Ultimate Electrical Engineering Calculator
This app provides a comprehensive suite of tools for electrical engineering calculations. Whether you’re working with basic circuits, power systems, or transformers, the app aims to simplify complex equations and enhance your workflow.
Download, Copy or Print your calculations when you’re finished. Thank you for using the AIExpert.world Electrical Engineering Calculator.
Select a Calculator
Calculator Placeholder
History
Formulas used in the Electrical Engineering Calculator App.
| Calculator | Formula | Explanation |
|---|---|---|
| Ohm’s Law | V = I * R, I = V / R, R = V / I | Ohm’s Law describes the relationship between voltage (V), current (I), and resistance (R) in an electrical circuit. It states that the voltage across a conductor is directly proportional to the current flowing through it, and the constant of proportionality is the resistance. |
| Power Calculation | P = V * I | Calculates the electrical power (P) in watts consumed or produced by a circuit element. Power is the rate at which electrical energy is transferred. This formula is derived from the definition of power as the product of voltage and current. |
| Series & Parallel Resistors | Series: Rtotal = R1 + R2 + … + Rn Parallel: 1/Rtotal = 1/R1 + 1/R2 + … + 1/Rn | Calculates the total equivalent resistance when resistors are connected in series or parallel. In series, the total resistance is the sum of individual resistances. In parallel, the reciprocal of the total resistance is the sum of the reciprocals of individual resistances. |
| Time Constants | RC Time Constant (τRC) = R × C RL Time Constant (τRL) = L / R | Calculates the time constant (τ) for RC (resistor-capacitor) and RL (resistor-inductor) circuits. The time constant represents the time it takes for the voltage or current in the circuit to change by approximately 63.2% of its final value. |
| AC Power | Single-phase: P = V × I × cosϕ Three-phase: P = √3 × VL × IL × cosϕ | Calculates the real power (P) in AC circuits, considering the power factor (cosϕ). In AC circuits, the power factor represents the phase difference between voltage and current waveforms. |
| Power Factor | Power Factor (cosϕ) = Pactive / Papparent | Calculates the power factor (cosϕ) in an AC circuit, which is the ratio of active power (Pactive) to apparent power (Papparent). It indicates how effectively electrical power is used in a circuit. |
| Reactance | Capacitive Reactance (Xc) = 1 / (2πfC) Inductive Reactance (Xl) = 2πfL | Calculates the opposition to current flow caused by capacitance (Xc) or inductance (Xl) in an AC circuit. Reactance depends on the frequency (f) of the AC signal. |
| Impedance (Z) | Impedance (Z) = R + jX, where j is the imaginary unit Magnitude of Impedance |Z| = √(R2 + X2) | Calculates the total opposition to current flow in an AC circuit, considering both resistance (R) and reactance (X). Impedance is a complex quantity. |
| Voltage Regulation | Voltage Regulation (V.R.) = (E2 – V2) / V2 Voltage Regulation (V.R.) = ((E2 – V2) / V2) * 100% | Calculates the voltage regulation in a power system, which is the change in voltage between no-load (E2) and full-load (V2) conditions, expressed as a fraction or percentage of the full-load voltage. |
| Power Losses | Copper Losses (Pcu) = I2R Hysteresis Loss (Ph) = ηBmax1.6fV Eddy Current Loss (Pe) = KBmax2f2t2V | Calculates various power losses in electrical systems. Copper loss is due to the resistance of conductors, hysteresis loss is due to magnetic domain reversal in ferromagnetic materials, and eddy current loss is due to circulating currents induced in conductive materials. |
| Back EMF | Back EMF (Eb) = (P × φ × N × Z) / (60 × A) | Calculates the back electromotive force (EMF) generated in a DC motor, which opposes the applied voltage. It depends on factors like power (P), flux (φ), speed (N), armature conductors (Z), and parallel paths (A). |
| Synchronous Speed | Synchronous Speed (Ns) = (120 × f) / P | Calculates the speed at which the rotating magnetic field of an AC motor rotates. It is determined by the frequency (f) of the AC supply and the number of poles (P) in the motor. |
| Transformer EMF | EMF (E) = 4.44 × φm × f × T | Calculates the electromotive force (EMF) induced in a transformer winding. It depends on the maximum flux (φm), frequency (f), and number of turns (T) in the winding. |
| Turns Ratio | Turns Ratio (a) = E1/E2 = T1/T2 = V1/V2 = I2/I1 | Calculates the ratio of the number of turns in the primary winding (T1) to the number of turns in the secondary winding (T2) of a transformer. This ratio determines the voltage and current transformation between the primary and secondary sides. |
| Op-Amp Gain | Voltage Gain (Av) = -Rf / R1 | Calculates the voltage gain of an inverting operational amplifier (op-amp) circuit. The gain is determined by the ratio of the feedback resistance (Rf) to the input resistance (R1). |
Here is a full Glossary of Terms for the Electrical Engineering Calculator App:
Ohm’s Law
- Voltage (V): The electrical potential difference between two points in a circuit, measured in volts (V).
