Alternating single‑phase
cosφ = P / (U₀ * I)
cosφ = (P * Z) / (U₀²)
cosφ = P / (I² * Z)
cosφ = P / S
cosφ = R / Z
sinφ = Q / S
sinφ = Q / (U₀ * I)
tanφ = Q / P
Alternating two‑phase
cosφ = P / (U * I)
cosφ = (P * Z) / (U²)
cosφ = P / (I² * Z)
cosφ = P / S
cosφ = R / Z
sinφ = Q / S
sinφ = Q / (U * I)
tanφ = Q / P
Alternating three‑phase
cosφ = P / (√3 * U * I)
cosφ = (P * Z) / (√3 * U²)
cosφ = P / (√3 * I² * Z)
cosφ = P / S
cosφ = R / Z
sinφ = Q / S
sinφ = Q / (√3 * U * I)
tanφ = Q / P
Where：
φ = Phase shift between voltage and current
P = Active power (W)
S = Apparent power (VA)
Q = Reactive power(VAr)
I = Current(A)
U₀ = Voltage [L − N] (V)
U = Voltage [L − N] (V)
R = Resistance(Ω)
Z = Impedance(Ω)
Calculate power factor (PF) in AC circuits using voltage, current, active power, reactive power, resistance, or impedance. Supports single-phase, two-phase, and three-phase systems. Based on IEC standards for electrical efficiency analysis.
| Input Parameter | Symbol | Unit | Required Combinations |
|---|---|---|---|
| Voltage | V | V (volts) | With current → S = V×I |
| Current | I | A (amperes) | With voltage → S = V×I |
| Active Power | P | W (watts) | With S or Q → PF = P/S or P/√(P²+Q²) |
| Reactive Power | Q | VAR | With P → PF = P / √(P² + Q²) |
| Resistance | R | Ω (ohms) | With Z → PF = R / Z |
| Impedance | Z | Ω (ohms) | With R → PF = R / Z |
Power factor (PF) is the ratio of active power (P) to apparent power (S):
PF = P / S = cosφ
PF = 1.0: Purely resistive load (e.g., heater), no reactive power
PF < 1.0: Inductive or capacitive load (e.g., motors, transformers)
Low PF consequences:
Increased line current
Higher copper losses
Reduced transformer capacity
Utility penalties (common if PF < 0.85–0.90)
The calculator uses one of the following equivalent formulas based on available inputs:
From P and S: PF = P / (V × I)
From P and Q: PF = P / √(P² + Q²)
From R and Z: PF = R / Z
From phase angle φ: PF = cosφ (if angle is known)
Note: DC circuits are not supported — power factor is always 1.0 in DC systems.
Single-phase AC
Enter Phase-Neutral voltage and per-phase current.
Two-phase AC
Enter Phase-Phase voltage; assumes balanced load.
Three-phase AC
Enter Line-to-Line voltage (V LL) and line current (I L). The calculator assumes a balanced system and computes total apparent power as S = √3 × V LL × I L.
Industrial motor systems: Verify PF before installing capacitor banks
Energy audits: Identify low-efficiency loads for correction
Electrical design: Size conductors and protection devices with accurate current estimates
Utility compliance: Ensure PF ≥ 0.95 to avoid demand charges
Educational labs: Demonstrate relationship between P, Q, S, and PF
Use RMS values for voltage and current in AC systems
For non-linear loads (e.g., VFDs, LED drivers), measured PF may include harmonic distortion effects
If only apparent power (VA) is known, active power (W) must also be provided
Resistance and impedance inputs assume linear, sinusoidal conditions
Utilities may impose penalties on customers with low power factors because they require larger capacity infrastructure to deliver the same amount of active power. Low PF increases transmission losses and reduces grid efficiency.
This calculator adheres to IEC 60050 terminology and is intended for use by electrical engineers, facility managers, technicians, and students in power systems analysis.
Yes, this calculator supports single-phase, two-phase, and three-phase systems. For three-phase calculations, enter line-to-line voltage and per-phase current values. Ensure balanced load conditions for accurate results.
Improving power factor often involves adding capacitor banks to compensate for reactive power, especially in industrial settings with many motors. Reducing the number of lightly loaded inductive devices and ensuring proper maintenance of existing equipment can also help.
A low power factor indicates that your system has significant reactive power, which means some of the electrical energy is being stored and then released by inductive or capacitive loads without doing useful work. This results in higher currents, increased losses, and possibly utility penalties.
No, power factor is a concept applicable only to AC systems. In DC systems, the power factor is always 1 because there is no phase shift between voltage and current.
To calculate power factor using just voltage and current, you need to measure or estimate the phase angle between them. The formula is: PF = cosφ, where φ is the phase angle. Alternatively, if you can also measure active power (P), then PF = P / (V × I).
The power factor (PF) is the ratio of active power to apparent power in AC circuits, indicating how effectively electrical energy is being used. A high PF means less wasted energy and more efficient use of electrical infrastructure.
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