📐 Standard Deviation Calculator

Calculate mean, variance, and standard deviation of a dataset.

Calculate Now

What is Standard Deviation Calculator?

Two datasets can share the exact same average yet look completely different once you examine how tightly the individual values cluster around that average. Standard deviation is the statistic that captures this spread — a low value means the data points sit close to the mean, while a high value means they're scattered widely. This calculator accepts any list of numbers and works out the mean, variance, and standard deviation in one pass.

The Standard Deviation Formula

The (population) standard deviation is calculated in three stages: first the mean, then the variance, then its square root:

Mean (μ) = Σx ÷ n
Variance (σ²) = Σ(x − μ)² ÷ n
Standard Deviation (σ) = √Variance

Worked Example

Take the dataset: 10, 12, 23, 23, 16, 23, 21, 16 (n = 8).

Step 1 — Mean: (10+12+23+23+16+23+21+16) ÷ 8 = 144 ÷ 8 = 18

Step 2 — Squared deviations from the mean: (10−18)²=64, (12−18)²=36, (23−18)²=25, (23−18)²=25, (16−18)²=4, (23−18)²=25, (21−18)²=9, (16−18)²=4. Sum = 192.

Variance = 192 ÷ 8 = 24
Standard Deviation = √24 ≈ 4.899

So this dataset has a mean of 18 and a standard deviation of roughly 4.9 — meaning most values sit within about 5 points of the average.

How to Use This Calculator

  1. Type your list of numbers into the Numbers field, separated by commas.
  2. Click Calculate.
  3. Read off the mean, variance, and standard deviation shown in the result.
💡 Tip: Standard deviation isn't just an academic statistic — quality control teams use it to check manufacturing consistency, and in finance it's a standard measure of an investment's volatility (a higher SD generally means higher risk).

Population vs Sample Standard Deviation

This calculator uses the population formula, dividing by n. If your numbers are only a sample drawn from a much larger group rather than the entire group itself, statisticians often divide by (n − 1) instead, which slightly inflates the result to correct for sampling bias. For most everyday uses — checking spread in a full dataset, comparing two batches of measurements, or classroom exercises — the population formula shown here is the standard starting point.

If you only need the average without the spread, our Average Calculator gets you there faster.

📅 Last reviewed: July 2026 · Formulas verified against RBI/SEBI/IT Dept guidelines.