Half-Life Calculator

Mode

Remaining amount Time to target

Half-life

Example: I-131 ≈ 8.02 days.

Initial amount (N₀)

Units are free-form (Ci, Bq, mg, count). Ratios only.

Elapsed time

Compute N(t) = N₀ × 0.5^(t / HL).

Target

Time to reach a given amount or percent of N₀.

Half-Life – Quick Cheat Sheet

Half-life (HL): time for quantity to reduce to 50%.
Decay constant: λ = ln(2) / HL (in s⁻¹ if HL in seconds).
Mean lifetime: τ = 1 / λ = HL / ln(2).
Remaining amount: N(t) = N₀ × 0.5^t/HL = N₀ × e^−λt.
Elapsed half-lives: n = t / HL.
Time to target fraction f (e.g., 25% ⇒ f=0.25): t = HL × log₂(1/f) = ln(1/f) / λ.
Units: Inputs can be in seconds, minutes, hours, days, or years; outputs include all for convenience.
Note: Amount units are relative—any consistent unit works (Ci, Bq, mg, count).

Edge cases & tips

Half-life must be positive; elapsed time can be zero (then N(t)=N₀).
For “time to target,” the target percent must be between 0 and 100; target amount must be >0 and <N₀.
Converting HL to seconds first ensures λ is consistent across all output units.