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Standard Deviation Calculator

Sample or population standard deviation, variance and standard error.

  • Formula checked
  • Editorially reviewed
  • Free · no signup
  • Updated June 27, 2026

Your details

Your result

Standard deviation

3.619392

Sample (n − 1)

Variance13.1
Mean6.5
Count6
Sum of squared deviations65.5
Coefficient of variation55.68%
Standard error of the mean1.477611
68% range (±1 SD)2.8806 to 10.1194

Key takeaway

Sample standard deviation = 3.619392 with mean 6.5.

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Cost breakdown

The same numbers as above, shown visually so the trade-offs are easy to see.

Cost breakdown
Sum of squared deviations
65.5
Variance
13.1
Mean
6.5
Count
6
Standard deviation
3.619392
68% range (±1 SD)
2.8806 to 10.1194

What to do next

What this means

Standard Deviation is 3.619392. This result is a directional estimate based on the values you entered.

Is this good or bad?

A result is useful when the inputs reflect your real situation — re-run it as your numbers change.

What's the risk?

Estimates use standard assumptions; your actual outcome depends on the terms you are offered.

What should you do next?

Save or print this result, then confirm the key assumptions with an official source.

Your action plan

  1. 1

    Double-check the inputs you estimated

    The output is only as good as the least certain input.

  2. 2

    Compare at least three alternatives

    One quote is a data point, not a market.

  3. 3

    Save this result

    It gives you a baseline to compare against later.

Your timeline

Today

  • Save or print this result.
  • Note which inputs you guessed at.

This month

  • Replace estimated inputs with real numbers and re-run.
  • Compare alternatives before committing.

Next 12 months

  • Re-run this calculation as your situation changes.
  • Track the outcome against this baseline.

Long term

  • Revisit the decision annually.
  • Adjust as rates, income or goals change.

Your next steps on this site

Result Intelligence

Understand your result

  • Your standard deviation is 3.619392. Use it as a directional estimate; always confirm with an official source before acting.

What should you do next?

  1. Debt-to-Income Calculator

    Check whether lenders will approve you.

  2. Credit Utilization Calculator

    Lower utilization can improve your APR.

  3. Affordability Calculator

    See the maximum loan you should carry.

  4. Compound Interest Calculator

    Compare paying debt vs. investing the difference.

Ways to improve your result

  • Compare at least 3 alternatives before deciding.
  • Document assumptions so you can re-run this calculation as inputs change.
  • Consult a licensed professional before signing.

Common U.S. scenarios

U.S. household

Median assumptions used above; your city and credit tier will shift the numbers.

Your result

Standard Deviation
3.619392
Variance
13.1
Mean
6.5
Count
6
Sum of Squared Deviations
65.5
Coefficient of Variation
55.68%

Sample standard deviation = 3.619392 with mean 6.5.

You may also want to check

What this result assumes

Confidence in a number depends on the assumptions behind it. Here are ours, in full.

Assumptions

  • Results are rounded for display; internal math uses full precision.

Limitations

This is an estimate for planning and education, not a quote or professional advice.

Estimates are for education and planning. They are not financial, tax or legal advice.

Formula source

Standard mathematical identities

Version
v1.3
Last reviewed
MethodologyReferences

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Next logical calculatorScientific CalculatorFull expression scientific calculator with trig, logs, roots, powers and factorials.Continue

Quick answer

What it does
Standard Deviation Calculator sample or population standard deviation, variance and standard error. It runs entirely in your browser, needs no signup, and uses standard published U.S. formulas.
When to use
Use it whenever you need a fast, reliable standard deviation estimate.
Inputs
  • Data set (comma, space or line separated)
  • Data type
Outputs
  • Standard Deviation
  • Variance
  • Mean
  • Count
  • Sum of Squared Deviations
  • Coefficient of Variation
Takeaway
In one line: enter your data set (comma, space or line separated) and data type and the Standard Deviation Calculator returns standard deviation and variance you can compare before deciding.

Last updated · 1 min read

How to read your result

Standard Deviation Calculator: Your result appears above. It's a fast estimate based on the inputs you entered — use it to compare options, then confirm with a professional before making a decision.

What your result means

  • The number is only as accurate as your inputs — small errors compound.
  • Compare 2–3 scenarios rather than acting on a single result.
  • Talk to a licensed professional before making a large financial or medical decision.

