How to use the standard deviation calculator
Compute sample and population standard deviation and variance. Enter data values in the field above; the mean, sample standard deviation, population standard deviation, sample variance, standard error are computed instantly and plotted on the chart so you can see how the answer changes.
Formula
Variables
- d — Data values
Worked example
With data values = 10,12,23,23,16,23,21,16, the calculator gives mean ≈ 18; sample standard deviation ≈ 5.237229; population standard deviation ≈ 4.898979; sample variance ≈ 27.42857; standard error ≈ 1.85164.
Frequently asked questions
What is the formula for the standard deviation calculation?
Mean = mean(d). Sample standard deviation = sd(d). Population standard deviation = sdp(d). Sample variance = vari(d). Standard error = sd(d) / √(len(d)). Here d is data values.
What inputs do I need for the standard deviation calculator?
You need data values. Each field is pre-filled with a typical example so you can see how the result responds as you edit the numbers.
How do I use this calculator?
Type values into the input fields. Results and the chart update instantly. Use Reset to restore the example values, Copy results to paste them elsewhere, or Share to copy a link that preserves your inputs.
Is the result exact?
Calculations use standard formulas and double-precision arithmetic, then display about seven significant figures. Real-world measurements carry uncertainty, so treat results as estimates unless your inputs are exact.