Standard Deviation Calculator
Calculate population and sample standard deviation with step-by-step deviation table, variance, and full statistics.
Dataset
Updates as you typeTreat data as
Sample vs population ?
Input method
How will you enter your data? ?
Values ?
—
Value × count rows ?
—
| Value | Count |
|---|
Bin ranges × count ?
—
| Lower | Upper | Count |
|---|
Display (optional)
Decimal places
2
Extras
Distribution
Histogram with mean and ±1σ, ±2σ bandsBin —
N —
Bar count
Mean (x̄)
±1σ (≈68%)
±2σ (≈95%)
Boxplot
Min · Q1 · Median · Q3 · MaxDeviation table
| Value (xᵢ) | Deviation (xᵢ − x̄) | Squared | Z-score |
|---|
Formula
s
=
√
Σ(xᵢ − x̄)²
N − 1
σ
=
√
Σ(xᵢ − μ)²
N
- s
- Sample standard deviation — use when the data is a sample from a larger population. Divides by N − 1 (Bessel’s correction).
- σ
- Population standard deviation — use when you have the entire population. Divides by N.
- x̄ / μ
- Mean of the data.
- xᵢ
- Each individual value.
- N
- Number of values in the data.
- Variance
- The square of the standard deviation (s² or σ²).
Worked example — your numbers
- N = —
- Σx = —
- Mean (x̄) = Σx / N = —
- Σ(xᵢ − x̄)² = —
- Variance = Σ(xᵢ − x̄)² / N − 1 = —
- SD = √variance = —
Choose Sample when you’re estimating the SD of a larger population from a sample — the N − 1 denominator corrects for the bias that would otherwise understate spread. Choose Population when every member of the group is in your data.