Math

Half-Life Calculator

Solve for remaining quantity, half-life, or elapsed time in exponential decay.

Inputs

Solve for

Initial quantity N₀

Remaining quantity N

Half-life T

Elapsed time t

Result

Remaining N

How it's calculated

N = N₀·(1/2)^(t/T) · λ = ln2 / T · mean lifetime τ = 1/λ.

Carbon-14 has T ≈ 5730 years; after 11 460 years, 25% of the original remains.

Does this work for any decay?

Any first-order exponential decay — radioisotopes, drug clearance, capacitor discharge.

Units?

Time units must match between T and t; the result inherits those units.

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