Impedance Triangle Explorer

How to Use

Resistance R slider — set the resistive component (0–100 Ω). The horizontal side of the triangle.
Reactance X slider — set the reactive component (−100 to +100 Ω). Positive = inductive (triangle points up), negative = capacitive (triangle points down).
The right panel shows live calculations of |Z|, θ, and power factor.

The blue horizontal side represents resistance R — always positive, dissipates power.
The vertical side is reactance X: red when positive (inductive), green when negative (capacitive).
The purple hypotenuse is the impedance magnitude |Z|.
The phase angle θ opens at the origin — positive for inductive, negative for capacitive.
When X = 0, the triangle collapses to a horizontal line and the circuit is purely resistive.
When R = 0, the triangle collapses to a vertical line and the circuit is purely reactive (θ = ±90°).
Power factor = cos(θ) = R/|Z|; ranges from 0 (purely reactive) to 1 (purely resistive).

\[Z = R + jX \quad \text{(rectangular form)}\]

\[|Z| = \sqrt{R^2 + X^2} \quad \text{(Pythagorean theorem)}\]

\[\theta = \tan^{-1}\!\left(\frac{X}{R}\right) \quad \text{(phase angle)}\]

\[Z = |Z|\angle\theta \quad \text{(polar form)}\]

\[\text{Power Factor} = \cos\theta = \frac{R}{|Z|}\]

Impedance Z: Complex ratio of voltage to current in an AC circuit (Ω)
Resistance R: Real part of Z — dissipates energy as heat
Reactance X: Imaginary part of Z — stores and returns energy
Phase angle θ: Angle by which current lags (positive) or leads (negative) voltage
Power factor: Fraction of apparent power that does real work