Theta Decay Calculator
Enter a contract below to get its Black-Scholes theta per day, and a schedule of what it is worth at each remaining day count with the stock price and implied volatility held constant.
Theta is reported per calendar day (annual Black-Scholes theta divided by 365). One contract = 100 shares.
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| Days Left | Option Value | Lost Since Prior Row | Theta / Day | Value Remaining |
|---|
Each row is a full Black-Scholes revaluation at that day count, not a straight-line projection from theta.
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ApexVol vs OptionsProfitCalculator, tastytrade & OptionAlpha
How the Theta Decay Calculator on ApexVol compares to the three most-used free alternatives. Last refreshed 2026-05-12.
| Feature | ApexVol | OptionsProfitCalculator | tastytrade | OptionAlpha |
|---|---|---|---|---|
| Live institutional data | ✓ Institutional feed | 15-min delayed | Brokerage account required | Paid tier required |
| No signup for AAPL | ✓ Plus SPY, NVDA, TSLA, +10 more | ✓ | ✗ Account required | ✗ Account required |
| All 5 Greeks (Δ Γ Θ V ρ) | ✓ | Δ only | ✓ | ✓ |
| Live IV rank lookup | ✓ On the calculator page | ✗ | Only inside platform | Paid tier |
| Multi-leg auto-fill from chain | ✓ One-click ATM / 15Δ short | Ticker-only | ✓ | Paid tier |
| Probability of profit + POT | ✓ N(d₂) + 2×POITM | ✗ | POP only | POP only |
| IV crush calculator | ✓ With Vega impact | ✗ | ✗ | Paid tier |
| 3D vol surface viewer | ✓ Free for AAPL | ✗ | Inside platform | ✗ |
| Stress-test scenarios | ✓ Six BSM scenarios per trade | ✗ | Manual | Backtest only |
| Free tier coverage | 13 tickers · all calculators | All tickers (delayed data) | Account-gated | Limited content |
Notes: OptionsProfitCalculator (OPC) is free with 15-minute-delayed quotes; tastytrade requires a brokerage account; OptionAlpha gates most features behind a paid platform subscription. ApexVol's free tier covers 13 of the most-traded tickers with live institutional data — see /methodology for full sourcing.
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See all free calculators →How to Use the Theta Decay Calculator
The calculator prices the contract with Black-Scholes, then reprices it at each remaining day count with the stock and implied volatility frozen. What is left on the curve is time decay in isolation.
The five inputs
- Stock price and strike — theta is largest, in dollar terms, when these are close together. Move the strike well away from spot and theta shrinks toward zero.
- Days to expiry — calendar days, not trading days. The 365-day year is the convention used throughout this page.
- Implied volatility — the annualised figure quoted on the chain, entered as a percentage. Higher IV means more extrinsic value to lose, so more theta.
- Risk-free rate — the short Treasury yield. It matters little for short-dated contracts and materially for LEAPS.
Reading the output
- Theta / day (contract) is the headline number: dollars lost per day on one 100-share contract if nothing else changes.
- Daily burn rate expresses that as a percentage of the option's current value, which is the fairer comparison across different priced contracts.
- Extrinsic value is the only part theta can consume. Intrinsic value is immune to the passage of time.
- The schedule shows the actual dollar path. Compare the loss between 30 and 21 days against the loss between 3 and 1 days.
A caveat worth stating: theta is a snapshot derivative, not a forecast. It tells you the instantaneous decay rate at today's inputs. Tomorrow the stock will have moved and IV will have reset, and the realised change in the option's price will reflect all of it. Theta is only the part attributable to one day passing.
What Theta Decay Actually Measures
An option's price splits into two parts. Intrinsic value is what the contract would be worth if it expired right now. Extrinsic value is everything above that — the premium the market charges for the chance the stock moves further your way before expiry. Theta measures the rate at which that second component drains away.
Because the extrinsic component must reach exactly zero at expiration, its disappearance is arithmetically certain. That is what makes theta different from delta or vega: those describe sensitivities to things that may or may not happen, while theta describes an outcome that is guaranteed to complete. What is not guaranteed is whether the stock's movement compensates for it.
The Black-Scholes Theta Formula
Call theta (per year)
−(S · φ(d₁) · σ) / (2√T) − rK·e−rT·N(d₂)
Put theta (per year)
−(S · φ(d₁) · σ) / (2√T) + rK·e−rT·N(−d₂)
Where
d₁ = (ln(S/K) + (r + σ²/2)T) / (σ√T) · d₂ = d₁ − σ√T · T = days / 365
φ is the standard normal density, N the standard normal CDF. Both formulas return theta per year; this page divides by 365 to show theta per calendar day, which is the convention nearly every broker platform uses.
