Math / Browser calculator

Standard Deviation Calculator

Standard Deviation Calculator works from the inputs you provide and returns count, sum, mean, median, minimum, maximum, range, population standard deviation, sample standard deviation, mode. Use the calculation panel to explore a scenario, then check the formula and limitations before applying the result.

Your inputs

Your results

Enter your values and calculate to see the result.

Formula and calculation method

Mean = Σx/n. Population standard deviation = √[Σ(x−mean)²/n]. Sample standard deviation uses n−1. Median is the middle sorted value.

Population and sample standard deviations are reported separately. Every repeated value tied for the highest frequency is included in the mode.

How to use standard deviation calculator

  1. Set Numbers separated by commas. The example below uses 2, 4, 4, 4, 5, 5, 7, 9.
  2. Select Calculate to update the result. Reset restores the illustrated inputs. Copy, print or download your own result if you need a record.

Worked example

Example inputs
Numbers separated by commas
2, 4, 4, 4, 5, 5, 7, 9
Count
8
Sum
40
Mean
5
Median
4.5
Minimum
2
Maximum
9
Range
7
Population standard deviation
2
Sample standard deviation
2.13808994
Mode
4

Factors affecting your result

Population and sample standard deviations are reported separately. Every repeated value tied for the highest frequency is included in the mode.

Changing numbers separated by commas changes the scenario being evaluated. Adjust one input at a time when comparing results, keep a copy of the assumptions, and compare values using the same unit and period. A precise arithmetic result does not make an uncertain assumption precise.

Frequently asked questions

How does the standard deviation calculator work?

Mean = Σx/n. Population standard deviation = √[Σ(x−mean)²/n]. Sample standard deviation uses n−1. Median is the middle sorted value.

What inputs does Standard Deviation Calculator need?

Enter numbers separated by commas. Choose values that correspond to the same situation and measurement convention.

How should I interpret the standard deviation calculator result?

Population and sample standard deviations are reported separately. Every repeated value tied for the highest frequency is included in the mode.

Are my standard deviation calculator inputs uploaded?

No. The calculation runs in this browser. Favorites, recent tool names, theme and formatting preferences may be saved locally, but calculation inputs are not sent to a calculation server or stored by this website. Shared links do not include entered values.

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