Welcome to our comprehensive list of Electrical and Electronics Engineering formulas! Whether you’re a student, a professional engineer, or simply someone with a keen interest in the world of electricity, this list of Electrical and Electronics Engineering is a go-to resource for understanding and applying the fundamental formulas in electrical engineering. From Ohm’s Law to Kirchhoff’s Laws, from power calculations to impedance equations, we’ll delve into the essential mathematical tools that underpin the principles of electrical circuits and systems. You can simply refer to below formulas or click on the links to have complete details of a specific formula.
100 Electrical and Electronics Engineering formulas:
| Formula | Explanation and Mathematical Equation |
| Ohm’s Law | Ohm’s Law relates current and voltage for resistive circuits. Formula: V = IR |
| Kirchhoff’s Voltage Law | States that the sum of all voltages in a closed loop in a circuit is equal to zero. |
| Kirchhoff’s Current Law | States that the sum of currents entering a node in a circuit is equal to the sum of currents leaving the node. |
| Power Calculation | Calculates power (P) in a circuit using the formula P = V * I, where V is voltage and I is current. |
| Resistor Color Code | Determines the resistance value of a resistor based on the color bands. |
| Voltage Divider Rule | Calculates the output voltage (Vout) in a voltage divider circuit using the formula Vout = Vin * (R2 / (R1 + R2)). |
| Current Divider Rule | Calculates the output current (Iout) in a current divider circuit using the formula Iout = Iin * (R2 / (R1 + R2)). |
| Capacitor Charge | Calculates the charge (Q) stored in a capacitor using the formula Q = C * V, where C is capacitance and V is voltage. |
| Capacitor Energy | Calculates the energy (E) stored in a capacitor using the formula E = 0.5 * C * V^2. |
| Inductor Energy | Calculates the energy (E) stored in an inductor using the formula E = 0.5 * L * I^2, where L is inductance and I is current. |
| Series Resistance | Calculates the total resistance (Rt) in a series circuit by summing individual resistances. |
| Parallel Resistance | Calculates the total resistance (Rt) in a parallel circuit using the formula 1/Rt = 1/R1 + 1/R2 + … + 1/Rn. |
| Series Capacitance | Calculates the total capacitance (Ct) in a series circuit using the formula 1/Ct = 1/C1 + 1/C2 + … + 1/Cn. |
| Parallel Capacitance | Calculates the total capacitance (Ct) in a parallel circuit by summing individual capacitances. |
| Inductors in Series | Calculates the total inductance (Leq) in a series circuit by summing individual inductances. Leq = L1 + L2 + L3 + … |
| Inductors in Parallel | Calculates the total inductance (Lt) in a parallel circuit using the formula 1/Lt = 1/L1 + 1/L2 + … + 1/Ln. |
| RC Time Constant | Calculates the time constant (τ) of an RC circuit using the formula τ = R * C, where R is resistance and C is capacitance. |
| RL Time Constant | Calculates the time constant (τ) of an RL circuit using the formula τ = L / R, where L is inductance and R is resistance. |
| RLC Time Constant | Calculates the time constant (τ) of an RLC circuit using the formula τ = L / (R + R’) or τ = C * (R + R’), where L is inductance, R is resistance, and R’ is reactance. |
| Power Factor | Measures the efficiency of power utilization in an AC circuit, calculated as cos(θ), where θ is the phase angle between voltage and current. |
| AC Power | Calculates the power (P) in an AC circuit using the formula P = Vrms * Irms * cos(θ), where Vrms is the RMS voltage, Irms is the RMS current, and θ is the phase angle. |
| Average Power | Calculates the average power (Pavg) in a periodic waveform using the formula Pavg = (1/T) ∫(0 to T) p(t) dt, where T is the period and p(t) is the instantaneous power. |
| Peak-to-Peak Voltage | Measures the voltage difference between the highest and lowest points in an AC waveform. |
| RMS Voltage | Calculates the root mean square (RMS) voltage of an AC waveform, equal to the DC voltage that would produce the same power dissipation in a resistor. |
| RMS Current | Calculates the root mean square (RMS) current of an AC waveform, equal to the DC current that would produce the same power dissipation in a resistor. |
| Decibel (dB) | Measures the relative power or amplitude of a signal using logarithmic scales. |
| dBm | Represents power measurement in decibels relative to 1 milliwatt. |
| Skin Depth | Determines the depth at which the current density decreases to 37% of its surface value in a conductor. |
| Superposition Theorem | States that the response (voltage or current) in a linear circuit is the sum of individual responses due to each independent source acting alone. |
