Implied volatility calculator
Implied volatility is the volatility that makes Black-Scholes return the price the option is actually trading at. There is no closed-form solution, so it has to be solved numerically. Enter the mid price and this calculator backs out the IV, the implied daily move and the one-sigma range to expiration.
What IV is telling you
It is an annualized standard deviation of returns, priced in by the market right now. A 28% IV on a 182.50 stock means the market expects a one standard deviation move of about 1.47% a day, and roughly 18 dollars either way over 45 days.
That last translation is the useful one. IV as a percentage is abstract. "The market is pricing a 164 to 200 range by expiration, about two times out of three" is a sentence you can actually make a decision with, and it is the sentence that tells you whether your 170 strike is aggressive or lazy.
Implied is not predicted
IV is the price of insurance, not a forecast. It runs above subsequent realized volatility most of the time, in most names, which is the structural reason premium selling has an edge at all. Buyers pay a risk premium for protection and sellers collect it.
Most of the time. The spread flips hard around events, and the losses are not evenly distributed across the calendar. Selling volatility that is expensive for a reason, an earnings print, an FDA decision, a pending deal, is how a strategy with a positive expected value produces a catastrophic month.
Feed it the mid, not the last trade
The solve is only as good as the price you put in. On a contract with a 2.10 bid and a 2.70 ask, the last trade might be either one, and the IV you get back swings by several points depending on which. Use the mid. If the spread is wide enough that the mid feels like a guess, that is information about the contract, and mostly it is telling you not to trade it.
Questions people actually ask
Why does the calculator sometimes return no solution?
Because no volatility can produce that price. Usually the price you entered is below the option's intrinsic value, which happens when a stale quote gets paired with a live spot price, or the expiration has already passed. Check the inputs rather than the math.
Which strike's IV should I look at?
For a general read on the name, the at-the-money contract in your expiration. For a specific trade, the strike you are actually selling, because skew means the 0.20 delta put and the 0.20 delta call carry different volatilities on the same stock and the same date.
How is this solved?
Brent's method, bracketed between 0.01% and 500% volatility, to a tolerance of 1e-6. It is the same root-finder the OptionsKing engine uses, ported to match the reference implementation exactly.
Is high IV always better for a seller?
Higher premium, yes. Better trade, not automatically. High IV means the market expects a big move and is often right about the direction of the risk if not its size. The question worth asking is whether the IV is high relative to what this stock actually does, which is what IV rank is for.