Standard Deviation Calculator

Standard deviation is a measure of how spread out values are around the mean of a dataset. A low standard deviation means values cluster tightly around the mean; a high standard deviation means values are widely dispersed. It is one of the most widely used statistics in science, finance, engineering, and data analysis. Our standard deviation calculator computes both the population standard deviation (σ = √(Σ(xᵢ−μ)² / n)) and the sample standard deviation (s = √(Σ(xᵢ−x̄)² / (n−1))) simultaneously, so you always have the right value for your use case.

1. 1. Enter Your Dataset: Type or paste your numbers into the input field — separated by commas, spaces, semicolons, or new lines. The standard deviation calculator accepts integers and decimals of any size.
2. 2. Instant Browser-Based Calculation: Click Calculate Standard Deviation and the tool instantly computes population SD, sample SD, variance, mean, and more. All processing happens locally in your browser — your data is never sent to any server.
3. 3. Explore Results and Z-Scores: View the full results panel including both SD types, variance, coefficient of variation, and the step-by-step deviation table. Use the Z-score calculator to find the percentile rank of any value in your dataset.

• Population vs. Sample Standard Deviation: Population SD (σ) divides the sum of squared deviations by n — use this when your dataset is the entire population. Sample SD (s) divides by n−1 (Bessel's correction) — use this when your data is a sample drawn from a larger group. The correction prevents underestimation of the true population spread.
• Variance: Variance is the average of the squared deviations from the mean. Standard deviation is simply the square root of variance, expressed in the same units as the original data. Our standard deviation calculator shows both population variance (σ²) and sample variance (s²).
• Z-Score: A Z-score (standard score) measures how many standard deviations a value is from the mean: Z = (x − μ) / σ. A Z-score of 0 means the value equals the mean; +1 means one SD above; −2 means two SDs below. Z-scores are used for normalization, outlier detection, and comparing values across different scales.
• Coefficient of Variation (CV): The coefficient of variation is the ratio of the standard deviation to the mean, expressed as a percentage: CV = (σ / |μ|) × 100%. It provides a relative measure of spread that is comparable across datasets with different units or magnitudes — useful when comparing variability between datasets.

Our standard deviation calculator uses JavaScript's 64-bit floating-point arithmetic (IEEE 754 double precision), which provides approximately 15–17 significant decimal digits of precision. For most practical datasets this is more than sufficient. For very large datasets with values spanning many orders of magnitude, consider using a dedicated statistical computing environment. The Z-score percentile rank uses the Abramowitz & Stegun error function approximation, accurate to within 1.5 × 10⁻⁷.