Standard Deviation Calculator

What does this calculator do?

A browser-based statistics console that ingests raw measurements, CSV exports, or ad-hoc lists and returns population and sample deviation side-by-side with quartiles, IQR, and coefficient of variation. It removes manual clean-up so analysts, operators, and students can focus on the story behind the spread.

Key features

Auto-detects separators and strips stray characters so you can paste directly from spreadsheets, BI exports, or JSON arrays.

Calculates population and sample variance/deviation simultaneously, plus quartiles, interquartile range, and coefficient of variation.

Precision controls and locale-aware formatting keep stats aligned with lab notes, QA logs, or finance decks.

Diagnostics explain each step with raw numbers so reviewers can audit the math or replicate it elsewhere.

Standard deviation formulas

Population deviation

σ = √(Σ(x - μ)² / N). Use when the dataset captures every member of the population.

Sample deviation

s = √(Σ(x - x̄)² / (n - 1)). Use when you only have a subset and need Bessel's correction.

How to use the Standard Deviation Calculator

Paste at least two numeric values separated by spaces, commas, tabs, or line breaks. Load a snippet from your clipboard or type manually.

Pick a delimiter preset only if your data uses tabs, semicolons, or pipes; otherwise leave auto-detect enabled.

Choose whether you want the summary to emphasize sample or population deviation and set the decimal precision that matches your report.

Run the calculator to receive deviation, variance, quartiles, IQR, range, and a diagnostic log you can paste into QA notes or lab books.

Common mistakes

Mixing labels or units with the numbers (e.g., '12 kg'), which prevents the parser from reading the value.

Submitting only one number—sample deviation requires at least two data points.

Using comma decimal separators while forcing the delimiter to comma, which slices numbers in half.

Switching between population and sample interpretations without updating the focus mode.

Population vs. sample cheat sheet

Population stats divide by N because every observation is known; sample stats divide by n-1 to reduce bias.

Sample deviation is always a little larger to compensate for the uncertainty of estimating the mean.

Pick population mode only when you are certain there are no missing records.

Example scenarios

A quality engineer pastes torque readings from ten assemblies to prove consistency before sign-off.

A product manager looks at week-over-week revenue spikes and watches sample deviation to flag volatility.

A math teacher shares cleaned quiz scores so students can see how quartiles and IQR explain outliers.

FAQ

What is the difference between sample and population deviation?

Population deviation (σ) divides by the full count and is used when you captured every member of the population. Sample deviation (s) divides by n-1 to correct for estimating the broader group. The calculator shows both every time so you can cite the right one.

How many numbers can I paste?

Practically hundreds of thousands. Everything runs in your browser, so the cap is whatever your device can hold in memory.

Can I include negative values or decimals?

Yes. The parser normalizes minus signs and decimal separators automatically as long as you do not mix them with units or text.

What about the coefficient of variation?

We compute CV using the population deviation divided by the absolute mean. If the mean is zero the tool shows a warning because CV would be undefined.

Does my dataset leave the browser?

No. All math runs locally so lab data, student records, or revenue logs never hit a server.