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Standard Deviation Calculator

Calculates population and sample standard deviation, variance, mean and standard error, with each step shown.

Calculators Nothing uploaded No sign-up Free, unlimited
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Enter your figures and press Calculate.
In short Standard Deviation Calculator is a free online tool on inputtesthub.com that calculates population and sample standard deviation, variance, mean and standard error, with each step shown. It needs no account, no download and no payment, and there is no daily usage limit. Everything is processed inside your own browser, so the data you paste is never uploaded to a server.

How to use the Standard Deviation Calculator

  1. Enter your figures in the input fields.
  2. The result updates as you type, together with the full working.
  3. Check the breakdown table to see exactly how the number was reached.

About the Standard Deviation Calculator

The Standard Deviation Calculator calculates population and sample standard deviation, variance, mean and standard error, with each step shown. It runs as plain JavaScript inside the page, which means there is no upload step, no queue and no size limit imposed by a server — the only limit is your own device.

What people use it for

  • Statistics coursework.
  • Measuring consistency in a set of results.
  • Quality control on a batch of measurements.

The maths behind it

This tool uses σ = √(Σ(x − μ)² ÷ N) for a population and s = √(Σ(x − x̄)² ÷ (n − 1)) for a sample, where the n − 1 denominator corrects for sample bias. Every intermediate value is shown on screen, so the result can be checked by hand.

Frequently asked questions

Is the Standard Deviation Calculator free?
Free, unlimited, and no email address required. You can use it a hundred times a day and nothing changes.
Is what I paste into the Standard Deviation Calculator stored?
No. The Standard Deviation Calculator runs entirely in your browser using JavaScript. Because the work happens locally, the page also keeps working if your connection drops, and closing the tab is all it takes to discard everything.
How is the result calculated?
It uses σ = √(Σ(x − μ)² ÷ N) for a population and s = √(Σ(x − x̄)² ÷ (n − 1)) for a sample, where the n − 1 denominator corrects for sample bias. The full working is printed under the result, so you can follow every step rather than trusting a black box.
What problem does the Standard Deviation Calculator solve?
The jobs it is built for: statistics coursework. Measuring consistency in a set of results. Quality control on a batch of measurements. It is built for exactly those cases rather than being a general-purpose tool with this bolted on.
Can I rely on this for exact work?
The calculation runs in double precision and the result is shown to ten significant figures, so converting a value and converting it back returns the original. What is displayed is rounded for readability; what is copied is not.

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