Black-Scholes Option Pricing Calculator

What does this calculator do?

The Black-Scholes (Black-Scholes-Merton) model is the standard formula for pricing European-style options — contracts that can only be exercised at expiry. Enter the spot price, strike price, days to expiry, volatility, risk-free rate and (optionally) a continuous dividend yield, and this tool returns the theoretical call and put price, both option's breakeven, intrinsic value and time value, plus the Greeks — delta, gamma, theta, rho and vega — that describe how the price reacts to small changes in each input.

Under the hood it computes d1 and d2 from the standard formula, then evaluates the cumulative standard normal distribution N() with a polynomial (Abramowitz & Stegun 7.1.26) approximation accurate to within about 1.5×10⁻⁷ — indistinguishable from a normal distribution table for any practical use.

How to use it

1. Enter the spot price (current price of the underlying) and strike price (exercise price of the option).
2. Enter days to expiry — the calendar days remaining until the option expires.
3. Enter volatility as an annualized percentage (e.g. 20 for 20% implied volatility) and the annualized risk-free rate (e.g. 5 for 5%, typically a short-term Treasury yield).
4. Leave dividend yield at 0 for non-dividend-paying assets, or enter the underlying's continuous annualized dividend yield.
5. Read the result table — call-side rows, put-side rows, and the Greeks that are shared between both (gamma and vega are identical for a call and put with the same strike and expiry; delta, theta and rho differ by side).

What are the Greeks?

• Delta — how much the option's price moves for a $1 move in the underlying. Calls range from 0 to 1; puts range from -1 to 0.
• Gamma — how fast delta itself changes as the underlying moves; the same for calls and puts.
• Theta — how much value the option loses per calendar day, all else equal ("time decay"), shown per day rather than per year.
• Vega — how much the price changes for a 1 percentage-point move in volatility.
• Rho — how much the price changes for a 1 percentage-point move in the risk-free rate.

Assumptions and limitations

Black-Scholes is a model, not a market guarantee, and it rests on assumptions that don't perfectly hold in real markets:

• It prices European options (exercise only at expiry) — American options, which can be exercised early, are worth at least as much and sometimes more, particularly for dividend-paying stocks.
• Volatility is constant over the life of the option. Real implied volatility varies by strike ("volatility skew/smile") and changes over time, so this calculator's output is only as good as the volatility figure you feed it.
• It assumes no transaction costs, continuous trading, and a constant risk-free rate.
• Dividends are modeled as a continuous yield, not discrete cash payments — a reasonable approximation for indices, a rougher one for single stocks with a known ex-dividend date.

Use it to sanity-check a quoted option price or to explore how price and Greeks move with each input — not as a substitute for a live market quote or a broker's risk tools.

Why is time to expiry entered in days?

Days-to-expiry is what you'll typically see on an option chain. Internally it's converted to years (days / 365) to match the model's formula, which is defined in annualized terms.

Privacy

All calculations run locally in your browser — your inputs are never sent to a server.