Worked Example: $100 Stock, $100 Strike, 30 Days
Take a 30-day at-the-money call with the stock at $100, implied volatility at 30% and a 4.5% risk-free rate — the calculator's default inputs. T = 30/365 = 0.0822, so d₁ = 0.086 and d₂ = 0.000 (d₂ lands on zero here only because a 4.5% rate happens to equal σ²/2). The call is worth $3.61, all of it extrinsic. Annual theta comes out at −$23.04, which divided by 365 gives −$0.0631 per share per day, or −$6.31 per contract per day. That is 1.75% of the option's value burning off every day.
Hold everything else still and roll the clock forward. At 7 days left the same call is worth $1.70 and theta has roughly doubled to −$12.44 per contract per day. At 1 day left it is worth $0.63 with theta at −$31.93 — five times the rate it started at, on a contract worth less than a fifth of what it was.
Why Theta Accelerates Near Expiry
Time decay is not linear, and the reason is visible in the formula. The dominant term of at-the-money theta is −(S · φ(d₁) · σ) / (2√T). The √T sits in the denominator, so as T shrinks toward zero the per-day charge grows without limit. Put the other way round: an at-the-money option's extrinsic value is roughly proportional to √T, so halving the time remaining removes about 29% of the value, not 50%. The leftover has to disappear somewhere, and it disappears in the final days.
This is why the decay curve above bends. In the default example, the first week of the 30-day call's life costs the holder about $0.47 of the $3.61. The final three days cost $1.10 — more than twice as much, in less than half the time. Nothing about the trade changed; only the shape of the function.
Theta and gamma are the same trade
Gamma also rises sharply into expiry, and for the same structural reason: gamma carries a 1/√T term too. The two Greeks move together because they are two views of one thing. A long option holder pays theta and receives gamma — the right to profit convexly from movement. A seller collects theta and is short gamma.
In the calculator's default example, gamma climbs from 0.046 at 30 days to 0.254 at 1 day, while theta per contract falls from −$6.31 to −$31.93. Both roughly five-fold. That is the trade being repriced, not two unrelated things happening.
What this implies for either side
Selling short-dated options collects the steepest decay, but the accompanying gamma means a single adverse move can erase weeks of collected premium in an afternoon. The high theta is compensation for that risk, not a free yield.
Buying short-dated options is the mirror: the position needs the stock to move enough, and soon enough, to outrun a decay charge that is itself increasing every day. Neither side is inherently favourable — the calculator tells you the size of the charge, not whether it is worth paying or collecting.
One practical wrinkle: the formula charges decay per calendar day, but markets are closed at weekends. Some desks handle this by using trading days, others by marking down implied volatility into a weekend. Either way, a Friday-to-Monday move is three calendar days of theta on this page's convention, and the option chain will usually have priced most of it in before the close on Friday.
Frequently Asked Questions
What is a theta decay calculator?
A theta decay calculator computes how much value an option loses to the passage of time. Enter the stock price, strike, days to expiration, implied volatility and risk-free rate, and it returns the Black-Scholes theta expressed per day, plus a schedule of what the contract is worth at 30, 21, 14, 7, 3, 1 and 0 days left with the stock and volatility held constant.
How is theta calculated in Black-Scholes?
Call theta is −(S · φ(d₁) · σ) / (2√T) − rK·e−rT·N(d₂). Put theta replaces the last term with + rK·e−rT·N(−d₂). The formula returns theta per year, so divide by 365 to express it per calendar day — the convention used on this page and on most broker platforms.
Why does theta decay accelerate near expiration?
An at-the-money option's extrinsic value is roughly proportional to the square root of time remaining, so it falls along a curve rather than a straight line. Halving the time left removes about 29% of the value, not 50%, which means the loss per day keeps rising as expiry approaches. The dominant theta term contains 1/√T, so as T approaches zero the per-day charge grows without bound for an at-the-money contract.
Is theta always negative?
Theta is negative for essentially every long at-the-money or out-of-the-money option, and positive for the short side of the same contract. The exception is a deep in-the-money European put, where interest earned on the strike proceeds can outweigh the loss of extrinsic value and produce a small positive theta. Long calls on a non-dividend-paying stock never have positive theta.
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Theta With Real Chain Data
This page uses the IV you type in. The platform uses the IV the market is actually quoting, strike by strike.
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