Electrical Formulas
Essential DC, AC single-phase, three-phase, power factor, and impedance formulas.
16 reference items · 5 sections
DC Circuit Formulas
Ohm's Law
V = I × R
Ohm's Law
| Variable | Description | Unit |
|---|---|---|
| V | Voltage | Volts |
| I | Current | Amperes |
| R | Resistance | Ohms (Ω) |
Variations:Find Current: I = V ÷ RFind Resistance: R = V ÷ I
The fundamental relationship between voltage, current, and resistance in an electrical circuit.
DC Power
P = V × I
DC Power
| Variable | Description | Unit |
|---|---|---|
| P | Power | Watts |
| V | Voltage | Volts |
| I | Current | Amperes |
Variations:Using R: P = I² × RUsing R: P = V² ÷ RFind Current: I = P ÷ VFind Voltage: V = P ÷ I
Power consumed by a DC circuit.
Electrical Energy
E = P × t
Electrical Energy
| Variable | Description | Unit |
|---|---|---|
| E | Energy | Watt-hours (Wh) |
| P | Power | Watts |
| t | Time | Hours |
Variations:In kWh: kWh = (W × h) ÷ 1000
1 kWh = 1,000 Wh. Utility billing is typically in kWh.
Series Resistance
R_total = R₁ + R₂ + R₃ + ...
Series Resistance
| Variable | Description | Unit |
|---|---|---|
| R_total | Total resistance | Ohms (Ω) |
| R₁,R₂ | Individual resistances | Ohms (Ω) |
In a series circuit, total resistance is the sum of all resistances. Current is the same through all components.
Parallel Resistance
1/R_t = 1/R₁ + 1/R₂ + 1/R₃ + ...
Parallel Resistance
| Variable | Description | Unit |
|---|---|---|
| R_t | Total resistance | Ohms (Ω) |
| R₁,R₂ | Individual resistances | Ohms (Ω) |
Variations:Two Resistors: R_t = (R₁×R₂)÷(R₁+R₂)
For two resistors: R_t = (R₁ × R₂) ÷ (R₁ + R₂). Voltage is the same across all branches.
AC Single-Phase Formulas
Single-Phase Power
P = V × I × PF
Single-Phase Power
| Variable | Description | Unit |
|---|---|---|
| P | Real power | Watts |
| V | Voltage | Volts |
| I | Current | Amperes |
| PF | Power factor | decimal 0-1 |
Variations:Find Amps: I = P ÷ (V × PF)Find Voltage: V = P ÷ (I × PF)
PF = 1.0 for purely resistive loads (heaters, incandescent). PF < 1.0 for motors, fluorescents.
Apparent Power (1Φ)
S = V × I
Apparent Power
| Variable | Description | Unit |
|---|---|---|
| S | Apparent power | Volt-Amperes (VA) |
| V | Voltage | Volts |
| I | Current | Amperes |
Variations:kVA: kVA = (V × I) ÷ 1000Find Amps: I = kVA × 1000 ÷ V
Apparent power is the product of voltage and current without considering power factor. kVA = VA ÷ 1000.
Amps from HP (1Φ)
I = (HP × 746) ÷ (V × Eff × PF)
Single-Phase Amps from Horsepower
| Variable | Description | Unit |
|---|---|---|
| I | Current | Amperes |
| HP | Horsepower | HP |
| V | Voltage | Volts |
| Eff | Motor efficiency | decimal |
| PF | Power factor | decimal |
1 HP = 746 Watts. Typical motor efficiency: 0.80-0.95. Typical PF: 0.80-0.90.
AC Three-Phase Formulas
Three-Phase Power
P = √3 × V × I × PF
Three-Phase Power
| Variable | Description | Unit |
|---|---|---|
| P | Real power | Watts |
| √3 | Square root of 3 | ≈ 1.732 |
| V | Line voltage | Volts |
| I | Line current | Amperes |
| PF | Power factor | decimal |
Variations:Find Amps: I = P ÷ (1.732 × V × PF)kW: kW = (1.732×V×I×PF)÷1000
Use line-to-line voltage (e.g., 208V, 240V, 480V). √3 ≈ 1.732.
