IP331.com | Online Tools
HomeElectronics & PhysicsReal Reactive Apparent Power Calculator

Real Reactive Apparent Power Calculator

Calculate P, Q, S and the Power Triangle for AC Circuits

Voltage V (V)
Current I (A)
Phase Angle φ (°)
Negative φ = capacitive (leading), positive φ = inductive (lagging)

AC Power Formulas

S = V × I (apparent, VA)
P = V × I × cos φ (real, W)
Q = V × I × sin φ (reactive, VAR)
S = √(P² + Q²), PF = P/S = cos φ

In AC circuits, power has three components. Real power (P) performs useful work and is measured in watts. Reactive power (Q) oscillates between source and reactive elements, measured in VAR. Apparent power (S) is the vector sum, measured in VA. Understanding these helps correctly size transformers, generators, and power factor correction equipment.

Inductive loads (motors) have positive Q (lagging PF). Capacitive loads have negative Q (leading PF). Power factor correction adds capacitors to cancel inductive Q, reducing apparent power S and line current.

Understanding AC Power

AC power is more complex than DC because voltage and current can be out of phase. Real power does work, reactive power represents energy stored and returned each cycle, and apparent power is what the utility must supply. The power factor measures the efficiency of power delivery.

Real Power P

P = VI cos φ (W). Does useful work. Resistive loads only. Measured by wattmeter. Billed by utility.

Reactive Power Q

Q = VI sin φ (VAR). Stored in L/C fields. Inductive = +Q, capacitive = -Q. No work but causes line loss.

Apparent Power S

S = VI (VA). Total power drawn. S = √(P²+Q²). Transformers and generators rated in kVA. Sizing based on S, not P.

Power Triangle

P on x-axis, Q on y-axis, S as hypotenuse. φ = arctan(Q/P). PF = cos φ = P/S. Unity PF when Q=0.

Teaching Example: V=120V, I=1.5A, φ=30°.
S = 120 × 1.5 = 180 VA. P = 120 × 1.5 × cos(30°) = 180 × 0.866 = 155.9 W.
Q = 120 × 1.5 × sin(30°) = 180 × 0.5 = 90 VAR (inductive).
Verify: S = √(155.9²+90²) = √32400 = 180 VA. PF = 155.9/180 = 0.866 (cos 30°).

Applications

Generator Sizing Transformer Rating PF Correction Utility Billing UPS Selection

Frequently Asked Questions

What is the difference between P Q and S?
P (real) does work, measured in W. Q (reactive) oscillates, measured in VAR. S (apparent) is total, measured in VA. S² = P²+Q².
Why is reactive power important?
Q doesn't do work but causes line current and losses. Utilities charge penalties for low PF. Q must be supplied by generators or capacitors.
How to size a transformer?
Use apparent power S = V×I in VA or kVA. A 100kVA transformer at PF=0.8 can supply 80kW real. Size for S, not P.
What is unity power factor?
PF=1 means P=S and Q=0. Voltage and current are in phase (φ=0). Purely resistive load. Maximum efficiency. No reactive power.

More Electronics Tools

Free online calculators and tools covering mathematics, unit conversion, text processing, and daily life. Accurate, fast, mobile-friendly, and completely free to use.

© 2026 IP331.com — Free Online Tools. All rights reserved.

About · Contact · Privacy Policy · Cookie Policy · Terms of Use · Disclaimer · Sitemap