha (α)
Common-base current gain of a BJT transistor.
BJT Transconductance
PROSmall-signal transconductance of a BJT at operating point.
This calculator is a Pro feature
Upgrade to Pro — $4.99/moWheatstone Bridge Balance
Balance condition for a Wheatstone bridge circuit.
Voltmeter Sensitivity
Sensitivity of a voltmeter in ohms per volt.
AM Modulation Index
PROAmplitude modulation index ratio of message to carrier amplitude.
This calculator is a Pro feature
Upgrade to Pro — $4.99/moFM Modulation Index
PROFrequency modulation index ratio of frequency deviation to message frequency.
This calculator is a Pro feature
Upgrade to Pro — $4.99/moShannon Channel Capacity
PROMaximum data rate of a noisy channel (Shannon-Hartley theorem).
This calculator is a Pro feature
Upgrade to Pro — $4.99/moSignal-to-Noise Ratio (dB)
Signal-to-noise ratio expressed in decibels.
Battery Capacity
Battery capacity in ampere-hours.
Battery Energy
Total energy stored in a battery.
Half-Wave Dipole Length
PROPhysical length of a half-wave dipole antenna.
This calculator is a Pro feature
Upgrade to Pro — $4.99/moFree Space Path Loss
PROSignal attenuation in free space between transmitter and receiver.
This calculator is a Pro feature
Upgrade to Pro — $4.99/moNorton Current
Norton equivalent current equals short-circuit current at terminals.
Capacitors in Series
Total capacitance of capacitors in series.
Capacitors in Parallel
Total capacitance of capacitors in parallel.
Inductors in Series
Total inductance of inductors in series.
Inductors in Parallel
Total inductance of inductors in parallel.
Electric Charge
Electric charge transferred by current over time.
Conductance
Electrical conductance is the reciprocal of resistance.
Resistance from Resistivity
Resistance of a conductor based on material and dimensions.
Resistance vs Temperature
Change in resistance due to temperature change.
Period and Frequency
Relationship between period and frequency of a signal.
Impedance Magnitude
Magnitude of complex impedance.
Phase Angle
Phase angle between voltage and current in AC circuit.
Filter Bandwidth
Bandwidth of a bandpass filter.
LC Filter Resonant Frequency
Resonant frequency of an LC filter circuit.
-3dB Cutoff Point
At cutoff frequency, output is 70.7% of maximum (−3dB).
Summing Amplifier
Output of an inverting summing op-amp amplifier.
Op-Amp Differentiator Gain
PROOutput of an op-amp differentiator circuit.
This calculator is a Pro feature
Upgrade to Pro — $4.99/moOp-Amp Integrator Gain
PROGain of op-amp integrator at a given frequency.
This calculator is a Pro feature
Upgrade to Pro — $4.99/moOp-Amp Gain-Bandwidth Product
Gain-bandwidth product is constant for an op-amp.
Binary to Decimal
Convert binary number to decimal.
Fan-Out
Maximum number of gates a logic gate output can drive.
CMOS Dynamic Power
PRODynamic power dissipation in CMOS logic gates.
This calculator is a Pro feature
Upgrade to Pro — $4.99/moSteady State Error (Step)
PROSteady state error for step input with position constant Kp.
This calculator is a Pro feature
Upgrade to Pro — $4.99/moPhase Margin
PROPhase margin indicates stability — positive PM means stable.
This calculator is a Pro feature
Upgrade to Pro — $4.99/moNatural Frequency from Char. Eq.
PRONatural frequency of a second order system.
This calculator is a Pro feature
Upgrade to Pro — $4.99/moTransmission Line Losses
Power lost in transmission line resistance.
Per Unit Value
Per unit system normalizes power system quantities.
Base Impedance
PROBase impedance for per unit calculations in power systems.
This calculator is a Pro feature
Upgrade to Pro — $4.99/moDC Motor Input Power
Electrical input power to a DC motor armature.
DC Motor Mechanical Power
Mechanical power developed in DC motor armature.
Shunt Field Current
Field current in a shunt DC machine.
Induction Motor Efficiency
Efficiency of an induction motor.
Synchronous Motor Speed
Synchronous motors run exactly at synchronous speed.