- Current (I): The flow of electric charge in a circuit, measured in amperes (A).
- Resistance (R): The opposition to the flow of electric current, measured in ohms (Ω).
- Power (P): The rate at which electrical energy is transferred, measured in watts (W).
Power Calculation
- Power (P): The amount of electrical energy consumed or produced in a circuit, measured in watts (W).
- Voltage (V): As defined in Ohm’s Law, the potential difference across a circuit.
- Current (I): As defined in Ohm’s Law, the flow of electric charge in a circuit.
Series & Parallel Resistors
- Resistor: A component that limits the flow of electric current, measured in ohms (Ω).
- Series Configuration: Resistors are connected end-to-end, resulting in the total resistance being the sum of individual resistances.
- Parallel Configuration: Resistors are connected alongside each other, resulting in the total resistance being less than any individual resistor.
Time Constants
- RC Time Constant (τ_RC): The time it takes for the voltage in an RC circuit to charge or discharge to about 63.2% of its full value.
- RL Time Constant (τ_RL): The time it takes for the current in an RL circuit to change to about 63.2% of its full value.
- Capacitance (C): The ability of a capacitor to store electrical energy, measured in farads (F).
- Inductance (L): The property of a conductor that opposes changes in current, measured in henries (H).
AC Power
- AC (Alternating Current): Electric current that reverses its direction periodically, used in most residential and industrial power systems.
- Single-phase Power: Power delivered through a single alternating current, typical in homes.
- Three-phase Power: Power delivered through three alternating currents, typically used in large industrial systems.
- Power Factor (cosϕ): A measure of how effectively the current is being converted into useful work, ranging from 0 to 1.
Power Factor
- Active Power (P_active): The actual power consumed by the circuit, measured in watts (W).
- Apparent Power (P_apparent): The combination of active and reactive power in a circuit, measured in volt-amperes (VA).
Reactance
- Capacitive Reactance (Xc): The opposition to the change in voltage in a capacitor, calculated as Xc=12πfCX_c = \frac{1}{2πfC}Xc=2πfC1, where f is frequency and C is capacitance.
- Inductive Reactance (Xl): The opposition to the change in current in an inductor, calculated as Xl=2πfLX_l = 2πfLXl=2πfL, where L is inductance and f is frequency.
Impedance (Z)
- Impedance (Z): The total opposition a circuit presents to the flow of alternating current, a combination of resistance (R) and reactance (X), calculated as Z=R2+X2Z = \sqrt{R^2 + X^2}Z=R2+X2.
Voltage Regulation
- Voltage Regulation (V.R.): The difference between the no-load and full-load voltages in a power system, expressed as a percentage.
Power Losses
- Copper Losses (P_cu): Power loss due to the resistance of conductors, measured in watts (W).
- Hysteresis Losses (P_h): Power loss in magnetic materials due to the repeated magnetization and demagnetization cycles, measured in watts (W).
- Eddy Current Losses (P_e): Power loss due to circulating currents in conductive materials subjected to changing magnetic fields, measured in watts (W).
Back EMF
- Back EMF (E_b): The electromotive force generated by a motor or generator that opposes the applied voltage, calculated based on flux (φ), speed (N), number of armature conductors (Z), and parallel paths (A).
Synchronous Speed
- Synchronous Speed (N_s): The speed at which the magnetic field in an AC motor rotates, calculated using the formula Ns=120fPN_s = \frac{120f}{P}Ns=P120f, where f is frequency and P is the number of poles.
Transformer EMF
- Electromotive Force (EMF): The induced voltage in a transformer winding due to changing magnetic flux, calculated as E=4.44×φm×f×TE = 4.44 \times φ_m \times f \times TE=4.44×φm×f×T, where φ_m is the maximum flux, f is frequency, and T is the number of turns.
Turns Ratio
- Turns Ratio (a): The ratio of the number of turns in the primary winding to the number of turns in the secondary winding of a transformer.
Op-Amp Gain
- Operational Amplifier (Op-Amp): A high-gain voltage amplifier with differential inputs.
- Voltage Gain (A_v): The ratio of the output voltage to the input voltage in an amplifier, calculated in an inverting configuration as Av=−RfRinA_v = -\frac{R_f}{R_{in}}Av=−RinRf, where R_f is feedback resistance and R_in is input resistance.
Background History
The equations used in the app have their origins in classical electrical engineering theory, based on fundamental laws such as Ohm’s Law (named after Georg Ohm, who formulated the relationship between voltage, current, and resistance in 1827), Kirchhoff’s Laws, and the principles of AC/DC circuit theory developed throughout the late 19th and early 20th centuries by scientists like James Clerk Maxwell and Heinrich Hertz.
These principles are the building blocks of modern electrical engineering and are still relevant today in the design, analysis, and operation of electrical and electronic systems.