Apparent Power (3Φ)
S = √3 × V × I
Three-Phase Apparent Power
| Variable | Description | Unit |
|---|---|---|
| S | Apparent power | VA |
| V | Line voltage | Volts |
| I | Line current | Amperes |
Variations:kVA: kVA = (1.732×V×I) ÷ 1000Find Amps: I = kVA×1000 ÷ (1.732×V)
Amps from HP (3Φ)
NEC 430.250
I = (HP × 746) ÷ (1.732 × V × Eff × PF)
Three-Phase Amps from Horsepower
| Variable | Description | Unit |
|---|---|---|
| I | Current | Amperes |
| HP | Horsepower | HP |
| V | Line voltage | Volts |
| Eff | Motor efficiency | decimal |
| PF | Power factor | decimal |
For motor circuit sizing, use NEC Table 430.250 FLC values instead of calculating from nameplate.
Power Factor & Power Triangle
Power Factor
PF = P ÷ S = cos(θ)
Power Factor
| Variable | Description | Unit |
|---|---|---|
| PF | Power factor | decimal 0-1 |
| P | Real power (true power) | Watts |
| S | Apparent power | VA |
| θ | Phase angle | degrees |
Variations:As %: PF% = (P ÷ S) × 100
Power Triangle
P (Watts) = Real Power — does actual work
S (VA) = Apparent Power — total circuit power
Q (VAR) = Reactive Power — stored/returned by inductors/capacitors
Q = √(S² - P²)
Reactive Power
| Variable | Description | Unit |
|---|---|---|
| Q | Reactive power | VAR |
| S | Apparent power | VA |
| P | Real power | Watts |
Variations:Find S: S = √(P² + Q²)
S² = P² + Q² (Pythagorean relationship)
Impedance, Reactance & Resonance
Impedance
Z = √(R² + X²)
Impedance
| Variable | Description | Unit |
|---|---|---|
| Z | Impedance | Ohms (Ω) |
| R | Resistance | Ohms (Ω) |
| X | Net reactance (X_L - X_C) | Ohms (Ω) |
Variations:AC Ohm's Law: I = V ÷ Z
Impedance is the total opposition to current flow in an AC circuit. Ohm's Law for AC: V = I × Z.
Inductive Reactance
X_L = 2π × f × L
Inductive Reactance
| Variable | Description | Unit |
|---|---|---|
| X_L | Inductive reactance | Ohms (Ω) |
| f | Frequency | Hertz (Hz) |
| L | Inductance | Henrys (H) |
Variations:Find L: L = X_L ÷ (2π × f)
At 60 Hz: X_L = 377 × L. Inductive reactance increases with frequency.
Capacitive Reactance
X_C = 1 ÷ (2π × f × C)
Capacitive Reactance
| Variable | Description | Unit |
|---|---|---|
| X_C | Capacitive reactance | Ohms (Ω) |
| f | Frequency | Hertz (Hz) |
| C | Capacitance | Farads (F) |
Variations:Find C: C = 1 ÷ (2π × f × X_C)
Capacitive reactance decreases with frequency — opposite of inductive reactance.
Resonant Frequency
f_r = 1 ÷ (2π × √(L × C))
Resonant Frequency
| Variable | Description | Unit |
|---|---|---|
| f_r | Resonant frequency | Hertz (Hz) |
| L | Inductance | Henrys (H) |
| C | Capacitance | Farads (F) |
Variations:Find L: L = 1 ÷ (4π²f²C)Find C: C = 1 ÷ (4π²f²L)
At resonance, X_L = X_C, so impedance is purely resistive (Z = R). Current is maximum in a series RLC circuit and minimum in a parallel RLC circuit.
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