Free online standard deviation calculator

How to use

1. Type or paste your numbers into the text area — commas, spaces, semicolons, and new lines all work as separators.
2. Results update as you type.
3. Use “Share with my numbers” to share the data set via URL.

Formulas

Population standard deviation:

σ = √( Σ(xᵢ − μ)² / n )

Sample standard deviation:

s = √( Σ(xᵢ − x̄)² / (n − 1) )

Where:

• μ (or x̄) = mean of all values
• n = count of values
• Σ(xᵢ − μ)² = sum of squared deviations from the mean

Worked example

Data: 2, 4, 4, 4, 5, 5, 7, 9 (n = 8)

1. Mean = 40 / 8 = 5
2. Squared deviations: (2−5)²=9, (4−5)²=1 × 3, (5−5)²=0 × 2, (7−5)²=4, (9−5)²=16
3. Sum of squared deviations = 9 + 3 + 0 + 4 + 16 = 32
4. Population variance σ² = 32 / 8 = 4 → σ = 2
5. Sample variance s² = 32 / 7 ≈ 4.5714 → s ≈ 2.1381

Notes

• Sample standard deviation requires at least 2 values; with only 1 value the result is 0.
• Results are rounded to six decimal places.
• Share URLs encode your data in the d query parameter.