Standard Deviation Calculator
Standard Deviation
What is the Standard Deviation Calculator?
Standard Deviation Calculator calculate population and sample standard deviation with step-by-step breakdown. It is part of Home of Calculators's Math Calculators suite for mathematical calculations, equations, formulas. The calculator is designed for students, engineers, scientists, but anyone can use it. No signup, no ads, no tracking. Just accurate math, computed locally in your browser using a BigNumber-precision math engine.
Standard deviation measures how spread out data values are from the mean. A low standard deviation means values cluster close to the mean; a high standard deviation means values are spread over a wider range.
xᵢEach data valueμMean of the dataNNumber of valuesHow to use the Standard Deviation Calculator
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Calculate the mean
Sum all values and divide by the count to get μ.
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Find deviations
Subtract the mean from each value: (xᵢ − μ).
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Square and average
Square each deviation, sum them, and divide by N (population) or N−1 (sample).
- 4
Take the square root
The square root of the variance is the standard deviation.
Quick tips
- All calculations run locally in your browser; your data never leaves your device.
- For best results on mobile, rotate to landscape when entering many values.
- Bookmark this page to come back to your calculation anytime.
- Need a different calculator? Try our visual builder to create your own.
Why Home of Calculators
- 100% private (calculations run in your browser)
- 128-bit BigNumber precision (no rounding errors)
- Works on any device: phone, tablet, desktop
- Free forever (no signup, no ads, no upsells)
Frequently asked questions
Is the Std Dev accurate?
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Yes. Home of Calculators uses a BigNumber-precision math engine (64-128 decimal digits) to ensure calculations are accurate. We run 96+ automated tests covering unit conversion, financial formulas, health formulas, and more. For critical decisions (financial, medical, legal), we still recommend consulting a qualified professional.
Is the Standard Deviation Calculator free?
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Yes. Every calculator on Home of Calculators is 100% free, with no signup, no ads, and no hidden fees. The entire platform is free forever.
Do you store the values I enter?
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No. All calculations happen in your browser. We never see, store, or transmit your inputs to any server. Your data stays on your device.
Can I use the Std Dev on my phone?
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Yes. Home of Calculators is fully responsive and works on any device (phone, tablet, laptop, or desktop). The interface adapts to your screen size.
Can I embed this calculator on my own website?
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Yes. Click the "Share" button to get an iframe embed code. The embedded calculator will look like any other Home of Calculators widget. You can also build a fully customized version using our visual builder.
Can I build my own custom calculator?
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Absolutely. Home of Calculators's visual builder lets you add fields, write formulas, choose a theme, and brand the result with your own logo, all without writing code.