Standard Deviation Calculator

Paste numeric data, choose sample or population, then inspect the selected standard deviation, variance, formula, substitution, and each observation’s deviation and squared deviation.

Dataset

Choose sample when the values are a sample from a larger population; choose population when the dataset is the full population you want to describe.

Sample result

Standard deviation s—

Variance s²—

Standard error—

Population result

Standard deviation σ—

Variance σ²—

RMS distance from mean—

—Both sample and population results are shown; the selected mode controls the headline denominator.

Deviation table

This table makes the variance calculation auditable: subtract the mean from each value, square each deviation, then sum the squared deviations.

#	Value x	x − mean	(x − mean)²

Core describe → test → interpret workflows

Use descriptive context first, choose the method that matches the design, then keep inputs, settings and result evidence reproducible instead of copying a p-value without its analysis recipe.

Start: Statistics Calculator Choose a statistical test

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Interpret statistical results in context

Use plots and descriptive summaries before formal tests. Check the sampling/design assumptions that matter for the chosen method, report effect size and uncertainty where available, and avoid treating a threshold such as p < .05 as proof of importance, causation, or truth. Browser calculations are educational/planning utilities, not domain-specific professional advice.

How to use this Standard Deviation Calculator

Paste your observations and choose Sample if the values are a sample from a larger population, or Population if they are the complete population you want to describe. The deviation table shows every subtraction and square used in the variance.

Sample versus population standard deviation

Paste numeric data, choose sample or population, then inspect the selected standard deviation, variance, formula, substitution, and each observation’s deviation and squared deviation.

Interpretation limits

Standard deviation measures spread around the mean and is sensitive to extreme values. A small or large value only has meaning relative to the measurement scale and context of the dataset.