Phasor Addition Visualizer

How to Use

V₁ magnitude / V₁ phase sliders — set the amplitude (0.5–10 V) and phase (−180° to 180°) of the first phasor.
V₂ magnitude / V₂ phase sliders — set the amplitude and phase of the second phasor.
Construction Lines button — toggle the head-to-tail construction (V₂ translated to tip of V₁).
The green arrow V_T is the resultant phasor; the right panel verifies it matches the waveform sum.

Phasor addition is simple complex number addition — no trig identities needed.
The head-to-tail construction (pink dashed arrow) shows geometrically how V₁ + V₂ = V_T.
The right panel plots v₁(t), v₂(t), and v_T(t) simultaneously — the green curve should match v₁(t) + v₂(t) point-by-point.
When V₁ and V₂ are in phase (same angle), |V_T| = |V₁| + |V₂|.
When V₁ and V₂ are 180° apart, they can cancel: |V_T| can be zero.
Try V₁ = 10∠0° and V₂ = 10∠90° — the result is 14.14∠45° (√2 amplification).

\[\mathbf{V}_1 = V_{m1}\angle\phi_1 = V_{m1}\cos\phi_1 + jV_{m1}\sin\phi_1\]

\[\mathbf{V}_2 = V_{m2}\angle\phi_2 = V_{m2}\cos\phi_2 + jV_{m2}\sin\phi_2\]

\[\mathbf{V}_{total} = \mathbf{V}_1 + \mathbf{V}_2 = (a_1+a_2) + j(b_1+b_2)\]

\[|\mathbf{V}_{total}| = \sqrt{(a_1+a_2)^2 + (b_1+b_2)^2}, \quad \phi_{total} = \tan^{-1}\!\left(\frac{b_1+b_2}{a_1+a_2}\right)\]