Standard Deviation Calculator
Mean, median, variance and standard deviation for any data set.
Inputs
Formula
- mean = Σx / n
- s = √( Σ(x − mean)² / (n − 1) )
- σ = √( Σ(x − mean)² / n )
Use the sample formula when your numbers are a subset of a larger group, the population formula when they are the whole group.
Step-by-step calculation
- 1
Mean
Σx / 6
20.5
- 2
Sum of squares
Σ(x − mean)²
241.5
- 3
Standard deviation
√(241.5 / 5)
6.9498
Frequently asked questions
What does the Standard Deviation Calculator do?
Mean, median, variance and standard deviation for any data set. The Standard Deviation Calculator on OneCalcApp returns the result instantly as you type, together with the formula and the substituted values.
How do I use the Standard Deviation Calculator?
Enter your values in the input fields, choose the relevant units or options, and the Standard Deviation Calculator recalculates automatically. You can copy, print or export the result.
Is the Standard Deviation Calculator free to use?
Yes. The Standard Deviation Calculator is completely free, needs no sign-up and has no usage limit on OneCalcApp.
How accurate is the Standard Deviation Calculator?
It uses the standard formula mean = Σx / n and full double-precision arithmetic, so results match a manual calculation to the displayed number of digits.
Does the Standard Deviation Calculator work on mobile and offline?
Yes. The Standard Deviation Calculator runs entirely in your browser on phones, tablets and desktops, and your inputs never leave your device.
Where can I find related tools?
OneCalcApp hosts 300+ calculators and converters, including the full Math collection. Related tools are linked at the bottom of every page.
Related calculators
Keep going with more math tools.
Quadratic Equation Solver
Roots, discriminant and vertex of ax² + bx + c = 0.
Percentage Calculator
Solve every common percentage problem: X% of Y, what percent one number is of another, percentage increase or decrease and reverse percentage.
Kinetic Energy Calculator
Energy of a moving body from its mass and speed.
Projectile Motion Calculator
Range, maximum height and flight time from launch speed and angle.
Molarity Calculator
Solution concentration from solute mass, molar mass and volume.
Dilution Calculator (C1V1 = C2V2)
Work out the stock volume needed for a target concentration.