Options Theta Calculator
Compute call and put Theta, an option's daily time decay, and see why decay accelerates as expiry approaches.
Θ What is the Options Theta Calculator?
Theta measures how much an option's price changes per day purely from the passage of time, with the stock price, volatility, and interest rate all held constant. It is often called "time decay", and it is almost always negative for a long option position: every day that passes without a favorable stock move erodes a bit of the option's time value, since there is simply less time left for the position to become profitable.
Options sellers deliberately position themselves to benefit from Theta. Covered call writers, cash-secured put sellers, and credit-spread traders are all "long Theta", meaning time decay works in their favor as long as the position doesn't move sharply against them. Options buyers face the opposite reality: even a stock that stays perfectly flat causes a long option position to lose value day after day, which is why "buy and hold" is a much riskier approach with options than with stocks.
A common misconception is that Theta decay is linear, the same dollar amount lost every day. In fact, Theta accelerates as expiry approaches for at-the-money options, following a curve that steepens sharply in the final weeks before expiration. This is why many options educators specifically warn against holding short-dated at-the-money long options through their final days, when time decay is at its most punishing.
This calculator is useful because it computes both call and put Theta from the same five Black-Scholes inputs used across this site's option tools, expresses it per day and per week for realistic planning, and charts how Theta changes across a range of times to expiry, making the acceleration near expiry directly visible.
📐 Formula
📖 How to Use This Calculator
Steps
💡 Example Calculations
Example 1 — At-the-Money Call and Put
A stock trades at $100, with a $100 strike, 1 year to expiry, a 5% risk-free rate, and 20% volatility.
Example 2 — In-the-Money Call, Shorter Expiry
A stock trades at $150, with a $140 strike, 6 months to expiry, a 4% risk-free rate, and 25% volatility.
Example 3 — Out-of-the-Money Put with Dividends
A dividend-paying stock trades at $50, with a $55 strike, 3 months to expiry, a 3% risk-free rate, 30% volatility, and a 1% dividend yield.
❓ Frequently Asked Questions
🔗 Related Calculators
What is Theta in options trading?
Theta measures how much an option's price changes per day, purely from the passage of time, holding the stock price, volatility, and rate constant. Theta is almost always negative for a long option position, meaning the option loses value every day simply because it has one less day until expiry.
What is the formula for call and put Theta?
Theta_call = [-S x e^(-qT) x phi(d1) x sigma / (2 x sqrt(T)) - r x K x e^(-rT) x N(d2) + q x S x e^(-qT) x N(d1)] / 365. Theta_put replaces the last two terms with +r x K x e^(-rT) x N(-d2) - q x S x e^(-qT) x N(-d1). Dividing by 365 converts the annualized rate into a per-day figure.
Why is Theta usually negative?
An option's value includes time value, compensation for the chance it becomes more profitable before expiry. As each day passes, less time remains for that chance to play out, so time value erodes, which shows up as a negative Theta for the option holder.
Why does Theta accelerate as expiry approaches for at-the-money options?
An at-the-money option's time value is highest relative to its price near expiry because so much of its value depends on a small remaining chance of finishing in the money. As that window shrinks, the daily erosion of value speeds up, producing the well-known 'Theta decay accelerates near expiration' pattern.
Who benefits from Theta decay?
Option sellers benefit from Theta decay, since they collected the premium upfront and profit as the option they sold loses time value. Strategies like covered calls, cash-secured puts, and credit spreads are built specifically to be 'long Theta', profiting from the passage of time.
Is Theta the same for calls and puts?
No, unlike Gamma and Vega, Theta differs between calls and puts because the interest-rate and dividend terms in the formula have opposite signs for the two option types. This calculator's call/put mode tabs compute each separately.
Why is my broker's Theta different from this calculator's Theta?
Some platforms divide the annualized Theta by 252 trading days instead of 365 calendar days, which produces a larger per-day figure. Both conventions are common; this calculator uses 365 calendar days, so multiply this result by 365/252 (about 1.45) to approximate the trading-day convention.
Does Theta ever become positive?
For a standard long vanilla option it is almost always negative, but certain deep in-the-money European puts can occasionally show a slightly positive Theta due to the interest-rate term, since holding the position defers receiving the strike proceeds. This is a rare edge case, not the typical pattern.
How does time to expiry affect the size of Theta?
For at-the-money options, Theta grows larger in magnitude (more negative) as expiry approaches. For deep in- or out-of-the-money options, Theta stays relatively small throughout most of the option's life since there is little time value to decay in the first place.
How is weekly Theta useful for options sellers?
Multiplying daily Theta by 7 gives a rough estimate of a week's worth of expected decay, useful for planning how long to hold a short option position or estimating income from weekly premium-selling strategies, assuming other factors like the stock price and volatility stay constant.