Price call and put options using the Black-Scholes model. Calculate premium, Greeks (delta, gamma, theta, vega), break-even price, and P/L at expiry.
Options give you the right — but not the obligation — to buy (call) or sell (put) an underlying asset at a specified price before a certain date. The Black-Scholes model is the foundational framework for pricing European-style options, and it remains widely used across finance.
This calculator prices both call and put options using the Black-Scholes formula, accounting for the underlying price, strike price, time to expiry, volatility, risk-free rate, and dividend yield. It computes the key Greeks — delta, gamma, theta, vega, and rho — which measure the option's sensitivity to various factors.
The profit/loss table shows your potential outcomes at expiry across a range of stock prices, helping you make informed decisions about whether an option trade fits your risk/reward profile. Preset scenarios for common trades let you quickly explore how different setups behave.
Use the preset examples to load common values instantly, or type in custom inputs to see results in real time. The output updates as you type, making it practical to compare different scenarios without resetting the page.
Options pricing involves complex stochastic calculus that Black and Scholes formalized. Rather than relying on broker-provided prices (which include spread markup), this calculator gives you the theoretical fair value. Understanding Greeks is essential for managing risk in any options position.
This tool is designed for quick, accurate results without manual computation. Whether you are a student working through coursework, a professional verifying a result, or an educator preparing examples, accurate answers are always just a few keystrokes away.
Call = S₀·e^(-qT)·N(d₁) − K·e^(-rT)·N(d₂) Put = K·e^(-rT)·N(−d₂) − S₀·e^(-qT)·N(−d₁) d₁ = [ln(S/K) + (r − q + σ²/2)T] / (σ√T) d₂ = d₁ − σ√T Where S = spot, K = strike, T = time, r = risk-free rate, σ = volatility, q = dividend yield.
Result: Premium ≈ $3.25
A call option with strike $180 on a $175 stock with 30 days to expiry and 25% IV is priced around $3.25. The break-even stock price at expiry is $183.25. Delta of ~0.38 means the option gains about $0.38 for every $1 stock increase.
Use consistent units throughout your calculation and verify all assumptions before treating the output as final. For professional or academic work, document your input values and any conversion standards used so results can be reproduced. Apply this calculator as part of a broader workflow, especially when the result feeds into a larger model or report.
Most mistakes come from mixed units, rounding too early, or misread labels. Recheck each final value before use. Pay close attention to sign conventions — positive and negative inputs often produce very different results. When working with multiple related calculations, keep intermediate values available so you can trace discrepancies back to their source.
Enter the most precise values available. Use the worked example or presets to confirm the calculator behaves as expected before entering your real data. If a result seems unexpected, compare it against a manual estimate or a known reference case to catch input errors early.
Delta measures how much the option price changes for a $1 move in the underlying. A delta of 0.50 means the option gains $0.50 when the stock rises $1.
Theta is time decay — the amount of value the option loses each day. Option sellers benefit from theta; buyers fight against it.
IV is the market's expectation of future volatility priced into the option. Higher IV means more expensive options.
Black-Scholes is designed for European options. American options (which can be exercised early) may be worth slightly more, especially puts.
For calls: strike + premium. For puts: strike − premium. The stock must pass this level at expiry for you to profit.
It provides a solid theoretical baseline, but real option prices deviate due to volatility skew, liquidity, and early exercise possibility. Use this as a practical reminder before finalizing the result.