| Thevenin’s Theorem | Simplifies complex circuits into an equivalent circuit with a single voltage source and a single resistor. |
| Norton’s Theorem | Simplifies complex circuits into an equivalent circuit with a single current source and a single resistor. |
| Maximum Power Transfer Theorem | States that the maximum power is transferred from a source to a load when the source impedance is equal to the complex conjugate of the load impedance. |
| Frequency to Wavelength | Converts frequency (f) to wavelength (λ) using the formula λ = c / f, where c is the speed of light. |
| Wavelength to Frequency | Converts wavelength (λ) to frequency (f) using the formula f = c / λ, where c is the speed of light. |
| Speed of Light | Represents the speed of light (c) in a vacuum, approximately equal to 299,792,458 meters per second. |
| Impedance | Represents the total opposition to current flow in an AC circuit, calculated as Z = R + jX, where R is resistance and X is reactance. |
| Real Power | Represents the power in an AC circuit that is dissipated as useful work, calculated as P = V * I * cos(θ), where V is voltage, I is current, and θ is the phase angle. |
| Reactive Power | Represents the power in an AC circuit that oscillates between the source and the load, calculated as Q = V * I * sin(θ), where V is voltage, I is current, and θ is the phase angle. |
| Apparent Power | Represents the total power in an AC circuit, calculated as S = V * I, where V is voltage and I is current. |
| Complex Power | Represents the total power in an AC circuit, calculated as S = P + jQ, where P is real power and Q is reactive power. |
| Three-Phase Power | Calculates the total power in a three-phase AC system using the formula P = √3 * Vline * Iline * cos(θ), where Vline is line voltage, Iline is line current, and θ is the phase angle. |
| Delta-Wye Transformation | Converts a delta-connected circuit to an equivalent wye-connected circuit, or vice versa. |
| RMS to Peak Voltage | Converts RMS voltage (Vrms) to peak voltage (Vp) using the formula Vp = Vrms * √2. |
| Peak to RMS Voltage | Converts peak voltage (Vp) to RMS voltage (Vrms) using the formula Vrms = Vp / √2. |
| Time Period | Represents the time taken for one complete cycle of an AC waveform. |
| Frequency | Represents the number of cycles of an AC waveform per unit of time. |
| Duty Cycle | Represents the ratio of the pulse duration to the total period in a periodic waveform. |
| Parallel Resistor-Inductor | Calculates the impedance (Z) of a parallel combination of resistor (R) and inductor (jXl), given by the formula Z = 1 / (1/R + 1/jXl). |
| Parallel Resistor-Capacitor | Calculates the impedance (Z) of a parallel combination of resistor (R) and capacitor (jXc), given by the formula Z = 1 / (1/R + 1/jXc). |
| Series Resistor-Inductor | Calculates the impedance (Z) of a series combination of resistor (R) and inductor (jXl), given by the formula Z = R + jXl. |
| Series Resistor-Capacitor | Calculates the impedance (Z) of a series combination of resistor (R) and capacitor (jXc), given by the formula Z = R + jXc. |
| Phase Angle | Represents the phase difference between voltage and current in an AC circuit. |
| Maxwell’s Equations | A set of four fundamental equations that describe the behavior of electromagnetic fields. |
| Biot-Savart Law | Calculates the magnetic field (B) produced by a current-carrying conductor, given by the formula B = (μ0 * I * l) / (4π * r), where μ0 is the permeability of free space, I is current, l is length, and r is distance. |
| Ampere’s Circuital Law | States that the magnetic field around a closed loop is proportional to the current passing through the loop. |
| Faraday’s Law of Electromagnetic Induction | States that the induced electromotive force (EMF) in a circuit is equal to the rate of change of magnetic flux through the circuit. |
| Lenz’s Law | States that the direction of an induced current in a conductor is always such that it opposes the change that produced it. |
| Coulomb’s Law | Calculates the electrostatic force (F) between two charged particles, given by the formula F = k * (q1 * q2) / r^2, where k is the electrostatic constant, q1 and q2 are charges, and r is the distance between them. |
| Gauss’s Law | Relates the electric flux passing through a closed surface to the net charge enclosed by the surface. |
| Electric Field | Represents the force exerted on a charged particle per unit charge, calculated as E = F / q, where E is electric field, F is force, and q is charge. |
| Capacitive Reactance | Represents the opposition to the flow of alternating current in a capacitor, given by the formula Xc = 1 / (2π * f * C), where f is frequency and C is capacitance. |
