Electrical Engineering Calculator

Power Factor Calculator

Calculate power factor, real power (kW), reactive power (kVAR), apparent power (kVA), and phase angle for AC electrical systems.

Power Triangle

Visual representation of real, reactive, and apparent power relationship

Calculation Method

Select input parameters based on available data.

Real Power (P)

Active power performing useful work.

Apparent Power (S)

kVA

Vector sum of real and reactive power.

Engineering Tip

Most utilities charge penalties for power factor below 0.95. Install capacitor banks to correct low power factor and reduce electricity costs.

Power Factor

0.800

Reactive Power

60.00 kVAR

Apparent Power

100.00 kVA

Phase Angle

36.87°

Low Power Factor Warning

Power factor below 0.85 indicates significant reactive power. Consider power factor correction using capacitor banks to reduce current, losses, and utility penalties.

Governing Formulas

PF = P / S = cos(φ)

S² = P² + Q²

Q = P × tan(φ)

PF—

Power factor

PkW

Real power

QkVAR

Reactive power

SkVA

Apparent power

φ°

Phase angle

Calculation Assumptions

Sinusoidal steady-state AC
Linear loads (no harmonics)
Single-phase or balanced 3-phase
Constant voltage and current
Lagging power factor (inductive load)
RMS values used

Engineering Code

Reuse the calculation in your own engineering workflow.

Python

import math

def power_factor_from_PS(P, S):
    """
    Calculate power factor from real and apparent power.
    P: Real power (kW)
    S: Apparent power (kVA)
    Returns: Power factor (0-1)
    """
    if P <= 0 or S <= 0 or S < P:
        raise ValueError("Invalid inputs: S must be >= P and both > 0")
    return P / S

def power_factor_from_VIP(V, I, P):
    """
    Calculate power factor from voltage, current, and real power.
    V: Voltage (V)
    I: Current (A)
    P: Real power (kW)
    Returns: Power factor (0-1)
    """
    if V <= 0 or I <= 0 or P <= 0:
        raise ValueError("All inputs must be positive")
    S = (V * I) / 1000  # Convert to kVA
    return P / S

def reactive_power(P, pf):
    """Calculate reactive power (kVAR)"""
    if pf <= 0 or pf > 1:
        raise ValueError("Power factor must be between 0 and 1")
    return P * math.tan(math.acos(pf))

def phase_angle(pf):
    """Calculate phase angle (degrees)"""
    if pf <= 0 or pf > 1:
        raise ValueError("Power factor must be between 0 and 1")
    return math.degrees(math.acos(pf))

# Example
P = 80
S = 100
pf = power_factor_from_PS(P, S)
Q = reactive_power(P, pf)
phi = phase_angle(pf)
print(f"Power Factor: {pf:.3f}")
print(f"Reactive Power: {Q:.3f} kVAR")
print(f"Phase Angle: {phi:.2f}°")

MATLAB

function [pf, Q, phi] = power_factor_calc(P, S)
% Calculate power factor and related quantities
%   P: Real power (kW)
%   S: Apparent power (kVA)
%   Returns: pf (power factor), Q (reactive power kVAR), phi (phase angle deg)

    if P <= 0 || S <= 0 || S < P
        error('Invalid inputs: S must be >= P and both > 0');
    end
    
    pf = P / S;
    Q = P * tan(acos(pf));
    phi = acosd(pf);
end

% Example
P = 80;
S = 100;
[pf, Q, phi] = power_factor_calc(P, S);
fprintf('Power Factor: %.3f\n', pf);
fprintf('Reactive Power: %.3f kVAR\n', Q);
fprintf('Phase Angle: %.2f deg\n', phi);

Excel Formula

=P/S

Example Calculation

For an industrial motor consuming 80 kW of real power with 100 kVA apparent power:

PF = P / S = 80 / 100

PF = 0.800

Q = P × tan(arccos(0.8)) = 80 × 0.75 = 60 kVAR

φ = arccos(0.8) = 36.87°

Technical Explanation: Power Factor

Power factor is a dimensionless number between 0 and 1 that represents the ratio of real power (kW) to apparent power (kVA) in an AC electrical system. It indicates how effectively electrical power is being converted into useful work output.

