Half Life Calculator
A half life calculator determines how long it takes for a quantity to decrease to half of its original amount. Half-life calculations are commonly used in nuclear science, chemistry, pharmacology, biology, and other areas involving exponential decay.
What Is Half-Life?
Half-life is the time required for half of a substance or quantity to remain after a process of exponential decay. After each additional half-life, the remaining amount is reduced by another half.
Half-Life Formula
If the initial amount is N0 and n half-lives have passed, the remaining amount is:
N = N0(1/2)n
The number of half-lives can be found using:
n = t Γ· t1/2
where t is the elapsed time and t1/2 is the half-life.
Half-Life Example
Suppose a substance has an initial amount of 80 grams and a half-life of 5 years.
After 5 years:
80 Γ· 2 = 40 grams
After 10 years:
40 Γ· 2 = 20 grams
After 15 years:
20 Γ· 2 = 10 grams
So after three half-lives, or 15 years, 10 grams remain.
Half-Life and Exponential Decay
Half-life is a form of exponential decay. The quantity decreases by the same fraction during each half-life, rather than by the same fixed amount.
For example, a quantity starting at 100 units becomes 50, then 25, then 12.5, and so on.
Finding the Number of Half-Lives
If the initial amount and remaining amount are known, the number of half-lives can be found from:
n = log(N Γ· N0) Γ· log(1/2)
For example, if 100 grams decreases to 25 grams:
25 Γ· 100 = 0.25
Since (1/2)2 = 0.25, two half-lives have passed.
Common Half-Life Values
| Half-Lives Passed | Remaining Amount | Remaining Percentage |
|---|---|---|
| 0 | N0 | 100% |
| 1 | N0/2 | 50% |
| 2 | N0/4 | 25% |
| 3 | N0/8 | 12.5% |
| 4 | N0/16 | 6.25% |
Where Is Half-Life Used?
Half-life is especially important for describing radioactive decay, but similar exponential decay models are also used in chemistry, pharmacology, environmental studies, and other scientific applications.
Common Mistakes to Avoid
Remember that each half-life reduces the remaining amount by half of what is currently present, not by half of the original amount every time.
Also keep the units consistent. If the half-life is given in years, the elapsed time should also be expressed in years before calculating the number of half-lives.
Quick Summary
Half-life is the time required for a quantity undergoing exponential decay to decrease to 50% of its previous amount. After n half-lives, the remaining quantity is N = N0(1/2)n. A half-life calculator can determine the remaining amount, elapsed time, or number of half-lives.