Electrical Power Calculator

3‑Phase Power Calculator

Calculate active (P), reactive (Q), and apparent (S) power in a balanced three‑phase system. Enter line voltage, line current, and power factor to get all results.

Balanced Three‑Phase AC Circuit

L1L2L3ZNVLILS = √3·VL·ILP = S·PFQ = S·sin(θ)

Input Parameters

V

Voltage between any two phases (e.g., 400 V)

A

Current flowing in each phase conductor

—

Cosine of phase angle (0 to 1)

Engineering Tip

Power factor correction capacitors are often added to industrial loads to reduce reactive power (kVAR) and improve overall efficiency, thereby lowering electricity bills and reducing cable losses.

Three‑Phase Power Results

Active Power (P)

29.44 kW

Reactive Power (Q)

18.25 kVAR

Apparent Power (S)

34.64 kVA

Governing Formula

S = √3 · VL · IL
SkVA

Apparent Power

Governing Formula

P = S · PF, Q = S · sin(acos(PF))
PkW

Active Power

QkVAR

Reactive Power

Engineering Code

Python
import math

def three_phase_power(V_L, I_L, PF):
    # V_L: line voltage (V), I_L: line current (A), PF: power factor (0-1)
    if V_L <= 0 or I_L <= 0 or not (0 <= PF <= 1):
        raise ValueError('Invalid input values.')
    S = math.sqrt(3) * V_L * I_L / 1000  # kVA
    P = S * PF                           # kW
    Q = S * math.sin(math.acos(PF))     # kVAR
    return {'P_kW': P, 'Q_kVAR': Q, 'S_kVA': S}

res = three_phase_power(400, 50, 0.85)
print(f"Active Power (P): {res['P_kW']:.2f} kW")
print(f"Reactive Power (Q): {res['Q_kVAR']:.2f} kVAR")
print(f"Apparent Power (S): {res['S_kVA']:.2f} kVA")

Technical Explanation: Three‑Phase Power

In a balanced three‑phase system, the total active power (P), reactive power (Q), and apparent power (S) are calculated from the line voltage (VL), line current (IL), and power factor (PF). The fundamental relationships are:

S = √3 · VL · IL

P = S · PF

Q = S · sin(acos(PF))

These formulas assume a balanced load and sinusoidal waveforms. The power factor (PF) is the cosine of the phase angle between voltage and current.

Key Concepts

  • Line Voltage (VL): Voltage measured between any two phases. In a star connection, VL = √3 · Vph.
  • Line Current (IL): Current flowing in each phase line. In a delta connection, IL = √3 · Iph.
  • Power Factor (PF): The ratio of real power to apparent power (0 to 1). A PF of 1 means purely resistive load.
  • Apparent Power (S): Total power supplied, measured in kVA.
  • Active Power (P): Actual power consumed, measured in kW.
  • Reactive Power (Q): Power that oscillates between source and load, measured in kVAR.

How to Use the Calculator

  1. Enter Line Voltage: in volts (V).
  2. Enter Line Current: in amperes (A).
  3. Enter Power Factor: a value between 0 and 1 (e.g., 0.85). Default is 1.
  4. The calculator instantly displays P (kW), Q (kVAR), and S (kVA).

Real-World Engineering Cases

Industrial Motor Load

A 400 V, 50 Hz three‑phase motor draws 50 A with a power factor of 0.85. The apparent power S = √3 × 400 × 50 = 34.6 kVA. Active power P = 34.6 × 0.85 = 29.4 kW, and reactive power Q = 34.6 × sin(acos(0.85)) ≈ 18.2 kVAR. The facility's power factor correction capacitors must compensate for this reactive power to avoid utility penalties.

Engineering Lesson

Understanding P, Q, and S is essential for sizing transformers, cables, and power factor correction equipment.

Data Center UPS Sizing

A data center has a total load of 500 kW at 0.9 PF. The apparent power required is S = 500 / 0.9 = 555.6 kVA. A UPS with at least 600 kVA rating should be selected to handle the load and provide margin. Ignoring reactive power can lead to undersized UPS and overheating.

Engineering Lesson

Always consider apparent power (kVA) when sizing backup power systems, not just kW.

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Frequently Asked Questions

What is the difference between kVA, kW, and kVAR?

kVA (apparent power) is the total power supplied to the circuit. kW (active power) is the useful power that does work. kVAR (reactive power) is the power that oscillates between the source and reactive components (inductors/capacitors). The relationship is: kVA² = kW² + kVAR².

Why do we use √3 in three‑phase power calculations?

In a balanced three‑phase system, the total power is the sum of the powers in each phase. For line quantities, the factor √3 appears because the line voltage is √3 times the phase voltage (in star) or the line current is √3 times the phase current (in delta). The formula S = √3 · VL · IL gives the total three‑phase apparent power.

What is a good power factor?

A power factor close to 1 (e.g., 0.95 or higher) is considered good because it means the load uses most of the supplied power efficiently. Low power factors (below 0.8) indicate reactive power and may incur penalties from utility companies. Power factor correction capacitors are often used to improve PF.