Implied Volatility Calculator
Implied volatility is the volatility that makes the Black-Scholes price equal the option's market price. It is how the market prices future movement. Enter the option price, stock price, strike, days to expiry and rate, and this calculator solves for IV. If no volatility can produce that price, it tells you why.
For education only, not financial advice. Read the disclaimer.
HOW IT WORKS
There is no closed-form formula for implied volatility, so it is solved numerically. Starting from 30%, Newton's method updates sigma = sigma - (BS(sigma) - price) / vega until the model price matches to 8 decimals. If a step leaves the 0.01% to 500% range or vega is too small, the solver switches to bisection, which always converges because option prices rise with volatility.
A price has no solution when it sits outside the no-arbitrage bounds: a call must be worth more than max(0, S - K e^(-rT)) and less than S; a put more than max(0, K e^(-rT) - S) and less than K e^(-rT). Prices at or below intrinsic value usually mean a stale quote or a dividend the model does not include.