— Stock Market
Volatility Calculator
Measure investment volatility from returns or prices. Paste a return series, or prices to derive returns, and see periodic and annualized volatility, variance, downside deviation, and the inputs used for Sharpe and Sortino ratios.
Annualized volatility
16.53%
- Daily volatility
- 1.04%
- Variance
- 1.08
- Mean return
- 0.24%
- Downside deviation (annualized)
- 9.12%
Try: A 10-period returns series, From a price series, Log returns, monthly, Monthly returns
— Returns
| Period | Return |
|---|---|
| 1 | 1.2% |
| 2 | -0.8% |
| 3 | 0.5% |
| 4 | 1.8% |
| 5 | -1.3% |
| 6 | 0.9% |
| 7 | -0.4% |
| 8 | 1.1% |
| 9 | 0.3% |
| 10 | -0.9% |
— Return distribution
Download— How it works
Volatility = standard deviation of returns. Annualized volatility = σ × √(periods per year) — √252 for daily, √52 weekly, √12 monthly. From prices, each return is (Pₜ − Pₜ₋₁) ÷ Pₜ₋₁ (simple) or ln(Pₜ ÷ Pₜ₋₁) (log). Variance is σ². Downside deviation counts only returns below the target.
What volatility measures
Volatility is just the standard deviation of returns — a measure of how spread out they are around their average. A stock whose daily returns cluster tightly around zero is calm; one that lurches between +3% and −3% is volatile. It’s the single most common risk number in finance, and the denominator of the Sharpe ratio. The calculator computes it from your returns directly, or derives the returns from a price series first — the period-to-period change from one price to the next.
Worked example — daily returns with a standard deviation of about 0.75%: Annualized = 0.75% × √252 ≈ 11.9%. That √252 is the key step: there are about 252 trading days a year, and volatility scales with the square root of time.
Annualizing — the √time rule
Volatility is almost always quoted as an annual figure, but it’s usually measured from daily, weekly or monthly returns. Because variance grows linearly with time, volatility (its square root) grows with the square root of time: multiply the daily figure by √252, weekly by √52, monthly by √12. Set the frequency and the calculator annualizes automatically. This is why a daily volatility that looks tiny — under 1% — becomes a double-digit annual number. The variance, shown alongside, is simply the volatility squared.
Simple vs log, sample vs population, downside
A few choices refine the result. From prices, log returns — ln(today ÷ yesterday) — are the standard for volatility because they add cleanly over time; simple returns are the everyday percentage change and differ only slightly for small moves. Sample standard deviation (dividing by n−1) is the right default for a sample of returns; population (n) treats your data as the whole universe. The downside deviation counts only returns below your target, ignoring upside swings — it’s the risk measure the Sortino ratio uses. Volatility rests on standard deviation, which assumes roughly normal returns and understates the risk of crashes. Not investment advice.
— Reader questions
How do I calculate volatility?
Take the standard deviation of the returns. To annualize it, multiply by the square root of the number of periods per year — √252 for daily returns, √52 weekly, √12 monthly. From prices, the returns are derived as the change from one price to the next first.
Why multiply by √252?
There are about 252 trading days in a year, and volatility scales with the square root of time (because variance scales linearly with time). So daily volatility is annualized by multiplying by √252 ≈ 15.87. Use √52 for weekly and √12 for monthly data.
What’s the difference between simple and log returns?
A simple return is (today − yesterday) ÷ yesterday. A log return is the natural log of today ÷ yesterday. Log returns are time-additive and the standard for volatility work, but the two are very close for small moves.
Should I use sample or population standard deviation?
For a sample of returns — which is almost always the case — use the sample standard deviation (dividing by n−1). Population (n) is appropriate only if your data represents the entire universe of outcomes, which is rare.
What is downside deviation?
A volatility measure that counts only returns below a target (often zero), ignoring upside swings. It’s the risk input the Sortino ratio uses, on the view that investors care about downside risk rather than all variability.