Standard Deviation Calculator

Understanding standard deviation for students and professionals

Standard deviation measures how spread out values are around the mean. A low standard deviation indicates that data points cluster tightly near the average; a high standard deviation shows greater variability. It’s a key metric in quality control, risk analysis, research methods, and performance reporting.

Core definitions

• Mean (average): Sum of all values divided by the count.
• Variance: Average of squared deviations from the mean; units are squared.
• Standard deviation (SD): Square root of variance; returns to the original units and is easier to interpret.

Population vs sample standard deviation

• Population (N): Use when your dataset includes the entire group of interest. Variance divisor = N.
• Sample (N−1): Use when your dataset is a sample from a larger population. Variance divisor = N−1 (Bessel’s correction) to reduce bias.

Weighted data and frequencies

When values have different importance or occur multiple times, weights or frequencies adjust the mean and variance accordingly. Weighted formulas use the sum of weights in place of N to reflect each value’s contribution.

Best practices

• Declare your method: State whether you used population (N) or sample (N−1) calculations.
• Check units: SD is in the same units as your data; variance is in squared units.
• Use appropriate precision: Round consistently to a sensible number of decimal places for reports.
• Inspect outliers: Large deviations influence SD strongly; evaluate whether outliers are valid or errors.

Frequently asked questions

HOW TO calculate sample standard deviation?

Steps: Paste your data, choose Sample (N − 1) in Type, set Precision if needed, and click Calculate.

HOW TO calculate population standard deviation?

Select Population (N) in Type, enter your dataset, and calculate. Use this when you have the entire population.

HOW TO compute weighted standard deviation?

Enter weights or frequencies with the same length as your data. The calculator uses weighted formulas for mean and variance.

HOW TO get z‑scores for a value?

Enter the value in the Z‑scores field. The tool returns z = (x − mean)/SD using your selected type (population or sample).

HOW TO export results for reports?

Choose Output format = CSV or Compact and click Copy result. Paste the output into your spreadsheet or document.

HOW TO embed this calculator on my website?

Copy this single‑file HTML into your project, link it in navigation, or embed via iframe with a descriptive title and lazy loading.