Black-Scholes Options Pricing Calculator

How to Use This Calculator

1. Enter the Stock Price and Strike Price.
2. Enter Time to Expiry in years (e.g., 90 days = 0.25).
3. Enter the Risk-Free Rate — use the current 1-year Treasury yield (~4.5% in 2026).
4. Enter Volatility — use the stock's implied or historical volatility.
5. Read the Call Price and Put Price. Switch to Professional for all 5 Greeks.

Formula

Example

Frequently Asked Questions

• What is the Black-Scholes model? ▼
  The Black-Scholes model, developed by Fischer Black and Myron Scholes in 1973, is a mathematical framework for pricing European-style options. It calculates the theoretical price of a call or put option based on the stock price, strike price, time to expiry, risk-free rate, and volatility.
• What are the inputs to the Black-Scholes formula? ▼
  The five inputs are: S (current stock price), K (strike price), T (time to expiry in years), r (risk-free interest rate), and σ (annualized volatility). A dividend yield q can be added for stocks paying dividends.
• What is d1 and d2 in Black-Scholes? ▼
  d1 = [ln(S/K) + (r + σ²/2)T] / (σ√T) and d2 = d1 − σ√T. N(d1) is the delta of the call option; N(d2) is the risk-neutral probability the option expires in-the-money.
• Does Black-Scholes work for American options? ▼
  No — the standard Black-Scholes formula prices European options only (exercisable at expiry). American options can be exercised early, so models like Binomial Trees or Barone-Adesi-Whaley approximations are used.
• What is put-call parity? ▼
  Put-call parity states: Call − Put = Stock − PV(Strike). This no-arbitrage relationship means if you know the call price, you can derive the put price (and vice versa) for the same strike and expiry.

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