THE INTERACTIVE POWER LAB

Three kinds of power.
One simple triangle.

Move the sliders. See how real and reactive power
combine — and what power factor really means.

A little geometry.
A lot of electrical engineering.

Set your load

Real power P

0 kW2,000 kW

Power that does work or becomes heat.

Reactive power Q

+kVAR

0 kVAR2,000 kVAR

Energy moves back and forth in electric or magnetic fields. The sign sets its direction.

TRY A SCENARIO

YOUR POWER TRIANGLE

Inductive · lagging

Real PReactive QApparent S

Apparent power S

1,000kVA

The combined equipment load

Power factor PF

0.80080%

Real ÷ apparent power

Phase angle φ

36.9°

Current lags voltage

At 800 kW, adding 600 kVAR raises apparent power to 1,000 kVA.

THE 800 / 600 / 1,000 MOMENT

Why isn’t the answer 1,400?

They combine at a right angle.

800²+600²=1,000²

640,000 + 360,000 = 1,000,000
√1,000,000 = 1,000 kVA

Think of walking 800 steps east and 600 steps north. Your straight-line distance is 1,000 steps, even though you walked 1,400.

Real and reactive power are also at right angles in the power triangle. That’s why we use the Pythagorean theorem:

S = √(P² + Q²)PF = P / S = 800 / 1,000 = 0.8

Power factor is a ratio, not efficiency. A PF of 0.8 does not mean 20% of the energy is wasted.

Same size. Different sign.

Switch +600 to −600 kVAR. Apparent power and PF stay the same, while the triangle flips and current leads instead of lags.

Less Q. Less loading.

Hold kW steady and move kVAR toward zero. kVA falls and PF approaches 1. At the same voltage, that means less current.

Zero has a special case.

With only reactive power, PF is 0. With no real or reactive power, PF is undefined because P/S becomes 0/0.

Model, units & sign convention

This tool models steady-state, sinusoidal AC with nonnegative real power consumed by a load. P is in kW, Q in kVAR, and S in kVA. The three values describe different aspects of the same electrical load.

Positive Q means an inductive load and lagging current. Negative Q means a capacitive load and leading current. The angle is φ = atan2(Q, P). Apparent power is a nonnegative magnitude: S = √(P² + Q²).

For a single phase, S = V_rmsI_rms. For a balanced three-phase system, total S = √3 V_LL,rmsI_L,rms. This simple triangle does not include harmonic distortion. With distorted waveforms, true PF may differ from the displacement factor cos φ.