Decay
Half-life calculator
Checked for single-exponential decay using two comparable, background-corrected measurements.
Half-life
From two activity measurements
Waiting for valid input
Decay
Checked for single-exponential decay using two comparable, background-corrected measurements.
Half-life
Waiting for valid input
The calculator determines a radionuclide half-life from two activity measurements of a single source and the time interval between them. From the radioactive decay law A = A₀·exp(−λt) with λ = ln2/T½ follows the direct formula T½ = t·ln2 / ln(A₀/A). You only need the original activity A₀, a later activity A (which must be lower than the original) and the elapsed time t — the activity unit does not matter because it cancels in the A₀/A ratio.
The calculator estimates a half-life from experimental data — for example, to verify a source certificate value or to determine the half-life of an unknown nuclide from repeated activity measurements. A correct result requires two activity measurements of the same source and the exact time between them; the half-life is returned in the chosen time unit.
Enter the initial activity A₀, the activity A after time t and the time t itself. The half-life follows from T½ = t·ln2/ln(A₀/A); the activity unit cancels, so any pair of identical units works.
The calculator rejects such input: in radioactive decay the activity can only decrease. Check the order of the measurements, the background and the detector efficiency — a rise usually means a measurement error or daughter ingrowth.
The accuracy is set by the two measurements: when A₀/A is close to 1, a small activity error produces a large half-life error. For a reliable estimate measure after a time comparable to the expected half-life.