Black-Scholes Option Pricer

European option price, Greeks, and payoff diagram

About this calculator

The Black-Scholes Option Pricer values European calls and puts with the Black-Scholes-Merton model, including a continuous dividend yield. From spot, strike, time to expiry, volatility, and the risk-free rate it returns the option price, the Greeks in display units (delta, gamma, vega and rho per percentage point, theta per calendar day), d₁ and d₂, intrinsic and time value, the break-even price at expiry, and a payoff diagram. Non-positive spot, strike, time, or volatility inputs return specific errors.

How to use the Black-Scholes Option Pricer calculator

  1. Enter your amounts, rates and terms into the input fields.
  2. Read the result — it updates instantly as you type.
  3. Adjust the inputs to compare scenarios side by side.
  4. Copy the page URL to share the exact calculation.

Common examples

  • ATM call: S=100, K=100, 1 yr, 20% vol, 5% rate → price 10.45, delta 0.637, break-even 110.45
  • Same inputs as a put → price 5.57, delta −0.363, break-even 94.43
  • Call S=150, K=155, 3 months, 30% vol, 1% dividend → price 7.27, theta −0.054/day, break-even 162.27

Frequently asked questions

How does the Black-Scholes Option Pricer calculator work?

Enter your amounts, rates and terms, and the calculator applies the standard financial formulas to show the outcome, including intermediate figures where they help you understand the result. All arithmetic runs at high precision, so rounding errors do not build up across periods.

When would I use the Black-Scholes Option Pricer calculator?

Use it when planning a purchase, loan, investment or budget, to compare options before committing, or to sanity-check figures quoted to you. It is an educational tool, not financial advice — confirm important decisions with your provider or a professional.

How accurate are the results?

The formulas are the standard ones used in finance and run at 30 significant digits internally. Real products may differ in fees, compounding conventions and rounding rules, so treat the result as a close estimate rather than a contractual figure.

Can I share a specific calculation with someone else?

Yes. Every value you enter updates the URL, so copying the address bar and sharing the link reopens the exact same calculation for whoever clicks it.