Power Factor Calculator
This power factor calculator is handy for analyzing the alternating current (AC) flowing in electrical circuits. In the case of AC, modeling is not as simple as DC (Ohm's law), because such circuits contain both real and reactive power.
Real, Reactive, and Apparent Power
To understand the power factor, you first need a deeper understanding of its components: the real, reactive, and apparent power.
- Real power (P) — also called true or active power — performs the real work in an electrical circuit and is dissipated in resistors. It is the only form of power that appears in a DC circuit. In an AC circuit with no phase shift, all transferred power is active. Measured in watts (W).
- Reactive power (Q) — transferred when the current and voltage are 90° out of phase. The net energy transferred in the AC circuit equals zero, so no real power is lost. Linked to the reactance produced by inductors and capacitors. Measured in Volt-Amps-Reactive (VAR).
- Apparent power (S) — the combination of real and reactive powers. It is the product of the RMS values of voltage and current, omitting the influence of the phase angle. Measured in Volt-Amps (VA).
The Power Triangle
Apparent power is found by vector addition of the real and reactive power. You can represent these three values as a right triangle called the power triangle:
- The legs represent real power (P) and reactive power (Q).
- The hypotenuse represents apparent power (S).
- The angle φ (phi) between the real and apparent power is the circuit's impedance phase angle.
By the Pythagorean theorem:
S² = P² + Q²
Power Factor Formula
The power factor (PF) is defined as the ratio of real power to apparent power:
PF = cos φ = P / S
It is a dimensionless number between 0 and 1 (or 0% to 100%). A power factor of 1 means all power is real — a purely resistive circuit. A power factor of 0 means all power is reactive — a purely inductive or capacitive circuit.
How to Calculate the Power Factor?
- Measure the RMS voltage (V) and RMS current (I) in the circuit.
- Calculate the apparent power: S = V × I (in VA)
- Measure or calculate the real power (P) using a wattmeter.
- Apply the formula: PF = P / S = cos φ
- The phase angle: φ = arccos(PF)
Resistance, Reactance, and Impedance
In an AC circuit, the total opposition to current flow is called impedance (Z), measured in ohms (Ω):
- Resistance (R) — opposition from resistive elements (dissipates energy as heat): R = Z × cos φ
- Reactance (X) — opposition from reactive elements (inductors, capacitors): X = Z × sin φ
- Impedance (Z) — vector sum of resistance and reactance: Z = V / I
Power Quality Classification
| Power Factor | Rating | Typical Applications |
|---|---|---|
| 0.95 – 1.00 | Excellent | Resistive heaters, incandescent lighting |
| 0.85 – 0.95 | Good | Most industrial motors (under load) |
| 0.70 – 0.85 | Acceptable | Lightly loaded motors, some HVAC systems |
| < 0.70 | Poor | Fluorescent lighting, welding equipment |
American vs. Metric Units
This calculator supports both unit systems:
- Metric (SI): Power in Watts (W), kilowatts (kW), and megawatts (MW)
- American: Real power also displayed in Horsepower (HP) — 1 HP = 746 W
Electricity Cost Calculator
Enable the cost section to calculate your monthly electricity bill. The calculator supports multiple currencies:
- $ USD — US Dollar
- ₽ RUB — Russian Ruble
- € EUR — Euro
- £ GBP — British Pound
- ¥ JPY — Japanese Yen
- ¥ CNY — Chinese Yuan
- R$ BRL — Brazilian Real
- ₹ INR — Indian Rupee
Formula: Monthly Energy (kWh) = (P / 1000) × hours/day × days/month
Monthly Cost = Energy × Rate per kWh
FAQs
What is a good power factor?
A power factor above 0.95 is considered excellent. Utility companies often charge penalties for commercial customers with power factors below 0.85 or 0.90.
How can I improve my power factor?
You can improve power factor by adding capacitor banks to counteract inductive loads, using power factor correction equipment, or replacing older motors with energy-efficient models.
What is the difference between leading and lagging power factor?
A lagging power factor (most common) occurs when the current lags behind the voltage, typical of inductive loads like motors. A leading power factor occurs when current leads voltage, typical of capacitive loads.
Why does power factor matter?
A low power factor means more current is drawn from the supply for the same amount of real work, leading to higher transmission losses, larger conductors needed, and higher electricity bills from utility surcharges.