RMS of a Number List

Formula and method

Square each entered value, average those squares, then take the nonnegative square root. Blank entries are omitted; an entered zero remains part of the average.

RMS = sqrt((x₁²+⋯+xₙ²)/n).

Worked example

Enter these known values and leave the other values blank.

Assumptions and limitations

• Enter up to thirty finite observations in one common unit, or use unitless numbers. The RMS has that same unit; this source does not offer separate unit selectors.
• An entered zero counts as an observation. Blank fields are omitted. Negative observations are valid because their squares are nonnegative.
• The original progressive fields remain: the first four inputs are available, and later fields appear as preceding values are entered. Clearing a value changes the observation count; it does not insert zero.
• The RMS is calculated from the exact decimal sum of squares, then rounded to 64 significant digits before display formatting. Each observation is zero or has magnitude from 1e-10000 through 1e10000. Values outside this computational domain are rejected.
• The captured fixed-four-decimal callback could erase small nonzero results or overflow binary arithmetic. This translation computes the RMS before rounding, then displays relative precision and scientific notation when needed. Readonly summary fields expose the original count/RMS numeric exports. It remains a forward-only list calculation.
• Inputs accept decimal or e notation and bounded arithmetic expressions only when each intermediate and final value can be verified exactly as a finite decimal. Repeating fractions, functions, symbols and expressions that lose digits are rejected with guidance. Enter their finite decimal value instead; the calculator-specific magnitude and precision limits still apply.

Common questions

References

• Captured RMS model and controls

Replace the captured optional-observation callback with a bounded local decimal RMS computation and explicit observation count. Preserve all30 original numeric controls, progressive visibility and source result context; translate its two numeric exports to named readonly output fields so partial optional input lists remain usable in the public API. Compute the RMS before presentation rounding, repairing binary underflow/overflow and the source callback fixed-four-decimal loss of small nonzero results. The original callback is retained as immutable evidence and is not executed in product. Only the complete captured RMS source and complete reviewed compiled schema receive optional aggregation. Count every entered observation, including zero and negative values; omit blanks without substituting zero. Support at most30 finite inputs, each zero or magnitude1e-10000 through1e10000. Align decimal coefficients exactly before squaring, then round the nonnegative square root once to 64 significant digits, with exact half-up rounding. All-zero lists return zero; an empty list has no result. Report unitless inputs or a consistent common unit. Show rounded relative-precision results and preserve finite nonzero values in scientific notation when fixed decimals cannot show them; ordinary input formatting and all controls remain.

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