standarddeviationcalculator.net

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Standard deviation and variance calculators

Every standard deviation and variance calculator on the site, from a quick sample SD of a short list to pooled, weighted and portfolio SDs. Pick the one that matches the shape of your data (a list, a frequency table, several groups or a file) and the answer comes with the steps behind it.

Which calculator do I need?

You have or wantUse
A list of numbers that is a sample from a larger groupSample standard deviation (s, n − 1)
A list that is the entire population, such as every student in one classPopulation standard deviation (σ, n)
The mean ± SD to report in a paper or lab write-upMean and standard deviation
A frequency table of values and countsFrequency table standard deviation
Class intervals such as 10–19, 20–29 with frequenciesGrouped data standard deviation
Two or more groups whose SDs you want to combinePooled standard deviation
A spreadsheet column or thousands of valuesStandard deviation from CSV data
The variance rather than the SDVariance calculator

Standard deviation of a list

Paste a list of numbers and get the standard deviation, alone or with the mean, variance and standard error.

Variance

The square of the standard deviation, for when a formula, ANOVA table or textbook asks for s² or σ².

Frequency tables, weights and several groups

When the data arrive as counts, class intervals, weights or separate groups rather than one plain list.

Files, large datasets and class scores

For data that are too long to type, or that come from a gradebook.

Using the standard deviation

What to do with an SD once you have it: standardise values, put an interval around it, express it as a percentage or draw it.

Which standard deviation do you need?

All the calculators here compute the same quantity: the square root of the average squared distance from the mean. They differ in two ways, the divisor and the shape of the input.

The divisor is n for a population SD and n − 1 for a sample SD. Dividing by n − 1 corrects for the fact that a sample’s own mean sits closer to its values than the true population mean does. If your numbers are a sample and you want to describe the wider group, which covers most lab, survey and classroom work, use the sample SD.

The input shape decides the page. A plain list goes into the main calculator. Values with counts go into the frequency table version, and class intervals such as 20–29 go into the grouped data version, which uses each class midpoint and so gives an estimate rather than an exact figure.

Worked comparison

For the values 2, 4, 4, 4, 5, 5, 7, 9 the mean is 5 and the squared deviations add to 32.

  • Population variance: 32 ÷ 8 = 4, so σ = 2.
  • Sample variance: 32 ÷ 7 ≈ 4.571, so s ≈ 2.138.
  • Standard error of the mean: 2.138 ÷ √8 ≈ 0.756.
  • Coefficient of variation: 2.138 ÷ 5 ≈ 42.8%.

With eight values the two SDs differ by about 7%. With 100 values the gap shrinks to about 0.5%, which is why the choice matters most for small samples.

Common mix-ups

  • SD vs variance. Variance is in squared units (cm², £²), so it is hard to read directly. Report the SD; use the variance inside formulas such as ANOVA or pooling.
  • SD vs standard error. Error bars labelled SE look much tighter than SD bars from the same data. The SD and SE calculator gives both so you can label them correctly.
  • Averaging SDs. The combined SD of two groups is not the mean of their SDs. Pool the variances, weighted by degrees of freedom, with the pooled SD calculator.

Guides to read alongside

Common questions

Should I use the sample or the population standard deviation?
Use the population SD (divide by n) only when your data include every member of the group you care about. If the data are a sample and you want to describe the wider group, use the sample SD (divide by n − 1), which is what Excel’s STDEV.S and most statistics software report by default.
How do I get the standard deviation from the variance?
Take the square root. A variance of 16 gives a standard deviation of 4; going the other way, square the SD to get the variance. The variance calculator converts in both directions.
Can I calculate a standard deviation from a frequency table?
Yes. With exact values and counts, the frequency table calculator gives the same answer as typing every value out. With class intervals, the grouped data calculator uses each class midpoint, so the result is a close estimate rather than the exact SD of the raw data.

Written and reviewed by our editorial team. Last updated . Method and sources: how these numbers are computed.