How to Calculate RMS Values

Written by mark stansberry
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RMS, which stands for root mean square, is a method to average numbers. Unlike the standard arithmetic averaging method, the RMS averaging method requires that you average the square of each number and then take the square root of that average. Scientists and engineers use the RMS average to analyse waveforms. This is because the RMS average of a waveform is used to calculate the amount of energy in a waveform.

Skill level:
Moderate

• Calculator
• Pencil
• Paper

Instructions

1. 1

Select a group of numbers that include negative and positive numbers. Use --5, -2, 0, 3, 10 for your first RMS calculation.

2. 2

Square each number to be averaged; multiply each number used by itself. For this example, the results are 25, 4, 0, 9 and 100, since--5 times --5 is 25, -2 times --2 is 4, 0 times 0 is 0, 3 times 3 is 9 and 10 times 10 is 100.

3. 3

Total the squares. Conclude that the total of the squares is 138, since 25 plus 4 plus 0 plus 9 plus 100 is 138.

4. 4

Calculate the average of the squares. First, count how many number values are used to calculate the average. Conclude for this example that the number of values used is 5.

5. 5

Divide the total obtained in step 3, 138, by the number of values used, in this case 5. Conclude that the average of the squares is 27.6, since 138 divided by 4 is 27.6.

6. 6

Take the square root of the average of the squares; use the square root key on your calculator. Conclude that the RMS value for your first calculation is 5.26.

Tips and warnings

• For many types of waveform patterns, simplified formulas for calculating the RMS level are available.
• For sine and cosine waveforms, two very common waveform patterns that are found in physics, the RMS level is obtained by multiplying the peak magnitude of the waveform by 0.707.
• The magnitude of a waveform is determined from the plot of the waveform. On such a plot, the magnitude is measured on the y-axis and time is measured on the x-axis. The peak magnitude is obtained by measuring the y-distance between the negative and positive peak of the wave and then dividing that number by 2.
• When calculating the RMS level of a waveform, the pattern of the waveform must be taken into consideration. This often requires advanced mathematical techniques.

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