Option Theta Calculator
Theta quantifies how much an option's theoretical price declines each calendar day due to the passage of time alone, with all other factors held constant. It is expressed as a negative number for long options (the option loses value over time) and represents the per-day cost of owning optionality. Time decay is not linear: it accelerates as expiration approaches, particularly for at-the-money options. Option sellers, such as covered call writers or cash-secured put sellers, benefit from theta because they collect premium that erodes in their favor. This calculator divides the annualized Black-Scholes theta by 365 to give a per-calendar-day figure, which is the industry standard convention.
Theta formula
d1 = [ln(S/K) + (r + sigma^2/2)*T] / (sigma*sqrt(T))
d2 = d1 - sigma*sqrt(T)
Call Theta (annual) = -(S*phi(d1)*sigma)/(2*sqrt(T)) - r*K*e^(-rT)*N(d2)
Put Theta (annual) = -(S*phi(d1)*sigma)/(2*sqrt(T)) + r*K*e^(-rT)*N(-d2)
Daily Theta = Annual Theta / 365
Where phi() is the standard normal PDF, N() is the cumulative standard normal CDF, S is stock price, K is strike, r is risk-free rate (decimal), T is years to expiration, sigma is annualized volatility (decimal).
Understanding theta decay
- Theta is negative for long calls and long puts, reflecting value lost to time each day.
- Option sellers (short calls, short puts) have positive net theta: they profit as time passes.
- At-the-money options have the highest theta in absolute terms; they have the most time value to lose.
- Theta accelerates in the last 30 days of an option's life, particularly for at-the-money contracts.
- To estimate the dollar impact: theta per share * 100 shares per contract * number of contracts.
Frequently asked questions
What is option theta?
Theta measures the daily time decay of an option's value, holding all other factors constant. A theta of -0.05 means the option loses $0.05 in value each calendar day that passes, purely from the passage of time.
Why is theta negative for option buyers?
Option buyers pay for time value, which erodes as expiration approaches. Since time always moves forward, this erosion is a cost to the buyer (negative theta). Option sellers benefit from time decay (positive theta from their perspective).
Which options decay fastest?
At-the-money options have the highest rate of time decay, especially in the final 30 days before expiration. Deep in-the-money or far out-of-the-money options have less extrinsic value to decay. Theta accelerates non-linearly as expiration nears.
How is theta expressed in dollars?
Standard option contracts represent 100 shares. To convert theta to a dollar amount: multiply the per-share theta by 100. A theta of -0.05 on one contract loses $5 per day in time value.
Can theta be positive?
For standard long options, theta is negative (time hurts the holder). However, certain deeply in-the-money put options on stocks that pay no dividends, or complex multi-leg strategies, can exhibit positive theta in edge cases. For practical purposes, bought options always have negative theta.
Official sources
- Black, F. and Scholes, M. (1973). "The Pricing of Options and Corporate Liabilities." Journal of Political Economy 81(3): jstor.org/stable/1831029.
- CBOE Options Institute: cboe.com/education.
Reviewed by the CalculatorHub team, edited by James Graham, 15 June 2026. See our methodology.