What is power factor (Cos ϕ)? How to Calculate Power Factor

Confused by high electricity bills or unexpected utility penalties? It might be due to a hidden issue: poor power factor.

Power factor (Cos ϕ) shows how efficiently electrical power is used. It’s the ratio between real power and apparent power. A perfect system has a power factor of 1.

If you’re running motors, drives, or heavy loads, understanding and improving power factor could save you a lot of money.

Understanding the Electric Power Formula?

Most people only care about watts, but in AC systems, not all power is useful.

Electric power in AC systems is divided into three types: real power (kW), reactive power (kVAR), and apparent power (kVA). Power factor is the ratio of kW to kVA.

Electric Power Breakdown

• Real Power (P)¹: The actual power used to run equipment (in kilowatts, kW)
• Reactive Power (Q)²: The power used to maintain electric and magnetic fields (in kilovolt-amperes reactive, kVAR)
• Apparent Power (S): The total power supplied by the source (in kilovolt-amperes, kVA)

The formula:
Power Factor³ (Cos ϕ) = Real Power (kW) / Apparent Power (kVA)

The closer Cos ϕ is to 1, the more efficient your system is.

Power Factor Triangle and Examples: beer analogy?

Power factor feels abstract. So let’s simplify it with a triangle—and a beer.

The power triangle shows the relationship between real, reactive, and apparent power. Imagine a beer: the foam is reactive power, the beer is real power, and the glass is apparent power.

Visual Triangle

• P (kW) = base of the triangle (beer)
• Q (kVAR) = vertical side (foam)
• S (kVA) = diagonal hypotenuse (glass)

A good beer = less foam, more beer.
A good power system = less reactive power, more real power.

Example

If your system consumes:

• 800 kW real power
• 1000 kVA apparent power

Then:
Power Factor = 800 / 1000 = 0.8

That means 20% of your power is wasted on non-productive energy.

The two causes of poor power factor?

Low power factor is common. But why does it happen?

There are two major causes: inductive loads⁴ and oversized no-load transformers⁵. Both create reactive power that reduces system efficiency.

1. Inductive Loads

Motors, transformers, welding machines, HVAC systems—all contain coils. Coils create magnetic fields, which draw reactive power.

The more motors you have, the worse your power factor usually gets—especially if motors are old or underloaded.

2. Oversized or No-Load Transformers

When transformers are energized but not loaded, they still draw magnetizing current. That adds to reactive power without doing useful work.

This is common in standby equipment or under-utilized backup systems.

Improving your load management and motor control helps reduce these inefficiencies.

Impacts of low Power Factor?

Low power factor might be invisible—but its effects are not.

Low power factor leads to higher electricity bills, increased losses, and overloaded equipment. Utilities may penalize customers for it.

Main Impacts

Improving power factor is not just about saving cost. It’s also about safety, stability, and compliance.

Steps to improve low Power Factor?

Low power factor isn’t a dead end. There are proven ways to fix it.

The most common way to improve power factor is to install power factor correction capacitors⁶. Other options include synchronous condensers⁷ and active filters.

Common Solutions

Pro Tip

Use a power analyzer to record your load profile. Then size your capacitor bank based on peak kVAR need. At Shangdian, we help clients calculate and install the correct setup.

Conclusion

Power factor tells you how efficiently you use electricity. Improve it—and you improve everything from cost to safety.