Rotor Copper Loss
Power lost in rotor resistance of induction motor.
SCR Average Output Voltage
PROAverage output voltage of half-wave SCR rectifier with firing angle α.
This calculator is a Pro feature
Upgrade to Pro — $4.99/moSingle Phase Inverter Output
PRORMS output voltage of single phase PWM inverter.
This calculator is a Pro feature
Upgrade to Pro — $4.99/moSwitching Losses
PROPower lost during switching transitions in power converters.
This calculator is a Pro feature
Upgrade to Pro — $4.99/moMagnetic Flux
Magnetic flux through a surface.
Faraday's Law
Induced EMF is proportional to rate of change of magnetic flux.
Ampere's Law (MMF)
Magnetomotive force in a magnetic circuit.
Magnetic Reluctance
Opposition to magnetic flux in a magnetic circuit.
Magnetic Field in Solenoid
Magnetic flux density inside a solenoid.
Solar Panel Power
Power output of a solar panel.
Wind Turbine Power
Power extracted from wind by a turbine.
Solar Cell Fill Factor
Fill factor measures quality of a solar cell.
Transformer Current Ratio
Current ratio is inverse of turns ratio in ideal transformer.
Transformer KVA Rating
Apparent power rating of a transformer.
Reflected Impedance
Impedance seen at primary when load is connected to secondary.
Transformer Max Efficiency Condition
Maximum efficiency occurs when core loss equals copper loss.
All Day Efficiency
Energy efficiency of transformer over 24 hours.
Auto-Transformer Ratio
Voltage ratio of an auto-transformer.
Short Circuit Voltage %
Percentage short circuit voltage of transformer.
AM Signal Bandwidth
Bandwidth of an amplitude modulated signal.
FM Signal Bandwidth (Carson)
Bandwidth of FM signal using Carson's rule.
AM Total Power
Total power of an AM signal including sidebands.
Bit Rate
Bit rate based on sampling frequency and modulation order.
Friis Transmission Equation
PROReceived power in a wireless link.
This calculator is a Pro feature
Upgrade to Pro — $4.99/moNoise Figure
Degradation of SNR through a component.
Wavelength from Frequency
Wavelength of electromagnetic wave at given frequency.
PCB Via Current Capacity
Maximum current a PCB via can carry.
Microstrip Impedance
PROCharacteristic impedance of a PCB microstrip trace.
This calculator is a Pro feature
Upgrade to Pro — $4.99/moPCB Crosstalk (3W Rule)
3W rule to minimize crosstalk between PCB traces.
Decoupling Capacitor Value
Decoupling capacitor needed for transient current demand.
PCB Component Power Dissipation
Junction temperature of component on PCB.
PCB Trace Voltage Drop
Voltage drop across a PCB trace carrying current.
Convolution (Length)
Output length of convolution of two discrete signals.
Signal Energy
Total energy of a discrete time signal.
Signal Power
Average power of a periodic signal.
Z-Transform Time Delay
PROTime delay property of Z-transform.
This calculator is a Pro feature
Upgrade to Pro — $4.99/moDFT Frequency Resolution
Frequency resolution of a Discrete Fourier Transform.
Aliasing Frequency
Apparent frequency when signal is undersampled.
Kirchhoff's Voltage Law (KVL)
Sum of all voltages around any closed loop equals zero.
Joule Heating
Heat generated by current flowing through resistance.
Electric Field Strength
Electric field between two parallel plates.
Q Factor (Series RLC)
Quality factor of a series RLC circuit at resonance.
Q Factor (Parallel RLC)
Quality factor of a parallel RLC circuit at resonance.
Zener Voltage Regulator
Series resistor for zener diode voltage regulator.
MOSFET Triode Region Current
PRODrain current of NMOS in triode (linear) region.
This calculator is a Pro feature
Upgrade to Pro — $4.99/moBJT Voltage Divider Bias
Base voltage in voltage divider bias circuit.
Short Circuit Current
Short circuit current in a power system.
Transmission Line Voltage Regulation
Percentage voltage regulation of a transmission line.
Closed Loop Transfer Function
PROClosed loop transfer function with feedback.