In AC circuits, voltage and current may not be perfectly in phase due to inductive or capacitive loads. This phase difference creates reactive power (kVAR), which does no useful work but increases the total current flow. The power factor is the cosine of this phase angle (φ).

How to Use This Calculator

Select Calculation Method: Choose "From P & S" if you know real and apparent power, or "From V, I & P" if you know voltage, current, and real power.
Enter Known Values: Input the electrical parameters in the appropriate fields.
View Results: The calculator displays power factor, reactive power, apparent power, and phase angle.
Analyze Power Triangle: Review the visualization to understand the relationship between P, Q, and S.

What is the Power Triangle?

The power triangle is a right triangle that visually represents the relationship between real power (P, horizontal), reactive power (Q, vertical), and apparent power (S, hypotenuse). The angle φ between P and S is the phase angle, and cos(φ) equals the power factor.

Why is low power factor problematic?

Low power factor (below 0.95) increases current flow for the same real power, causing higher I²R losses in conductors, larger voltage drops, and the need for oversized equipment (transformers, cables, switchgear). Utilities often impose penalties for power factor below 0.90-0.95 to recover the cost of infrastructure needed to supply reactive power.

How is power factor corrected?

Power factor correction typically involves adding capacitor banks in parallel with inductive loads. Capacitors supply leading reactive power that cancels the lagging reactive power from inductive loads (motors, transformers), reducing the total current and improving power factor toward 1.0. Automatic power factor correction units switch capacitor stages based on real-time load conditions.

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Real-World Engineering Cases

Texas Industrial Plant Power Factor Penalties (2019)

A large manufacturing facility in Houston received monthly utility penalties averaging $12,000 due to power factor consistently below 0.82. The plant operated over 200 induction motors with minimal power factor correction. After installing a 2,500 kVAR automatic capacitor bank, power factor improved to 0.97, eliminating penalties and reducing current by 18%.

Engineering Lesson

Low power factor has direct financial consequences. Regular power factor monitoring and automatic correction systems provide rapid ROI through penalty elimination, reduced I²R losses, and improved voltage regulation. Most industrial facilities should maintain PF above 0.95.

Hospital Generator Overload During Emergency (2017)

During a power outage, a hospital's 1,500 kVA emergency generator tripped on overload after 20 minutes despite the connected load being only 1,200 kW. Investigation revealed the power factor had dropped to 0.72 due to numerous medical imaging equipment and HVAC motors starting simultaneously, causing apparent power to exceed generator capacity.

Engineering Lesson

Generator sizing must account for apparent power (kVA), not just real power (kW). Emergency systems require power factor analysis under worst-case starting conditions. Install power factor correction capacitors on the emergency bus to ensure generators can supply the required kVA without overload.

Frequently Asked Questions

What is power factor?

Power factor (PF) is the ratio of real power (kW) to apparent power (kVA) in an AC electrical system. It represents how effectively electrical power is being used. A power factor of 1.0 indicates all power is being used effectively, while lower values indicate reactive power losses.

How do I calculate power factor?

Power factor = Real Power (kW) / Apparent Power (kVA). Alternatively, PF = cos(φ), where φ is the phase angle between voltage and current. For example, if a load consumes 80 kW with 100 kVA apparent power, PF = 80/100 = 0.8.

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

kW (kilowatts) is real power that performs useful work. kVAR (kilovolt-amperes reactive) is reactive power that sustains electromagnetic fields. kVA (kilovolt-amperes) is apparent power, the vector sum of kW and kVAR. The relationship is: kVA² = kW² + kVAR².

Why is power factor correction important?

Low power factor increases current flow, causing higher I²R losses, larger voltage drops, and oversized equipment. Utilities often charge penalties for PF below 0.95. Power factor correction using capacitor banks reduces current, improves efficiency, and avoids penalties.