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What Is the Mathematical Relationship between Time to Expiration and Theta?

Theta is non-linear and accelerates rapidly as time to expiration approaches zero, proportional to $1/sqrt{T}$.
Greeks.Live23.11.25

What Is the Mathematical Relationship between Time to Expiration and Theta?

The relationship between time to expiration (T) and Theta is non-linear and inverse. Theta decay accelerates as T approaches zero, following a concave curve.

The mathematical models show that Theta is roughly proportional to $1/sqrt{T}$. This means that an option with 1 day to expiration loses value much faster than an option with 30 days to expiration, even though the time difference is small.

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