The Root Mean Square Calculator provided by Hesapstan squares each value, averages the squares, and takes the square root to return the RMS of your number list.
RMS measures magnitude relative to zero
RMS stands for root mean square. It is also called the quadratic mean. The idea is simple: square each value, find the average of those squares, then take the square root. Because of the squaring step, RMS focuses on the magnitude of the values rather than their signs.
RMS measures magnitude relative to zero. Standard deviation measures spread around the mean. This calculator does not calculate standard deviation or variance.
The formula is the square root of the mean of the squares
The RMS formula is RMS = √(Σx² / n). Here n is the number of values, and Σx² is the sum of the squared values. The calculator also shows Σx²/n, the mean square, before taking the square root.
Giriş / Input: 3; 4 — Sonuç / Output: Σx² = 3² + 4² = 25, mean square = 25/2 = 12.5, RMS = √12.5 ≈ 3.535 — The square root is calculated numerically, so some results are shown as decimal approximations.
Negative and zero values are valid RMS inputs
This calculator accepts positive values, negative values, and zero. A negative value is not an error in RMS, because every value is squared. For example, the squares of 1 and -1 are both 1, so the RMS is 1.
Giriş / Input: 1; -1 — Sonuç / Output: Σx² = 1² + (-1)² = 2, RMS = √(2/2) = 1 — The negative sign disappears during the squaring step, which is why RMS can be useful for magnitude.
The input list can use spaces, new lines, or semicolons
Enter your values in the text area separated by spaces, line breaks, semicolons, or comma + space. Decimal dot and decimal comma are both supported, but using both in the same number would be ambiguous.
A value like 1,5 may be read as a decimal value. For separating list items, line breaks or semicolons are clearer.
RMS appears in physics and engineering, but this page is purely mathematical
RMS is common in math, physics, electrical topics, and signal contexts. This calculator, however, only applies the mathematical RMS formula to a list of numbers. It does not handle voltage units, signal frequency, engineering conversions, or domain-specific rules.
Giriş / Input: 0; 2; 4 — Sonuç / Output: Σx² = 0 + 4 + 16 = 20, mean square = 20/3, RMS ≈ 2.449 — Zero is accepted and contributes 0 to the sum of squares.
Frequently Asked Questions
What is RMS?
RMS, or root mean square, is the square root of the average of the squared values in a list.
How do I calculate RMS?
Square each value, add the squares, divide by the number of values, then take the square root: RMS = √(Σx² / n).
Is RMS the same as standard deviation?
No. RMS measures magnitude relative to zero. Standard deviation measures spread around the mean.
Can RMS use negative numbers?
Yes. Negative inputs are accepted because the values are squared before averaging.
Can I enter zero?
Yes. Zero is a valid value, and its square is 0.
Is RMS the same as the quadratic mean?
Yes. Root mean square and quadratic mean refer to the same calculation.
Does this calculator handle physics units?
No. It calculates mathematical RMS from numbers only. It does not convert or interpret units such as volts or amperes.
Can I use decimal comma?
Yes. Decimal comma and decimal dot are supported. For list separation, line breaks or semicolons are usually clearer.