Black-Scholes Theta Calculator

About this calculator

Theta measures how much an option's price is expected to decay per day (or per year) purely from the passage of time, holding everything else constant. Under the Black-Scholes model, theta for a call is Θ = −(S·N'(d1)·σ)/(2√T) − r·K·e^(−rT)·N(d2), and for a put it's Θ = −(S·N'(d1)·σ)/(2√T) + r·K·e^(−rT)·N(−d2), where S is spot price, K is strike, T is time to expiration, r is the risk-free rate, σ is volatility, and N(·)/N'(·) are the normal CDF and PDF.

Theta is almost always negative for long option positions — it's the daily “rent” an option buyer pays for holding time value, and it accelerates as expiration approaches, especially for at-the-money options. Options traders, market makers, and quantitative analysts monitor theta alongside the other Greeks (delta, gamma, vega) to manage time decay in a portfolio, and options sellers specifically structure trades to collect theta as their primary source of profit.