**Root Mean Square (RMS)** is a statistical measure of the effective value of a varying quantity — most commonly applied to alternating current (AC) voltage and power. The RMS value of an AC signal is the equivalent DC value that would deliver the same amount of energy to a resistive load over one complete cycle. --- ### First Principle: RMS converts fluctuation into a single usable number. AC power oscillates sinusoidally. You cannot simply average it (the average of a sine wave is zero). RMS squares each instantaneous value, averages those squares, then takes the square root — giving a single figure that represents the true heating or working capacity of the signal. --- ### Key Considerations - **Mathematical Definition**: For a sinusoidal AC signal with peak voltage V_peak, the RMS voltage is V_peak / √2 ≈ 0.707 × V_peak. A 230V AC mains supply has a peak voltage of roughly 325V. - **Power Calculation**: Real power (watts) in AC circuits uses RMS values: P = V_rms × I_rms × power factor. This is the figure that matters for sizing [[Power Infrastructure|power infrastructure]]. - **Distinction from [[Peak Power Output]]**: Peak power is the instantaneous maximum; RMS power is the effective continuous equivalent. Infrastructure must handle peak, but billing and thermal design use RMS. - **Three-Phase Systems**: In data center power distribution, three-phase AC is standard. RMS values apply per phase, and total power depends on phase balance. --- ### Actionable Insights When reading equipment specifications for [[UPS Batteries|UPS systems]], [[Single Line Diagram|PDUs]], or generators, confirm whether ratings are given in RMS or peak values. Most reputable manufacturers spec in RMS (which is the useful number), but confusion between the two can lead to undersized power chains. For modular data center deployments, always verify that the RMS power budget per rack aligns with the actual workload profile measured under load — not just nameplate ratings. --- ### Quick Reference | Term | Meaning | Relationship | |------|---------|-------------| | V_peak | Maximum instantaneous voltage | V_peak = V_rms × √2 | | V_rms | Effective (heating-equivalent) voltage | V_rms = V_peak / √2 | | P_rms | Effective continuous power | Used for thermal and billing | | P_peak | Maximum instantaneous power | Used for protection sizing | [[Peak Power Output]] | [[Power Infrastructure]] | [[Single Line Diagram]] | [[IT Load]]