Half-Life Calculator

How it works

Matching the decay model to the question

The half-life calculator uses an exponential-decay model with a constant rate. Choose remaining quantity, initial quantity, elapsed time, or half-life according to what is unknown. Keep the time unit consistent across the inputs. The mathematical model does not establish the actual half-life of a substance or account for additional production, changing conditions, or multiple interacting decay processes.

Remaining quantity: formula and assumptions

N(t) = N₀ × 2^(−t / half-life).

Use the same unit for half-life and elapsed time.

Find half-life: formula and assumptions

Half-life = t × ln(2) / ln(N₀/N).

This mode assumes a positive quantity that decreases exponentially.

Initial quantity or elapsed time: formula and assumptions

N₀=N×2^(t/T); t=T ln(N₀/N)/ln(2).

All time quantities must use the same unit.

Convert decay constants: formula and assumptions

T½=ln(2)/λ; mean lifetime=1/λ.

The decay constant has reciprocal time units.

Worked example

Using the Remaining quantity example:

Initial quantity

100

Half-life (time units)

10

Elapsed time (same units)

20

N(t) = N₀ × 2^(−t / half-life).

Example result

These are illustrative inputs. Change the values to explore a different scenario.

Formula references

• OpenStax: Algebra and Trigonometry (opens in a new tab)

References explain the underlying methods; they do not imply endorsement or individual professional review of Finflo.

Common questions