Calculator Inputs
Choose a mode, enter values, and calculate. The result appears above this form.
Example Data Table
This example shows how RMS grows with squared magnitude, even when the average is small.
| Observation | Value | Value² |
|---|---|---|
| 1 | 3 | 9 |
| 2 | -4 | 16 |
| 3 | 5 | 25 |
| 4 | -6 | 36 |
| 5 | 2 | 4 |
| RMS | √((9 + 16 + 25 + 36 + 4) / 5) = 4.243 | |
Formula Used
Dataset RMS
RMS = √[(Σx²) / n]. Square each value, average the squares, then take the square root.
Frequency Weighted RMS
RMS = √[(Σf·x²) / Σf]. Each squared value is multiplied by its frequency before averaging.
AC RMS and Total RMS
AC RMS = √[(Σ(x - mean)²) / n] and Total RMS = √(AC RMS² + DC²) when a DC offset is present.
Common waveform relations
Sine: Vrms = Vp / √2. Square: Vrms = Vp. Triangle or sawtooth: Vrms = Vp / √3.
How to Use This Calculator
Choose the mode that matches your problem. Use Value list for direct measurements, Frequency weighted for grouped data, and Waveform for standard signal shapes.
Enter your numbers carefully. Lists accept commas, spaces, semicolons, or new lines. Weighted rows need one value and one positive frequency on each line.
Set the decimal precision, then press Calculate RMS. The page places the main result below the header and above the form for quick review.
Use the detailed tables to inspect squared values, deviations, and summary metrics. Export the current result as CSV or PDF when you need a shareable copy.
Frequently Asked Questions
1. What does RMS measure?
RMS measures the effective size of varying values. It emphasizes larger magnitudes because values are squared before averaging. That makes it useful for signals, errors, and datasets with both positive and negative entries.
2. Is RMS the same as the arithmetic mean?
No. The arithmetic mean averages raw values, while RMS averages squared values first. RMS is always nonnegative and is usually larger than the absolute mean when magnitudes vary.
3. When should I use the weighted mode?
Use weighted mode when one value represents several repeated observations. Frequencies let you compute RMS from grouped data without entering every repeated value manually.
4. What is AC RMS?
AC RMS is the RMS of the varying part after removing the mean. It helps separate ripple or oscillation from any steady offset in the data or waveform.
5. Why is a DC offset shown?
The DC offset equals the mean value. Showing it helps explain why total RMS can stay high even when the varying component is modest.
6. Can negative values be used?
Yes. RMS handles negative values naturally because each value is squared. Opposite signs do not cancel each other as they would in a simple average.
7. Why is crest factor useful?
Crest factor compares peak magnitude with RMS. It reveals how spiky a waveform or dataset is, which matters in power, vibration, and reliability work.
8. What export options are included?
The page can export the active result tables as CSV or PDF. That makes it easier to archive calculations, attach them to reports, or share them with classmates and colleagues.