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Half-life calculator

Solve exponential decay from any three measurements, or convert between half-life, mean lifetime and decay constant.

Get started

  1. Use the example values or enter your own measurements.
  2. Calculate, then copy the result or download the available details.

Example

Input

100 to 10 in 50 time units

Expected result

Half-life ≈ 15.0515

Try it

Good to know

The calculation runs in your browser. Use consistent units in fields with no explicit unit.

Calculation method

Exponential decay is N(t) = N₀ · 2^(−t/T). T is half-life, mean lifetime is T/ln(2), and the decay constant is ln(2)/T. The conversion uses ln(2) rounded to ten decimal places. Use the same time unit for all fields.

N(t)=N0 2−t/T,λ=ln⁡2T,τ=1λN(t)=N_0\,2^{-t/T},\qquad \lambda=\frac{\ln 2}{T},\qquad \tau=\frac1\lambda

Pick the unknown first. Use consistent time units across the other three fields. For an initial amount of 100 and a half-life of 10, the remaining amount after 20 time units is 25.

Calculation mode

Find half-life
  • Remaining quantity
  • Initial quantity
  • Elapsed time
Find remaining quantity
  • Initial quantity
  • Elapsed time
  • Half-life
Find initial quantity
  • Remaining quantity
  • Elapsed time
  • Half-life
Find elapsed time
  • Remaining quantity
  • Initial quantity
  • Half-life
Convert decay measures
  • Known measurement · Half-life / Mean lifetime / Decay constant
  • Value