Electrical Engineering Calculator

AC Power Calculator

Calculate active, reactive and apparent power for single-phase and three-phase AC circuits from voltage, current and power factor.

System Type

Select single-phase or three-phase AC

Input Parameters

Enter line-to-line voltage and line current

V

Line-to-line voltage of the three-phase system.

A

RMS current drawn by the load.

Power factor between 0 and 1 (e.g. 0.85).

Engineering Tip

Generators and transformers are rated in kVA. Always size them according to apparent power (S), not only active power (P).

Active Power (P)

29.44kW

29,445 W

Reactive Q

18.25 kVAR

Apparent S

34.64 kVA

Power Factor

0.850

Power Triangle

S² = P² + Q²
pf = P / S = cos φ
PW / kW

Active (real) power

QVAR / kVAR

Reactive power

SVA / kVA

Apparent power

pf

Power factor (cos φ)

VV

Line-to-line voltage

IA

Line current

Assumptions & Notes

  • Sinusoidal voltage and current
  • Balanced three-phase system
  • RMS values used
  • Constant power factor

Engineering Code

Reuse the AC power calculation in your own engineering workflow.

Python
import math

def ac_power(system, V, I, pf):
    """
    Calculate AC power components.

    system: 'single' or 'three'
    V: voltage (V) – line-to-line for three-phase
    I: current (A)
    pf: power factor (0 to 1)
    """

    if not (0 < pf <= 1):
        raise ValueError("Power factor must be between 0 and 1")

    phi = math.acos(pf)
    sin_phi = math.sin(phi)

    if system == 'three':
        S = math.sqrt(3) * V * I
    else:
        S = V * I

    P = S * pf
    Q = S * sin_phi

    return {
        "P_W": P,
        "Q_VAR": Q,
        "S_VA": S,
        "P_kW": P / 1000,
        "Q_kVAR": Q / 1000,
        "S_kVA": S / 1000,
        "pf": pf
    }


# Example
results = ac_power('three', 400, 50, 0.85)
for k, v in results.items():
    print(f"{k}: {v}")
MATLAB
function results = ac_power(system, V, I, pf)
    % AC power calculation
    % system: 'single' or 'three'
    % V = line-to-line voltage for three-phase

    if pf <= 0 || pf > 1
        error('Power factor must be between 0 and 1');
    end

    phi = acos(pf);
    sin_phi = sin(phi);

    if strcmp(system, 'three')
        S = sqrt(3) * V * I;
    else
        S = V * I;
    end

    results.P = S * pf;
    results.Q = S * sin_phi;
    results.S = S;
    results.P_kW = results.P / 1000;
    results.Q_kVAR = results.Q / 1000;
    results.S_kVA = results.S / 1000;
    results.pf = pf;
end

% Example
r = ac_power('three', 400, 50, 0.85);
disp(r);
Excel Formulas
S = SQRT(3)*V*I
P = S*pf
Q = S*SIN(ACOS(pf))

Example Calculation

Three-phase system: VL = 400 V, IL = 50 A, power factor = 0.85 (lagging):

P = √3 × 400 × 50 × 0.85 = 29,445 W ≈ 29.45 kW
S = √3 × 400 × 50 = 34,641 VA ≈ 34.64 kVA
Q = √3 × 400 × 50 × sin(φ) ≈ 18.25 kVAR
Power Factor = 0.85 lagging

Technical Explanation: AC Power in Single and Three-Phase Systems

In alternating-current circuits the power is divided into three components: active (real) power that performs useful work, reactive power that oscillates between source and load, and apparent power that is the vector sum of the two.

The power factor (cos φ) indicates how effectively the current is being converted into useful work. A low power factor increases current for the same active power and therefore increases losses and voltage drop.

How to Use This Calculator

  1. System Type: Select Single-phase or Three-phase.
  2. Voltage: Enter line-to-line voltage for three-phase or phase voltage for single-phase (V).
  3. Current: Enter the line current (A).
  4. Power Factor: Enter the power factor (0 to 1) or the phase angle.

Key Formulas

  • Single-phase: P = V × I × cos φ  |  S = V × I  |  Q = V × I × sin φ
  • Three-phase: P = √3 × VL × IL × cos φ  |  S = √3 × VL × IL

Power Triangle

Active power P, reactive power Q and apparent power S form a right triangle: S² = P² + Q². The angle of the triangle is the phase angle φ between voltage and current.

Real-World Engineering Cases

Industrial Plant with Low Power Factor Penalties

A manufacturing facility was paying significant monthly penalties because its overall power factor remained around 0.72. After measuring the actual active and reactive power of the largest motor loads, capacitor banks were installed and the power factor was raised above 0.95, eliminating the penalties.

Engineering Lesson

Knowing the real (kW) and reactive (kVAR) power of major loads is essential for correct power-factor correction. Simply measuring current is not enough.

Undersized Generator for a Construction Site

A temporary generator repeatedly tripped under load even though the calculated kW demand was within its rating. The loads had a low power factor (≈ 0.7), so the apparent power (kVA) exceeded the generator’s kVA rating.

Engineering Lesson

Generators and transformers are rated in kVA (apparent power). Always check both kW and kVA when sizing sources for AC loads.

Frequently Asked Questions

What is the difference between kW, kVAR and kVA?

kW (active power) is the useful power that performs work. kVAR (reactive power) is the power stored and released by inductors and capacitors. kVA (apparent power) is the vector sum of the two and determines the current drawn from the supply.

What is a good power factor?

A power factor of 0.95 or higher is generally considered good. Many utilities impose penalties below 0.90 or 0.95.

Do I use line-to-line or phase voltage for three-phase?

This calculator uses line-to-line voltage (V_L) and line current (I_L) together with the √3 factor, which is the most common practical approach.

What units should I use?

Voltage in volts (V), current in amperes (A), power factor dimensionless (0–1). Results are shown in W / kW, VAR / kVAR and VA / kVA.

Is the power factor leading or lagging?

Most industrial loads (motors, transformers) are inductive and have a lagging power factor. Capacitive loads produce a leading power factor. The calculator treats the numerical value; the sign of reactive power depends on the nature of the load.

Engineering calculations provided by this tool are for educational and preliminary design purposes. Always verify results against actual measurements, equipment nameplates and applicable electrical codes before use in final design.