Plug a motor into the wall and its current does not quite keep step with the voltage — it lags behind by an angle, and that angle is the phase. In AC circuits, phase angle φ measures how far the current waveform trails or leads the voltage waveform, computed as the arctangent of reactance divided by resistance: φ = arctan(X/R). A purely resistive heater has 0° of phase (current and voltage march together), a pure inductor pushes toward +90°, and a pure capacitor toward −90°.

Utilities care because phase determines real power: a factory with a large phase angle draws current that does no useful work, and power companies bill penalties for it — hence 'power factor correction' capacitor banks on industrial rooftops. Audio engineers meet the same angle when aligning subwoofers, and navigators when comparing signal phases. This calculator performs the ratio step: type the reactance X in ohms in the Variable A box — say 30 for a motor winding — and type 1 ÷ R in the Variable B box (1 ÷ 40 = 0.025 for 40 ohms of resistance). The Result box shows 0.75, the X/R ratio; take its arctangent on paper (about 36.9°) to get the phase angle. Positive means current lags voltage (inductive); negative means it leads (capacitive).

With the pre-filled defaults — Variable A 10, Variable B 5 — the Phase Calculator returns Result 50.0000. Change any input and those results update instantly, so you can see exactly how each number you enter moves the answer.