| Inductive Reactance | Represents the opposition to the flow of alternating current in an inductor, given by the formula Xl = 2π * f * L, where f is frequency and L is inductance. |
| Inductive Impedance | Represents the total opposition to current flow in an AC circuit due to inductance, calculated as Zl = jXl, where j represents the imaginary unit. |
| Capacitive Impedance | Represents the total opposition to current flow in an AC circuit due to capacitance, calculated as Zc = 1/jXc, where j represents the imaginary unit. |
| RMS Value of a Half-Wave Rectifier | Calculates the RMS value (Vrms) of a half-wave rectified voltage using the formula Vrms = Vp / √2, where Vp is peak voltage. |
| RMS Value of a Full-Wave Rectifier | Calculates the RMS value (Vrms) of a full-wave rectified voltage using the formula Vrms = Vp / 2, where Vp is peak voltage. |
| Voltage Gain (dB) | Calculates the voltage gain (Av) in decibels using the formula Av = 20 log (Vout / Vin), where Vout is output voltage and Vin is input voltage. |
| Current Gain (dB) | Calculates the current gain (Ai) in decibels using the formula Ai = 20 log (Iout / Iin), where Iout is output current and Iin is input current. |
| Power Gain (dB) | Calculates the power gain (Ap) in decibels using the formula Ap = 10 log (Pout / Pin), where Pout is output power and Pin is input power. |
| Operational Amplifier (Op-Amp) Gain | Calculates the voltage gain (Av) of an operational amplifier circuit using the formula Av = -Rf / R1, where Rf is feedback resistance and R1 is input resistance. |
| Bandwidth | Represents the range of frequencies within which a device or system can operate effectively. |
| Bandpass Filter | Passes a specific range of frequencies while attenuating others. |
| Lowpass Filter | Passes frequencies below a certain cutoff frequency while attenuating higher frequencies. |
| Highpass Filter | Passes frequencies above a certain cutoff frequency while attenuating lower frequencies. |
| Notch Filter | Attenuates a narrow band of frequencies while allowing others to pass. |
| Miller’s Theorem | Simplifies the analysis of a circuit with a large capacitor by representing it as a voltage amplifier with a smaller capacitor. |
| Electromotive Force (EMF) | Represents the energy supplied per unit charge by a source, measured in volts. |
| Wheatstone Bridge | Balances resistive elements in a bridge circuit to measure an unknown resistance value. |
| Maximum Efficiency of Power Transfer | Occurs when the load resistance is equal to the complex conjugate of the source resistance. |
| Superheterodyne Receiver | Converts the incoming radio frequency signal to an intermediate frequency for better selectivity and amplification. |
| Antenna Gain | Measures the directional property of an antenna, calculated as the ratio of radiated power to the power radiated by an isotropic antenna. |
| Transmission Line Reflection Coefficient | Calculates the reflection coefficient (Γ) of a transmission line using the formula Γ = (Zl – Z0) / (Zl + Z0), where Zl is the load impedance and Z0 is the characteristic impedance of the transmission line. |
| Attenuation | Represents the decrease in amplitude or power of a signal as it propagates through a medium or device. |
| Total Harmonic Distortion (THD) | Measures the distortion level in an AC waveform caused by harmonics, expressed as a percentage of the fundamental frequency. |
| Signal-to-Noise Ratio (SNR) | Measures the ratio of the power of a signal to the power of background noise or interference. |
| Bit Error Rate (BER) | Represents the number of bit errors per unit of transmitted data in a digital communication system. |
| Smith Chart | Graphical tool used in radio frequency (RF) engineering for analyzing and designing impedance matching networks. |
| Slew Rate | Represents the rate of change of voltage per unit of time in an operational amplifier circuit. |
| Bandwidth Product | Represents the product of the gain bandwidth and the unity gain bandwidth of an operational amplifier. |
| Shannon Capacity | Calculates the maximum achievable data rate (C) in a communication channel using the formula C = B * log2(1 + S/N), where B is bandwidth and S/N is the signal-to-noise ratio. |
| Delta Modulation | Converts an analog signal into a digital signal by sampling the difference between consecutive signal samples. |
| Demodulation | Extracts the original baseband signal from a modulated carrier signal. |
| Euler’s Identity | Relates exponential functions, trigonometric functions, and complex numbers using the equation e^(iθ) = cos(θ) + i * sin(θ), where e is Euler’s number and i is the imaginary unit. |
| Laplace Transform | Transforms a time-domain function into the frequency-domain, useful for analyzing linear time-invariant systems. |
