Physics
Continuous decay form
The same decay written with the decay constant instead of counting half lives. Equivalent at every time.
The Formula
N = N0 x e^(-lambda x t)
The same decay written with the decay constant instead of counting half lives. Equivalent at every time.
| 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. |
| lambda | Decay constant | per unit time | Fraction of the sample decaying per unit time. |
| t | Elapsed time | time | How long has passed. |
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.
lambdaper unit time
Decay constant
Fraction of the sample decaying per unit time.
ttime
Elapsed time
How long has passed.
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.