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Volatility Calculator (Standard Deviation of Returns)

Calculate the standard deviation of returns from prices or returns, and annualise it correctly for daily, weekly or monthly data.

Risk MetricsIntermediate
Your inputs
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24 values
Standard deviation
Results
Annualised volatility10.32%σ × √12
Volatility per period2.979%24 returns
Mean return / period+1.471%
Within ±1σ54%≈68% if normal
Largest move6.16%
Bars in the accent colour fall within one standard deviation of the mean; green and red bars are the larger moves. Volatility measures how widely returns spread — it treats big gains and big losses alike.
Returns vs ±1σ band

Not financial advice. Results are estimates based on the values you enter and simplified assumptions; real trades are affected by fees, slippage, gaps and other factors. Trading involves substantial risk of loss. Read the full disclaimer.

How to calculate volatility

σ = √( Σ(rᵢ − r̄)² ÷ (n − 1) ) (sample; use n for population) Annualised σ = σ_period × √(periods per year)

Daily data uses √252, weekly √52 and monthly √12. Prices are converted to percentage returns first.

Worked example

  1. Monthly returns have a standard deviation of 3.0%.
  2. Annualised volatility = 3.0% × √12 = 10.4%.
  3. Daily volatility of 1.2% annualises to 1.2% × √252 ≈ 19.0%.

How to interpret volatility

If returns were normally distributed, about 68% of periods would fall within one standard deviation of the average and 95% within two. Real markets produce more extreme moves than that, so treat volatility as a typical-range measure, not a worst case — for tail risk use Value at Risk or Expected Shortfall.

Volatility is also the denominator of the Sharpe ratio, so it directly shapes risk-adjusted performance.

Limitations and common mistakes

  • Volatility treats upside and downside moves the same. For downside-only risk, see the Sortino ratio.
  • Historical volatility changes over time — the last 20 days and the last 5 years can tell very different stories.
Risk-Adjusted Ratios

Sharpe Ratio Calculator

Measure excess return per unit of volatility from annual figures or a series of returns.

12% return · 2% Rf · 8% σ → 1.25
Risk Metrics

Value at Risk (VaR) Calculator

Estimate the loss threshold you should only exceed on a small share of days — parametric or historical.

$100k · σ 1.2% · 95% → VaR $1,924
Risk Metrics

Beta Calculator

Measure how sensitive an asset or portfolio is to market moves from two return series.

Asset vs index returns → β, correlation, R²

Volatility calculator FAQ

Sample or population standard deviation?

Use sample (n − 1) when your data is a sample of a longer history — the usual case. Population (n) assumes you have every possible observation.

Why multiply by the square root of time?

Variance of independent returns adds up over time, so standard deviation grows with the square root of the number of periods.