How does the formula work?

Sample: s = √( Σ(xᵢ − x̄)² ÷ (n − 1) ). Population: σ = √( Σ(xᵢ − μ)² ÷ n ). Variance is the same quantity before taking the square root; the standard error of the mean is s ÷ √n.

How it works

Standard deviation measures how far values typically sit from the mean, in the same units as the data. Use the sample formula (dividing by n − 1) whenever your numbers are a subset drawn from a larger group — which covers nearly all classroom, lab and survey work — and the population formula only when you have measured every member of the group. Bessel's correction of n − 1 exists because a sample's own mean sits closer to its data than the true population mean does, which would otherwise understate the spread.

Step-by-step guide

  1. 1Enter each input value into the calculator above.
  2. 2Review the result and any auto-generated breakdowns.
  3. 3Adjust inputs to compare scenarios.
  4. 4Copy, share, or print the results.

Example calculation

Example: Six measurements with a mean of 6.5 and a sample standard deviation of about 3.62.

Who should use this calculator?

  • Anyone who needs a fast, transparent estimate before making a decision.
  • Professionals validating a client-facing number.
  • Students learning the underlying formula.

When should you use it?

  • Any time you need a quick sanity check.
  • When comparing several scenarios side-by-side.
  • Before making a decision that depends on this number.

What affects the result?

  • Every input value you enter
  • The formula and assumptions displayed on this page
  • Rounding — small differences in inputs compound in the result

Common mistakes to avoid

  • Entering values in the wrong units.
  • Assuming the result includes taxes or fees when it may not.
  • Using rounded inputs and expecting exact figures.

Pro tips

  • Double-check your inputs before acting on the result.
  • Run 2–3 scenarios and compare — don't rely on a single number.
  • Save or print the results so you can review them later.

Why use this calculator

  • Instant results with no signup, no tracking and no ads inside the calculator.
  • Transparent formulas — you can see exactly how the number is produced.
  • Save, share, print or embed your results anywhere.
  • Reviewed and updated regularly by our editorial team.

Limitations to keep in mind

  • Estimates only — real-world results depend on many factors we cannot see.
  • Not professional advice — consult a qualified expert before acting.
  • Assumptions are shown; changing them will change the result.

Key terms explained

Input
A value you enter into the calculator. Small differences in inputs can compound into large differences in the result.
Assumption
A fixed value the calculator uses when it isn't asked from you. Assumptions are documented in the formula section.
Estimate
A directional figure produced from your inputs and standard formulas. Always sanity-check before acting.

Before you decide

  • Double-check every input for units and typos.
  • Compare 2–3 scenarios rather than trusting one result.
  • Confirm the assumptions in the formula match your situation.
  • Consult a qualified professional before acting on any large decision.

Trust & Accuracy

Accuracy tested

Verified against standard mathematical and financial conventions. Edge cases, formula validation and manual verification completed (last reviewed June 27, 2026).

Educational use

This tool is provided for education and planning only. It is not financial, tax, legal or medical advice.

Available for

United States, Canada, United Kingdom, Australia, India, European Union.

Currency support

USD · INR · CAD · AUD · GBP · EUR

Privacy

No information entered into this calculator is stored on our servers unless you explicitly choose to save or share your calculation.

Print, share & save

Use the Save, Share, Copy, PDF, CSV and Print actions under the result panel.

Accessibility

Keyboard navigable, screen-reader friendly labels, responsive on mobile and desktop.

Learn more: How we verify formulas · How we test accuracy · Methodology · Editorial policy

Recent Updates

We continuously review and improve our calculators to keep formulas, assumptions and references accurate.

View change log (4)Show
  1. v1.3

    Added Trust & Accuracy panel and machine-readable change log.

  2. v1.2

    Added Save, Share, PDF, CSV and Print actions to results.

  3. v1.1

    Added global currency selector (USD, INR, CAD, AUD, GBP, EUR).

  4. v1.0

    Initial calculator release with verified formulas and Official Sources.

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What's next?

Your next step

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Reviewed by the CreditLoanCalculator editorial team·Last reviewed ·Editorial policy·How we verify formulas
Disclaimer: Results are estimates for informational purposes only and should not be considered financial, medical, legal, or professional advice. Always consult a qualified professional before making decisions.