Implied volatility calculator

Type an option's market price and get the volatility the market is charging — solved by bisection, the same way the rest of this site does it.

Quick answer: The implied volatility calculator solves for the single volatility figure that makes the Black–Scholes price of an option equal the market price you type in. It uses bisection, so it converges for deep out-of-the-money options and near expiry, where Newton's method fails.

Implied Volatility Calculator

Enter the option's mid price, not its last trade. Everything runs in your browser; nothing you type is sent anywhere.

Figures are per unit of the underlying and exclude brokerage, STT, exchange charges, stamp duty and GST.

How this calculator works

It inverts the model rather than evaluating it

Every other input to Black–Scholes can be observed: spot is on the screen, the strike is in the contract, the days are on a calendar, the rate is published. Volatility is the exception, because it describes movement that has not happened. So this calculator does the arithmetic backwards — it searches for the volatility that makes the model agree with the price you typed.

Why bisection and not Newton–Raphson

Newton's method converges faster, and it converges by dividing by vega. Vega collapses toward zero for deep out-of-the-money options and for any option close to expiry, so Newton either diverges or returns nonsense exactly where a beginner most wants an answer. Bisection cannot fail: the Black–Scholes price is strictly increasing in volatility, so a sign change always brackets exactly one root. It costs about forty iterations, which is nothing.

When it correctly refuses to answer

If the premium you enter is below the option's discounted intrinsic value, or richer than the model can produce at 500% volatility, no volatility solves the equation. The calculator says so rather than inventing a number. That is not a bug: a price outside those bounds violates a no-arbitrage condition, and the honest conclusion is that the quote is stale, the spot you paired it with is wrong, or you have the option type the wrong way round.

The number is only as good as the quote

On an illiquid strike the implied volatility of the bid and the implied volatility of the offer can differ by several volatility points. A last-traded price may be hours old. Use the bid-ask midpoint. And in the final sessions before expiry, ignore the output entirely — the at-the-money premium is collapsing toward zero with the square root of remaining time, so the solver is dividing by almost nothing.

Defined implicitly, solved numerically

Find σ such that BS(S, K, T, r, σ) = P_market

No closed form exists. Bisection on [0.01%, 500%] converges to the unique root because the price is strictly increasing in σ.

σImplied volatility, annualised, as a decimal — the unknown.
BS(·)Black–Scholes–Merton price of a European option.
P_marketThe option's market price. Use the bid-ask midpoint.
SSpot price of the underlying.
KStrike price.
TTime to expiry in years = calendar days ÷ 365.
rRisk-free rate. 6.5% is used as an Indian rupee proxy.

Using it, step by step

Take the option's bid-ask midpoint, not its last traded price.
Enter the spot price of the same underlying, at the same moment. A spot from ten minutes ago paired with a live premium produces a fictional implied volatility.
Enter calendar days to expiry, not trading days. Interest accrues on weekends.
Choose call or put. If you get an implausible answer, check this first — it is the most common input error.
Read the implied volatility, then sanity-check it against the neighbouring strikes. A figure wildly out of line with its neighbours is almost always a stale quote, not a discovery.

Worked example

NIFTY

NIFTY is at 24,000 and the 30-day 24,000 call is quoted at ₹470. Enter those numbers with r = 6.5% and the solver returns an implied volatility of about 14.7%. Interpret it rather than stopping there: 14.7% annualised implies a one-standard-deviation move over the next 30 days of 24,000 × 0.147 × √(30/365) ≈ 1,012 points. That is what you are being charged to find out where NIFTY goes — not a forecast that it will move 1,012 points, and by construction roughly one expiry in three closes outside that band.

Assumptions and limitations

What this calculator assumes. Every number it produces is only as good as the assumptions below, and each of them is wrong to some degree in a real market. The output is a model's opinion, not a measurement.

