Historical Volatility Calculator (Annualized)
Calculate annualized historical volatility from daily return standard deviation.
Uses 252 trading days for stocks or custom days for crypto and forex.
Volatility annualization is just the square root of time. If daily log returns have standard deviation σ_daily, then:
σ_annual = σ_daily × √(trading days per year)
For US equities the convention is 252 trading days. Forex uses 252 (weekend gaps make weekly returns weird, so dailies are still based on weekday closes). Crypto uses 365 because the market never closes. Use whatever matches the asset.
Why √t and not just t. Variance scales linearly with time when returns are independent. σ is the square root of variance. Daily variance × 252 = annual variance, and σ_annual = √(daily variance × 252) = σ_daily × √252.
Realized vs implied. This calculator gives realized (historical) volatility — what actually happened. Implied volatility is what the options market is pricing for the future. The two diverge constantly. Implied minus realized is the volatility risk premium that options sellers earn on average.
Reading the numbers.
- 10-15% annual: very calm, most stable mega caps and bonds
- 20-25%: typical S&P 500 over multi-year averages
- 30-40%: small caps, single-name stocks, post-earnings periods
- 50-80%: speculative names, biotech, growth stocks during corrections
- 100-200%: crypto majors, meme stocks
- 300%+: garbage altcoins, low-float pumps
Gotcha 1: log returns versus simple returns. Annualized vol math assumes log returns. Most people compute simple percent changes and call it close enough. For daily moves under 5% the difference is negligible. For asset classes with regular 10%+ days (crypto, leveraged products), use log returns to avoid systematic bias.
Gotcha 2: window length matters more than people admit. 30-day realized vol versus 1-year realized vol can give double-or-half answers on the same asset. Pick a window that matches your trading horizon: weeks for swing trades, months for options strategies, year for asset allocation.
Worked example. S&P 500 daily log returns over the last 30 days have σ = 0.0085 (0.85% per day).
- Annualized = 0.0085 × √252 = 0.0085 × 15.87 = 0.135 (13.5%)
Below the long-run average — a calm month. If σ_daily was 0.018 (1.8%), annualized would be 28.6% — a stressed market.