This page shows how to convert implied volatility (typically annual standard deviation or returns) to daily volatility and how to interpret it in terms of expected daily price changes with given probabilities.

Note that in the Implied Volatility Calculator you don’t need to do the conversion, as the calculated implied volatility is already shown for all the common time periods – annual, monthly, weekly, daily, and for the exact time period until the option’s expiration (cells D17-D21).

## Implied Volatility as Annual Standard Deviation

Implied volatility, either in the form of volatility index (such as the VIX for S&P500 index) or implied volatility for a single option (see how to calculate that from option price), is typically expressed as annualized standard deviation of the underlying asset’s returns (price changes).

However, if your time horizon is short, it is often useful to work with volatility or expected price changes over a shorter period. You may want to convert the (annualized) implied volatility to daily or weekly.

## Converting Volatility to Daily

Converting volatility (standard deviation) from annual to daily is quite simple. The only thing to keep in mind is that **volatility is proportional to the square root of time**, and not to time itself. This is because volatility, and more generally standard deviation, is the square root of variance and because variance is proportional to time. Therefore volatility is proportional to square root of time (more detailed explanation here).

Knowing this, you can easily convert annual volatility to daily volatility by dividing it by the square root of the number of trading days per year. Assuming 252 trading days per year, which has been the average for US stock and option markets in the last years, you can convert annual implied volatility to daily volatility by dividing it by the square root of 252, or approximately 15.87. In Excel, you can use the function SQRT to calculate square root.

For example, is you find that implied volatility of a particular option is 25% (either by observing it in a trading platform or calculating it from the option’s price), the daily implied volatility is:

25% / 15.87 = 1.57%

Traders sometimes round the square root of the number of trading days per year to 16 (this is sometimes referred to as the volatility rule of 16). It allows quicker and easier calculation and is still accurate enough for most purposes (16 is actually the square root of 256). In our example, dividing by 16 rather than 15.87 would make the resulting daily volatility equal to 1.56%.

## Interpreting Daily Volatility as Expected Moves

The daily implied volatility which we have just calculated can be interpreted as the expected standard deviation of daily price changes (over the remaining life of the option) being 1.57%.

Of course, this doesn’t mean that every day the stock will move by 1.57%. Even if the actual realized volatility turns out matching the market’s expectations (which is rarely the case), some moves will be smaller, some bigger, some positive, and some negative. Only *on average*, the general size of the moves will be so big that their standard deviation will be 1.57%.

Assuming normal distribution of returns and mean expected return of zero, we can expect the actual daily price moves to fall within 1 standard deviation from zero (i.e. greater than -1.57% and smaller than +1.57%) on **68% of days** (about 2 out of every 3 days) and within 2 standard deviations (between -3.15% and +3.15%) on approximately **95% of days** (about once a month).