| Fourier Series | Represents a periodic function as a sum of sine and cosine functions with different amplitudes and frequencies. |
| Fourier Transform | Transforms a time-domain function into the frequency-domain, providing a continuous spectrum representation. |
| Z-transform | Transforms a discrete-time function into the Z-domain, useful for analyzing discrete-time systems. |
| Bode Plot | Graphical representation of the frequency response of a system, showing magnitude and phase information. |
| Nyquist Stability Criterion | Determines the stability of a system by examining the location of poles in the complex plane. |
| Transfer Function | Represents the relationship between the input and output of a system in the frequency domain. |
| Root Locus | Graphical representation of the possible locations of system poles as a parameter is varied. |
| State-Space Representation | Mathematical modeling of a system using differential equations in the time domain. |
| Shannon’s Channel Capacity | Calculates the maximum achievable data rate (C) in a communication channel using the formula C = B * log2(1 + S/N), where B is bandwidth and S/N is the signal-to-noise ratio. |
| Shannon-Hartley Theorem | Relates the channel capacity (C) of a communication system to the bandwidth (B) and signal-to-noise ratio (S/N) using the formula C = B * log2(1 + S/N). |
| Bit Error Rate (BER) for Digital Modulation | Estimates the probability of bit errors in a digital communication system, influenced by noise and channel conditions. |
| Shannon-Fano Coding | An entropy encoding technique that assigns codewords to symbols based on their probabilities, achieving variable-length encoding. |
| Hamming Code | An error-correcting code that adds extra parity bits to a block of data, enabling detection and correction of single-bit errors. |
| Gray Code | A binary numeral system where consecutive values differ by only one bit, useful in reducing errors in analog-to-digital and digital-to-analog conversions. |
| Fast Fourier Transform (FFT) | Efficient algorithm for calculating the discrete Fourier transform of a sequence of data points. |
| Discrete Fourier Transform (DFT) | Transforms a sequence of discrete data points from the time domain to the frequency domain. |
| Convolution | Mathematical operation that combines two functions to produce a third function, representing the integral overlap of the two input functions. |
| Probability Density Function (PDF) | Describes the probability distribution of a continuous random variable. |
| Cumulative Distribution Function (CDF) | Describes the probability that a random variable takes on a value less than or equal to a given value. |
| Central Limit Theorem | States that the sum or average of a large number of independent and identically distributed random variables approximates a normal distribution. |
| Law of Large Numbers | States that as the number of trials in a probability experiment increases, the experimental probability approaches the theoretical probability. |
| Bayes’ Theorem | Calculates the conditional probability of an event based on prior knowledge of related events. |
| Markov Chain | Mathematical model for describing a sequence of events where the probability of each event depends only on the previous event. |
| Mutual Inductance | Represents the coupling between two inductors, inducing a voltage in one coil due to the changing current in the other coil. |
| Skin Effect | Describes the tendency of alternating current to distribute itself within a conductor, resulting in higher current density near the surface. |
| Shannon Entropy | Measures the amount of uncertainty or information content in a random variable or source of information. |
| Transmission Line Equations | Mathematical equations that model the behavior of electrical signals propagating along transmission lines. |
| Maximum Power Point Tracking (MPPT) | Technique used in solar power systems to optimize the output power of photovoltaic modules by dynamically adjusting the load impedance. |
| Transformer Turns Ratio | Represents the ratio of the number of turns in the primary winding to the number of turns in the secondary winding of a transformer. See complete list of Transformer formulas here |
| Switching Losses | Power losses in electronic switches due to the transition between ON and OFF states. |
| Impulse Response | Represents the output of a system when an impulse function is applied as input. |
| Step Response | Represents the output of a system when a step function is applied as input. |
| Error Function | Represents the integral of the Gaussian probability density function, used in statistics and signal processing. |
