The Nobel-winning formula that built the modern derivatives market. Price an option from five inputs and see how the Greeks measure its every sensitivity.
Black-Scholes Option PricingLive
fair value + the Greeks
Controls
Presets
The Black-Scholes formula prices a European option from spot, strike, time, rate, and volatility. The Greeks measure sensitivity: delta to price, gamma to delta, vega to volatility, theta to time decay. Educational tool — not investment advice.
Reading this result: Spot 100 vs strike 100 makes this call at-the-money (intrinsic value 0.00). A higher volatility σ (now 25%) and a longer time to expiry (now 0.50 yr) both raise the option's value by adding time value — more room for the underlying to finish favorably. As the option moves deeper in-the-money its delta approaches 1 and it behaves like the underlying itself.
Runs locally in your browser — free forever. Scale to the cloud when reality gets heavy.
★ Sign in to save this setupSave your tuned setup, or drop this simulation into your own site, docs, or course page.
How it works
The Black-Scholes model gives the fair value of a European option from spot price, strike, time to expiry, risk-free rate, and volatility. The Greeks — delta, gamma, vega, theta, rho — quantify how that value responds to each input, and are the language of options hedging. This is an educational tool, not investment advice.
✦
Ask the AI about this model
The math, the assumptions, real-world uses, or a code translation — explained for this exact simulation.
Is this Black-Scholes calculator tool really free?▾
Yes. Black-Scholes Option Pricing runs entirely in your browser using your device's own compute, so local use is free forever. You only pay Compute Tokens if you scale a job to the cloud.
Do I need to install anything?▾
No. Everything runs client-side in a modern browser — no downloads, no license, no account required to start.
Can I save or share my simulation?▾
Create a free account to save projects, and use a shareable embed or minted DOI to publish a live, interactive version anywhere.
How accurate are the results?▾
The solver uses established numerical methods, but results are for research and educational purposes and should be validated against experiment or professional review before you rely on them.