RMS to Watts Calculator — AC Power from V_rms & I_rms
Enter the RMS voltage, RMS current and power factor of an AC circuit to find the real power in watts, apparent power in VA, and reactive power in VAR. Works for single-phase AC loads: mains appliances, motors, transformers and audio amplifiers.
V
A
Actual power consumed — real watts delivered to the load
- 1
Apparent power S (VA)
230 × 5 = 1,150 - 2
Real power P (W)
1,150 × 1 = 1,150
How does this calculator work?
Real power P (watts) = V_rms × I_rms × cos φ. Apparent power S (VA) = V_rms × I_rms. Reactive power Q (VAR) = S × sin φ. For a resistive load (power factor = 1), watts = VA. A typical motor with power factor 0.85 uses only 85% of its apparent power as real work.
Formula
How this is calculated
In an AC circuit, the RMS (root-mean-square) values of voltage and current are the equivalent DC values that would deliver the same power to a resistive load. Their product S = V_rms × I_rms is the apparent power in volt-amperes (VA) — what the supply "sees." However, if the load is reactive (inductor or capacitor), some energy is stored and returned each cycle rather than consumed. The power factor cos(φ) — the cosine of the phase angle between voltage and current — captures this. Real power P = S × cos(φ) is actual energy consumed per second (watts). Reactive power Q = S × sin(φ) circulates between source and reactive elements without being converted to work.
For resistive loads (heaters, incandescent bulbs, ovens) the power factor is 1 and P = S exactly. For inductive loads such as motors and transformers, the power factor is typically 0.7–0.9; the apparent current drawn from the supply is larger than the real-power current alone would suggest. Utilities care about this because reactive current heats transmission lines without delivering useful energy.
This calculator assumes a single-phase sinusoidal AC supply. For three-phase systems, multiply the result by √3 (line-to-neutral voltage) or √3 × V_LL for line-to-line voltage, depending on connection.
Frequently asked questions
The power factor (cos φ) is the ratio of real power (W) to apparent power (VA). A power factor of 1.0 means all supplied energy does useful work. Lower power factors (common with inductive loads like motors) mean the supply must push more current than strictly necessary, increasing cable losses and supply costs. Power-factor correction capacitors bring it back toward 1.0.
For a pure sine wave, V_rms = V_peak ÷ √2 ≈ 0.707 × V_peak and I_rms = I_peak ÷ √2. Mains supply ratings (230 V UK/EU, 120 V US) are already RMS. For non-sinusoidal waveforms, a true-RMS meter gives the correct reading; average-responding meters are inaccurate.
Watts (W) measure real power — energy converted to heat, light or mechanical work per second. Volt-amperes (VA) measure apparent power — the product of RMS voltage and RMS current. For resistive loads they are equal; for reactive loads, VA > W. Equipment like UPS units and generators are rated in VA because they must supply the full current regardless of load power factor.
Also known as
TG we-Calculate Editorial Team. (2026). RMS to Watts Calculator — AC Power from V_rms & I_rms [Online calculator]. TG we-Calculate. https://we-calculate.com/calculator/rms-to-watts-calculator
TG we-Calculate Editorial Team. "RMS to Watts Calculator — AC Power from V_rms & I_rms." TG we-Calculate. 2026. https://we-calculate.com/calculator/rms-to-watts-calculator.
TG we-Calculate Editorial Team, "RMS to Watts Calculator — AC Power from V_rms & I_rms," TG we-Calculate, 2026. [Online]. Available: https://we-calculate.com/calculator/rms-to-watts-calculator
@misc{wecalculate_rms_to_watts_calculator, title = {RMS to Watts Calculator — AC Power from V_rms & I_rms}, author = {{TG we-Calculate Editorial Team}}, howpublished = {\url{https://we-calculate.com/calculator/rms-to-watts-calculator}}, year = {2026}, note = {TG we-Calculate} }
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