No, RMS (Root Mean Square) is not the same as a simple arithmetic average, although the term "RMS power" is sometimes erroneously used as a synonym for average power, particularly in the audio industry.
Understanding RMS and Average
While both RMS and average are measures of central tendency, they are calculated differently and represent different things. Let's break it down:
Average (Arithmetic Mean)
- Calculated by summing all values and dividing by the number of values.
- Sensitive to outliers.
- Represents the typical value.
RMS (Root Mean Square)
- Calculated by:
- Squaring all values.
- Calculating the mean (average) of the squared values.
- Taking the square root of that mean.
- Gives a greater weight to larger values.
- Represents the "effective" or "equivalent DC" value, especially for AC signals.
Table: RMS vs. Average
| Feature | Average (Arithmetic Mean) | RMS (Root Mean Square) |
|---|---|---|
| Calculation | Sum of values / Number of values | Square each value, find the average of the squares, then take the square root. |
| Sensitivity | Sensitive to both positive and negative values. | Sensitive to magnitude, treats positive and negative values similarly because they are squared. |
| Use Cases | Finding a typical value; useful when values fluctuate randomly around a central point. | Finding the equivalent DC value of an AC signal; measuring power; situations where magnitude is important regardless of sign. |
| Example of Audio | Would represent the average signal level without regard to its power. | Would represent the effective voltage or current which directly relates to the power delivered to a speaker. |
| Common mistake | The term RMS power can be misused in the audio industry as a synonym for mean power or average power. | N/A |
Why RMS is Important
RMS is particularly useful when dealing with alternating current (AC) signals because AC voltage and current oscillate between positive and negative values. A simple average of an AC signal over a complete cycle would be zero (because the positive and negative portions cancel each other out). The RMS value, however, provides a meaningful measure of the signal's magnitude, representing the equivalent DC voltage or current that would deliver the same amount of power to a resistive load.
Example: A 120V RMS AC voltage will deliver the same power to a resistor as a 120V DC voltage.
RMS Power in Audio
As the reference states, the term "RMS power" is sometimes misused in the audio industry. While RMS voltage and current are used to calculate power, "RMS power" itself is often used loosely to refer to the average power output of an audio amplifier. For a more detailed discussion on this and the shortcomings of audio power measurements, see Audio power.
