Statistics

Standard Deviation Calculator

Paste your data to calculate sample or population standard deviation — with variance, coefficient of variation, z-scores, σ-zone breakdown, and a histogram with normal curve overlay.

Formulas
s = √[Σ(x−x̄)² / (n−1)]
σ = √[Σ(x−μ)² / n]
CV = (s / x̄) × 100%
z = (x − x̄) / s

Enter your data

Paste numeric values separated by commas, spaces, or new lines. Minimum 2 values required.

Standard deviation type
Use sample when your data is a subset of a larger process (most common in quality work).
Separate by commas, spaces, tabs, or new lines Enter at least 2 valid numeric values.
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Ready to calculate

Choose sample or population standard deviation, paste your data, and press Calculate to see the full breakdown.

Sample standard deviation (s)
Descriptive statistics
Mean
Average (x̄)
Median
50th percentile
Variance
CV
Coeff. of variation
Std error
SE of mean
n
Count
Min
Minimum value
Max
Maximum value
Range
Max − Min
Data within σ zones (empirical rule check)
±1σ
~68%
±2σ
~95%
±3σ
~99.7%
What this means

Frequency Distribution with Normal Curve
Histogram of your data overlaid with a normal curve based on the calculated mean and standard deviation
Frequency
Normal curve
Mean
±1σ / ±2σ
Z-Score Table
How many standard deviations each value lies from the mean
# Value Deviation (x − x̄) Z-score Visual
How to Use Standard Deviation
Practical interpretation and next steps based on your results
How it works

Understanding standard deviation

s

Sample vs population

Use sample (n−1) when your data is a sample drawn from a larger process — which is almost always the case in quality and manufacturing. Use population (n) only when you have every single data point from a closed, finite group. The n−1 denominator corrects for bias in estimating the true population variance.

CV

Coefficient of variation

The coefficient of variation (CV = σ/μ × 100%) expresses standard deviation as a percentage of the mean. This lets you compare variability across processes with different scales. A CV below 10% is generally low variation; above 30% signals high relative variability.

68-95

The empirical rule

For data that is approximately normally distributed: 68% of values fall within ±1σ of the mean, 95% within ±2σ, and 99.7% within ±3σ. If your data deviates significantly from these expectations, it may be non-normal — consider a Box Plot or normality test before applying Cp/Cpk analysis.