This calculator is a Pro feature
Upgrade to Pro — $4.99/moDelay Time
PROTime for response to reach 50% of final value.
This calculator is a Pro feature
Upgrade to Pro — $4.99/moCoulomb's Law
Force between two point charges.
Gauss's Law
Total charge enclosed equals permittivity times electric flux.
Lorentz Force
Force on a charged particle in electric and magnetic fields.
Parallel Plate Capacitance
Capacitance of a parallel plate capacitor.
Signal Bandwidth
Bandwidth is difference between highest and lowest frequencies.
Power Gain in dB
Power gain of an amplifier expressed in decibels.
Maximum Power Dissipation (Resistor)
Maximum power a resistor can safely dissipate.
Electron Drift Velocity
PROAverage velocity of electrons in a conductor.
This calculator is a Pro feature
Upgrade to Pro — $4.99/moRMS of Triangle Wave
RMS value of a triangular waveform.
Crest Factor
Ratio of peak value to RMS value of a waveform.
Form Factor
Ratio of RMS value to average value of a waveform.
RC Charging Current
Current during capacitor charging in an RC circuit.
Second Order Filter Passband Gain
PROPassband gain of a Sallen-Key second order active filter.
This calculator is a Pro feature
Upgrade to Pro — $4.99/moOp-Amp CMRR
PROCommon Mode Rejection Ratio of an op-amp.
This calculator is a Pro feature
Upgrade to Pro — $4.99/moJFET Drain Current
PRODrain current of a JFET in saturation region.
This calculator is a Pro feature
Upgrade to Pro — $4.99/moHalf Adder Sum & Carry
Boolean expressions for half adder circuit.
Transformer No-Load Current
No-load current of a transformer combining core loss and magnetizing components.
SVC Reactive Power Compensation
PROReactive power provided by a Static VAR Compensator.
This calculator is a Pro feature
Upgrade to Pro — $4.99/moRoot Locus Gain at Point
PROGain value at a specific point on the root locus.
This calculator is a Pro feature
Upgrade to Pro — $4.99/moSpeed of Light
Speed of light in vacuum — exact defined value.
Elementary Charge
Charge of a single electron or proton.
Vacuum Permittivity
Electric constant — permittivity of free space.
Vacuum Permeability
Magnetic constant — permeability of free space.
Characteristic Impedance of Vacuum
Free space impedance for electromagnetic waves.
Planck Constant
PROFundamental constant relating energy and frequency.
This calculator is a Pro feature
Upgrade to Pro — $4.99/moBoltzmann Constant
Relates energy at the particle level to temperature.
Avogadro Constant
PRONumber of particles in one mole of substance.
This calculator is a Pro feature
Upgrade to Pro — $4.99/moElectron Mass
PRORest mass of an electron.
This calculator is a Pro feature
Upgrade to Pro — $4.99/moProton Mass
PRORest mass of a proton.
This calculator is a Pro feature
Upgrade to Pro — $4.99/moThermal Voltage (300K)
Thermal voltage at room temperature, used in diode equations.
Silicon Bandgap Energy
Energy gap of silicon at room temperature.
Intrinsic Carrier Concentration (Si)
Intrinsic carrier concentration of silicon at room temperature.
Copper Resistivity
Electrical resistivity of copper at room temperature.
Aluminum Resistivity
Electrical resistivity of aluminum at room temperature.
Silver Resistivity
Electrical resistivity of silver — best conductor.
Standard PCB Copper Thickness (1oz)
Standard 1oz copper thickness used in PCB manufacturing.
Fine-Structure Constant
PRODimensionless constant characterizing electromagnetic interaction strength.
This calculator is a Pro feature
Upgrade to Pro — $4.99/moBohr Radius
PROMost probable distance between proton and electron in hydrogen atom.
This calculator is a Pro feature
Upgrade to Pro — $4.99/moGaAs Bandgap Energy
PROEnergy gap of Gallium Arsenide — used in high frequency devices.
This calculator is a Pro feature
Upgrade to Pro — $4.99/moGaN Bandgap Energy
PROEnergy gap of Gallium Nitride — used in power electronics.
This calculator is a Pro feature
Upgrade to Pro — $4.99/mo