How to Calculate an RMS


The Root Mean Square, or quadratic mean, is a statistical function for finding the average of a series even if it contains negative numbers. When you have a series with negative numbers, the normal formula for averaging -- adding all the numbers and dividing by the number of numbers -- will give you the "middle value," but it won't give you a sense of the average magnitude. RMS tells you how big the average number is, no matter which side of the number line it's on. Most real-world RMS problems must use calculus, but you can find the RMS of a small series with basic math and a calculator.

Things You'll Need

  • Calculator
  • Count the number of numerals you are finding the RMS for. For example, if you have the series 5, -3 and -7, you have three numerals.

  • Square each of the numbers, either in your head or with a calculator. Write each one down on a piece of paper as you go so you don't lose track of them. For example, the squares of 5, -3 and -7 are 25, 9 and 49.

  • Add all the squares together. For our series, 25 + 9 + 49 = 83.

  • Divide the sum of the squares by the number of numbers. 83 divided by 3 is 27.67.

  • Take the square root of the sum divided by the number of numbers. The square root of 27.67 is 5.26, so for the series 5, -3 and -7, the RMS is 5.26.


  • Photo Credit calculator image by Szymon Apanowicz from
Promoted By Zergnet


You May Also Like

  • How to Calculate RMSD

    The root mean square deviation (RMSD) is a measure of the differences between predicted values and actual values. The RMSD aggregates these...

  • How to Calculate RMS Value

    Technically, the root mean square (RMS) of a variable is the square root of the average of the square of the variable....

  • How to Convert AC Voltage to DC

    A regulated power supply system can be assembled to electrically convert high-voltage alternating current (AC) to a fixed direct current (DC) in...

  • How to Calculate RMS Watts

    Alternating current (AC) rises and falls following a sinusoidal rhythm, making it difficult to describe average values associated with AC electrical circuits....

  • How to Calculate RMS Wattage for a Car Amplifier

    Anyone who has purchased an amplifier or set of speakers has seen an "RMS wattage" figure printed on the outside of the...

  • How to Calculate IRMS

    The current in an alternating current circuit varies continuously in direction and magnitude. Calculations involving the current don't therefore consider the current...

  • How to Calculate the Root MSE in ANOVA

    In statistics, the analysis of variance (ANOVA) is a way of analyzing different groups of data together to see if they are...

  • How to Calculate Mean Squares Within

    Analysis of Variance (ANOVA) is a statistical technique for seeing whether three or more groups differ on the mean of some quantitative...

  • How to Calculate the RMSE or Root Mean Squared Error

    When you graph several scientific data points, you may wish to fit a best-fit curve to your points, using software. However, the...

Related Searches

Check It Out

How to Build and Grow a Salad Garden On Your Balcony

Is DIY in your DNA? Become part of our maker community.
Submit Your Work!