Implied volatility is the option's price, spoken as a percentage

Implied volatility looks like a forecast and behaves like a price tag. An option's market price is the thing everyone can see; implied volatility is what you get when you feed that price back into a pricing model and ask what level of volatility would justify it. Higher price, higher IV. It's the option's price restated as an annualized percentage, so that different strikes and expirations can be compared on one scale.

Turning the number into dollars

An IV of 30% on a $100 stock says the options are priced as though the stock's move over a year will land within about 30% of where it is now roughly two-thirds of the time. Nobody trades one-year windows, so you scale it to the time you care about by the square root of the fraction of a year:

expected move ≈ price × IV × √(days ÷ 365)

For 30 days: 100 × 0.30 × √(30 ÷ 365) ≈ 100 × 0.30 × 0.287 ≈ $8.60. The market is pricing a one-standard-deviation range of roughly $91.40 to $108.60 for the month, and about a third of the time the stock should finish outside it. This is the single most useful calculation a premium seller can do, because it puts every strike in context: a $90 put sits just outside one standard deviation, which is why it pays what it pays.

Why the premium is fat

When IV is high, the same put pays more. The temptation is to read that as a bargain, more premium for the same strike. But IV is high because the market expects bigger moves: an earnings report, a lawsuit, a sector selling off. The extra premium is compensation for extra risk, set by people who price it for a living. Sometimes they overpay. On average in equities, implied volatility has run somewhat above the volatility that later showed up, and that gap is the edge premium sellers live on. But the average includes the months where a 30%-IV stock moves 40%.

Implied against realized

Realized volatility is what the stock actually did: the standard deviation of its daily returns over some window, annualized. Comparing the two is how you judge, after the fact, whether premium was rich or cheap. If IV was 30% and the stock realized 18%, sellers were paid for movement that never came. If it realized 45%, they weren't paid enough, however generous the credit looked at entry.

High relative to what

A 30% IV is low for a small biotech and high for a utility. The useful comparison is the stock against its own history. IV rank tells you where today's IV sits between the past year's low and high; IV percentile tells you what fraction of days in the past year had lower IV than today. Either answers the question that matters, whether this stock's premium is expensive by its own standards, better than the raw number does.

What IV does after the event

IV rises into scheduled events and collapses once they pass. An option bought before earnings can lose a third of its value overnight even when the stock moves in the buyer's favor, because the uncertainty it was pricing is gone. Sellers see the mirror image. The collapse works for them, on the condition that the actual move stayed inside what was priced. When it doesn't, the collapse is a footnote to a much larger number.