| Root-Mean-Square Error (RMSE) | Measures the difference between predicted and actual values in regression or estimation problems. |
| Electromagnetic Compatibility (EMC) | Ensures that electronic devices can function without interfering with each other or being affected by external electromagnetic disturbances. |
| Quality Factor (Q-Factor) | Measures the damping characteristics of a resonant circuit, calculated as the ratio of reactance to resistance. |
| Johnson-Nyquist Noise | Thermal noise generated by the random motion of charge carriers in a resistor at finite temperature. |
| Shot Noise | Fluctuations in current or voltage due to the discrete nature of electrons and their flow through a conductor. |
| Flicker Noise | Low-frequency noise caused by the random trapping and releasing of charge carriers in electronic devices. |
| Avalanche Breakdown | Phenomenon in a semiconductor where a sudden increase in current occurs due to the impact ionization of charge carriers. |
| Hall Effect | Describes the generation of a voltage perpendicular to the direction of both an electric current and a magnetic field in a conductor. |
| Eddy Currents | Circulating currents induced in a conductor due to changing magnetic fields, leading to power losses and heating. |
| Skin Effect | Describes the tendency of alternating current to distribute itself within a conductor, resulting in higher current density near the surface. |
| Magnetic Hysteresis | Phenomenon where a magnetic material exhibits a lag in its magnetization when subjected to changing magnetic fields. |
| Electric Vehicle Range Calculation | Estimates the range of an electric vehicle based on factors such as battery capacity, efficiency, and driving conditions. |
| Stray Capacitance | Undesired capacitance between conductors or components in a circuit, leading to crosstalk and coupling effects. |
| Stray Inductance | Undesired inductance in a circuit, causing parasitic effects such as signal delay and interference. |
| Thermal Resistance | Measures the ability of a material or component to dissipate heat, calculated as the temperature difference across it divided by the power dissipated. |
| Heat Sink Design | Designing a heat sink to efficiently dissipate heat generated by electronic components in order to maintain safe operating temperatures. |
| SNR Improvement (Dithering) | Technique used to improve the signal-to-noise ratio by introducing low-amplitude noise or randomness. |
| Charge Pump | Circuit that generates a higher or lower DC voltage from a lower or higher DC voltage, respectively, using the charge-discharge action of capacitors. |
| Bootstrap Circuit | Provides a boosted voltage supply for driving high-side MOSFETs in half-bridge and full-bridge configurations. |
| Digital-to-Analog Converter (DAC) | Converts digital signals into analog voltages or currents, enabling the generation of continuous waveforms. |
| Analog-to-Digital Converter (ADC) | Converts continuous analog signals into digital representations for processing and storage. |
| Automatic Gain Control (AGC) | Adjusts the gain of an amplifier circuit to maintain a constant output signal level despite varying input signal strengths. |
| Electret Microphone | Converts sound waves into electrical signals by using a permanently charged material that generates voltage variations in response to pressure changes. |
| Active Filter Design | Designing electronic filters that utilize active components such as operational amplifiers for improved performance and flexibility. |
| Oscillator Circuits | Generate repetitive waveforms at a specific frequency, commonly used as timing references in electronic systems. |
| Voltage Multiplier | Circuit that generates a higher DC voltage from an AC or pulsating DC input by using diodes and capacitors in a cascaded configuration. |
| Electromagnetic Interference (EMI) | Undesired electromagnetic radiation or noise that interferes with the proper operation of electronic devices or systems. |
| Grounding Techniques | Methods and practices for establishing safe and effective electrical grounding in electronic systems to prevent electric shock and noise issues. |
| Electromechanical Relay | Electrically operated switch that uses electromagnetism to control the flow of current in a circuit. |
| Solid-State Relay | Electronic switch that uses semiconductor devices such as transistors or thyristors to control the flow of current in a circuit. |
| Logic Gates | Basic building blocks of digital circuits that perform Boolean logic functions such as AND, OR, and NOT. |
| Boolean Algebra | Mathematical system for expressing and manipulating logical statements using operators such as AND, OR, and NOT. |
