Physics
Exponential decay by half lives
Count the half lives that have passed, raise one half to that power, and scale the starting amount.
The Formula
N = N0 x (1/2)^(t / t1/2)
Count the half lives that have passed, raise one half to that power, and scale the starting amount.
| Symbol | Meaning | Unit | Notes |
|---|---|---|---|
| N | Remaining amount | same as N0 | How much is left after the elapsed time. |
| N0 | Starting amount | mass or count | The amount at the beginning. |
| t | Elapsed time | same as half life | How long has passed. |
| t_1/2 | Half life | time | The time for half the sample to decay. |
What Each Symbol Means
Nsame as N0
Remaining amount
How much is left after the elapsed time.
N0mass or count
Starting amount
The amount at the beginning.
tsame as half life
Elapsed time
How long has passed.
t_1/2time
Half life
The time for half the sample to decay.
See It Worked With Real Numbers
A formula on its own does not tell you which number goes where. The how to calculate half life page applies this equation to a concrete case, shows every intermediate step, and names the mistakes that produce a wrong answer even when the algebra is right.
Where This Formula Appears
This equation is the working core of How To Calculate Half Life, filed under Science. Every number the guide produces comes from substituting into this one line.