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Root Mean Square

In AC circuits, measurements are usually in RMS instead of Peak.
230 Volts RMS Alternating Current (AC) has the same heating effect as 230 Volts Direct Current (DC).

RMS   =   Root Mean Square

Alternating voltages (sine waves) have an average voltage of zero because they spend equal times above and below the zero volt line.
Clearly it's not useful to say the AC mains supply voltage is zero.

For Voltage, the RMS calculation works like this.

V_rms    =   V_peak / √2   ≈   0.707 V_peak   ≈   0.7 V_peak

V_peak   =   √2 V_rms   ≈   1.414 V_rms   ≈   1.4 V_rms

For Current, the RMS calculation works like this.

I_rms    =   I_peak / √2   ≈   0.707 I_peak   ≈   0.7 I_peak

I_peak   =   √2 I_rms   ≈   1.414 I_rms   ≈   1.4 I_rms

• Square: The voltage is squared. This makes any negative parts positive
• Root: The voltage is square rooted to undo the squaring but - the negative parts are still positive
• Mean: Take the average

The mains supply in Europe is 230 Volts RMS. The peak voltage is 325 Volts and the peak-to-peak voltage is 650V.

Power

P   =   E / t   =   I V   =   V² / R   =   I² R        Use RMS values if you need RMS power.

RMS Power Calculation

P_rms = 0.5 P_peak

P_peak = 2 P_rms