| Multiplexer (MUX) | Device that selects one of several input signals and routes it to a single output line based on control inputs. |
| Demultiplexer (DEMUX) | Device that takes a single input signal and routes it to one of several output lines based on control inputs. |
| Phase-Locked Loop (PLL) | Feedback control system that locks the phase and frequency of an oscillator to a reference signal, used in frequency synthesis and clock generation. |
| Operational Amplifier (Op-Amp) Applications | Various application circuits utilizing operational amplifiers, such as amplifiers, filters, comparators, and oscillators. |
| Field-Effect Transistor (FET) | Semiconductor device that uses an electric field to control the flow of current, commonly used in amplifiers and switching applications. |
| Bipolar Junction Transistor (BJT) | Three-terminal semiconductor device that amplifies or switches electronic signals, commonly used in amplifiers and digital circuits. |
| Diode Characteristics | Describes the behavior of diodes in terms of forward and reverse biasing, voltage drop, and current flow. |
| Voltage Regulator | Circuit that maintains a constant output voltage despite variations in input voltage or load conditions. |
| Transistor Biasing | Setting the operating point or quiescent point of a transistor amplifier to ensure proper amplification and stability. |
| Differential Amplifier | Amplifier circuit that amplifies the voltage difference between two input signals, commonly used in analog signal processing and measurement applications. |
| Frequency Modulation (FM) | Modulation technique where the frequency of a carrier signal varies in proportion to the instantaneous amplitude of a modulating signal. |
| Amplitude Modulation (AM) | Modulation technique where the amplitude of a carrier signal varies in proportion to the instantaneous amplitude of a modulating signal. |
| Pulse Width Modulation (PWM) | Modulation technique where the width of a pulse train is varied to encode information or control the average value of a waveform. |
| Quadrature Amplitude Modulation (QAM) | Modulation technique where both amplitude and phase of a carrier signal are simultaneously varied to encode multiple bits per symbol. |
| Single-Sideband Modulation (SSB) | Modulation technique where only one sideband of the modulated signal is transmitted, reducing bandwidth requirements. |
| Frequency Shift Keying (FSK) | Digital modulation scheme where the frequency of a carrier signal is switched between discrete values to represent digital data. |
| Phase Shift Keying (PSK) | Digital modulation scheme where the phase of a carrier signal is shifted between discrete values to represent digital data. |
| Orthogonal Frequency Division Multiplexing (OFDM) | Digital modulation scheme used in high-speed communication systems, dividing the data stream into multiple subcarriers for increased spectral efficiency. |
| Error Detection and Correction Codes | Coding techniques used to detect and correct errors that may occur during the transmission or storage of digital data. |
| Coaxial Cable Characteristics | Describes the properties of coaxial cables, including impedance, attenuation, and bandwidth. |
| Ethernet Standards | Set of protocols and specifications that define the physical and data link layers of wired computer networks, such as Ethernet. |
| Digital Subscriber Line (DSL) | Broadband communication technology that uses existing telephone lines to provide high-speed internet access. |
| Bluetooth | Wireless communication technology used for short-range data exchange between devices. |
| Zigbee | Low-power wireless communication standard for small-scale automation and control applications. |
| Power Amplifier Design | Designing amplifiers that deliver high-power signals to drive speakers, antennas, or other loads. |
| Harmonic Distortion | Describes the presence of unwanted harmonics in a waveform due to nonlinearity in a system. |
| Decibel (dB) | Unit of measurement used to express the ratio of two values, commonly used in signal strength and power calculations. |
| Amps to kVA | Enables to convert current in Amps to Power in kVA. |
| Amps to kW | Enables to convert current in Amps to Power in kW. |
| Amps to HP | Enables to convert current in Amps to Power in HP. |
| HP to Amps | Enables to convert power known in HP to current in Amps. |
| kVA to Amps | Enables to convert power known in kVA to current in Amps. |
| kW to Amps | Enables to convert power known in kW to current in Amps. |
These formulas cover a wide range of topics in Electrical and Electronics Engineering, including circuit analysis, power systems, semiconductor devices, digital logic, and more.