Standard Deviation Calculator
Calculate standard deviation, variance, and descriptive statistics for any dataset. Universal tool for analyzing volatility and data dispersion.
Enter any numerical values separated by newlines
N−1 corrects variance under IID sampling, not the square-root estimate.
Sample standard deviation (n-1)
Average value
σ² (squared)
Lowest value
Highest value
Additional Statistics
Quick Reference
Calculate Dispersion in the Right Units
Standard deviation is the square root of variance. Custom mode keeps the original units; returns mode reports percentage-point dispersion. Prices mode first computes adjacent returns, so its output is return volatility, not price-level variation.
A Reproducible Check
Enter 2, 4, 4, 4, 5, 5, 7, 9 in Custom mode. The mean is 5 and squared deviations sum to 32. Population variance is 32/8 = 4 and standard deviation is 2. Sample variance is 32/7 and sample standard deviation is approximately 2.1381.
Choose the Convention
Use N when describing the entered population, or N−1 when estimating population variance from a sample under the relevant sampling assumptions. A small descriptive standard deviation does not establish predictability, measurement accuracy, or a safe investment.
Extreme observations receive more weight because deviations are squared. Investigate data errors before deleting an outlier; removing a valid extreme observation changes the question being measured. Relative standard deviation also depends on the measurement scale and becomes unstable near a zero mean.
References: NIST Measures of Scale and Coefficient of Variation and Relative SD.
Frequently Asked Questions
What is the difference between population and sample standard deviation?
Population mode divides squared deviations by N; sample mode divides by N−1. Under independent identically distributed sampling, N−1 makes the variance estimator unbiased. Its square root is not generally an unbiased estimator of standard deviation.
What do Prices and Returns modes measure?
Prices mode converts positive chronological prices into simple or log percentage returns before calculating dispersion. Returns mode uses the entered percentages directly. Custom mode measures the original values without conversion.
How many inputs are required?
This tool accepts 2–10,000 numeric values, or at least three positive prices to obtain two returns. This is a calculation minimum, not a guarantee of statistical precision. Blank tokens, malformed numbers, and non-finite values are rejected.
What is relative standard deviation?
The displayed relative SD is 100 times SD divided by the absolute mean. It is undefined at zero mean and unstable near zero. Meaningful comparisons generally require a ratio scale with a meaningful zero; do not use it to rank return streams around zero.
Are observations uploaded?
These calculations run in your browser. This form does not fetch market data or upload the entered observations to a calculation API.
Analyzed Data Variability? Build Custom Indicators
You've measured dispersion and volatility with standard deviation—now take your analysis further. Use Pineify's AI-powered Pine Script generator to create custom volatility indicators and trading strategies for TradingView.
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