Half Life Calculator

The following tools can generate any one of the values from the other three in the half-life formula for a substance undergoing decay to decrease by half.

Half Life Calculator

Please provide any three of the following to calculate the fourth value.

quantity remains
Nt
initial quantity
N0
time
t
half-life
t1/2


Half Life, Mean Lifetime, and Decay Constant Conversion

Please provide anyone of the following to get the other two.

half-life
t1/2
  mean lifetime
τ
  decay constant
λ
= =


Definition and Formula

By definition, half-life is the period of time it takes for a substance undergoing decay to decrease by half. An exponential decay process can be described by any of the following three equivalent formulas:

Nt = N0(1/2)t/t1/2
Nt = N0e-t/τ
Nt = N0e-λt

where
    N0 is the initial quantity
    Nt is the quantity that still remains after a time t,
    t1/2 is the half-life
    τ is the mean lifetime
    λ is the decay constant

t1/2 = ln(2)τ = ln(2)/λ