MATH

Standard Deviation Calculator

Estimate standard deviation from number of values, value 1, value 2 with the Standard Deviation Calculator.

How should the data be treated?Use sample when these values represent part of a larger group.

2 options

Dataset values8 of 100

Values (comma, space, tab, or new line separated)

Paste up to 100 values from a row, column, or spreadsheet.

STANDARD DEVIATION2.29128785

Population method; n = 8, mean = 4.5, variance = 5.25. Uses N for a population or N−1 for a sample, then reports count, sum, mean, variance, standard deviation, standard uncertainty, and a 95% uncertainty margin.

Count: 8
Sum: 36
Mean: 4.5
Population variance: 5.25
Population standard deviation: 2.29128785
Standard error: 0.81009259
95% margin of error: 1.58778147

Estimate based on the values shown

MethodUses N for a population or N−1 for a sample, then reports count, sum, mean, variance, standard deviation, standard uncertainty, and a 95% uncertainty margin.

Before you use the result

The result depends on the entered values, selected mode, and displayed mathematical assumptions.

EDITORIAL NOTES

Using the Standard Deviation Calculator responsibly

Page-specific guidance based on this calculator’s implemented method, inputs, and known limits.

What this result is useful for

Standard deviation describes spread around a mean. The population and sample formulas answer different questions, so the selected mode should reflect whether the entered values are the entire population of interest or a sample used to estimate it.

Assumptions and limits

The calculation describes the numbers entered; it does not establish that the data are representative, independent, normally distributed, or free of outliers. Sample standard deviation uses the stated degrees-of-freedom correction.

How to check the result

Confirm the count and mean, inspect the deviations, and compare the squared-deviation total with the displayed variance. A dataset with identical values should produce zero spread. Review unusual observations before interpreting a large value as meaningful variation.

CALCULATOR GUIDE

How to use the Standard Deviation Calculator

Estimate standard deviation from number of values, value 1, value 2 with the Standard Deviation Calculator. It includes Population, Sample workflows, so choose the one that matches the values you actually know. Use it to check the arithmetic while keeping the displayed method and entered values with your work.

Step by step

For the Standard Deviation example, select Population and enter number of values, value 1, value 2, value 3, value 4, and the remaining settings listed in the worked example. Keep each value in the unit displayed beside its field.
Review the selected Standard Deviation workflow and inputs, then read standard deviation in the result panel.
Change one Standard Deviation assumption at a time to compare scenarios. Use Reset to restore this tool's worked example values.

How the calculation works

Uses N for a population or N−1 for a sample, then reports count, sum, mean, variance, standard deviation, standard uncertainty, and a 95% uncertainty margin.

Worked example

To reproduce the Standard Deviation worked example, reset the calculator. Select the Population workflow. Use number of values 8; value 1 1; value 2 2; value 3 3; value 4 4; value 5 5; value 6 6; value 7 7; value 8 8. The result is standard deviation of 2.29128785. Population method. Review the displayed units before comparing the result.

Understanding the result

The Standard Deviation reports standard deviation. Use it to check the arithmetic while keeping the displayed method and entered values with your work. The result depends on the entered values, selected mode, and displayed mathematical assumptions.

How to check the answer

Check the Standard Deviation answer by substituting standard deviation back into the stated relationship. Test a simple value such as zero, one, or an equal pair, then confirm that sign, scale, units, and rounding match Uses N for a population or N−1 for a sample, then reports count, sum, mean, variance, standard deviation, standard uncertainty, and a 95% uncertainty margin.

Common questions

What does the Standard Deviation calculate?

Estimate standard deviation from number of values, value 1, value 2 with the Standard Deviation Calculator.

Which inputs does the Standard Deviation example use?

The worked example uses number of values, value 1, value 2, value 3, value 4, and the remaining settings listed in the worked example in the Population workflow. Other workflows can show different fields. Keep the chosen workflow and units with the result when comparing calculations.

Is the Standard Deviation result exact?

The result depends on the entered values, selected mode, and displayed mathematical assumptions. Recheck number of values, value 1, value 2 and use standard deviation only for a decision where that level of precision is appropriate.

INTERPRET THE RESULTRead the math guideCheck assumptions, limitations and comparison methods →

KEEP GOING

Useful next steps

AverageEstimate average from value 1, value 2, value 3 with the Average Calculator.Random NumberEstimate random number from seed, minimum, maximum with the Random Number Calculator.Sample SizeEstimate required sample size from confidence level, expected proportion, target margin of error with the Sample Size Calculator.