Black–Scholes–Merton for a EUROPEAN option. NIFTY and BANKNIFTY index options are European and cash-settled, so this is correct for them. Indian single-stock options are American-style and physically settled, and this calculator does not model early exercise.
Dividend yield is zero. Correct for NIFTY and BANKNIFTY, which are price indices. Wrong for a single stock with an ex-dividend date before expiry.
Volatility is assumed constant across strike and time — which is exactly the assumption the volatility smile, the skew and the term structure disprove. The implied volatility you extract is contaminated by the errors of the model you inverted.
Time to expiry is calendar days ÷ 365. Some platforms use trading days ÷ 252 here, which will give you a different answer for the same option. Neither is wrong; they are different conventions.
The risk-free rate matters little for short-dated options and materially for long-dated ones. 6.5% is a proxy, not a measurement.

Common mistakes

Entering the last traded price of an illiquid strike. It may be hours old, and its implied volatility is a fossil.
Computing implied volatility in the final sessions before expiry and building an IV Rank or an alert on it. The premium has decayed to almost nothing, so σ is being solved by dividing by almost nothing.
Pairing a live option premium with a stale spot price — or with the futures price instead of the index, which will shift your answer by the cost of carry.
Reading the output as a forecast. It is a price. A high number means the option is expensive, which is a statement about supply and demand, not about where the underlying is going.
Comparing the raw output across two different underlyings. BANKNIFTY at 18% is not 'more expensive' than NIFTY at 14%; it is a more volatile index.

Frequently asked questions

What does this implied volatility calculator do?

It takes an option's market price and finds the volatility input that makes the Black–Scholes formula reproduce that exact price. Because volatility cannot be observed directly, this inversion is the only way to know what the option market is charging for expected movement.

Why does it use bisection instead of Newton's method?

Newton's method divides by vega, and vega collapses toward zero for deep out-of-the-money options and near expiry, so it diverges precisely where you most want an answer. Bisection cannot fail, because the option's price rises strictly with volatility and a sign change always brackets exactly one root.

Why does the calculator sometimes say there is no solution?

Because the premium you entered lies outside the range the model can produce — below the option's discounted intrinsic value, or above its price at 500% volatility. No volatility solves that equation. The honest answer is that the quote is stale or one of the other inputs is wrong.

Should I enter the bid, the ask, or the last traded price?

The bid-ask midpoint, in almost every case. On a wide market the implied volatility of the bid and of the offer can differ by several volatility points, and a last trade on an illiquid strike may be hours old.

Do I enter calendar days or trading days?

Calendar days. The formula converts them with T = days ÷ 365, because interest accrues on weekends even though prices do not move. Note the inconsistency with the 252-day convention used to annualise realised volatility — both are standard, and the mismatch is the most common reason two correct calculations disagree.

Does this work for BANKNIFTY and stock options?

It is exactly right for NIFTY and BANKNIFTY, which are European and cash-settled index options with no dividend yield. For Indian single-stock options it is an approximation only: those are American-style, physically settled, and may have an ex-dividend date inside the option's life, none of which this model captures.

Why is the answer different from what my broker shows?

Because you are solving different equations. Brokers vary in whether they price against spot or futures, whether they use the last trade or the midpoint, what interest rate they assume, and whether they use Black–Scholes or a binomial model. On a liquid at-the-money strike the answers agree closely; on an illiquid wing they need not.

Is my data sent anywhere?

No. The entire calculation runs in your browser using the same volcharts.js engine that pre-rendered every diagram on this site. There is no back end to send it to, and nothing is logged or stored.

What is a normal implied volatility for NIFTY?

As a rough guide, NIFTY at-the-money implied volatility spends most of its time between about 11% and 16%, dipping below 11% in the calmest stretches and exceeding 25% only in genuine stress. These are conventions drawn from recent history, not rules.

Voice search & related questions

How do I calculate implied volatility?

Take the option's mid price, spot, strike, calendar days to expiry and a risk-free rate, then search for the volatility that makes Black–Scholes reproduce the price. This calculator does that search by bisection, in your browser, in about forty iterations.

Can implied volatility be negative?

No. Volatility is a standard deviation and cannot be negative. If a solver returns something nonsensical, the quoted price violates a no-arbitrage bound — usually it is below intrinsic value, meaning the quote is stale or the spot is wrong.

What is a good implied volatility?

There is no such thing in the abstract. Whether an implied volatility is attractive depends on what the underlying subsequently realises, which nobody knows. Compare it against the same underlying's own history using IV Rank and IV Percentile.

Last reviewed 10 July 2026. Educational content only — not investment advice.