Half-Life Calculator
Solve exponential decay problems: remaining amount, elapsed time, or half-life. Useful for radioactive decay, drug clearance, and carbon dating.
Half-Life Calculator
Given the starting amount, half-life, and elapsed time.
Any positive quantity: mass, atoms, drug dose, or signal.
In the same time unit as the elapsed time below.
Same unit as the half-life (seconds, minutes, years, etc.).
Remaining amount
25
Number of half-lives
2
Fraction remaining
0.25
Percent remaining
25%
Percent decayed
75%
Decay constant (k)
0.138629 per unit time
Mean lifetime (tau)
7.213475
Frequently Asked Questions about the Half-Life Calculator
What is a half-life?
A half-life is the time it takes for a quantity to drop to half of its starting value. After one half-life, 50% remains. After two, 25%. After three, 12.5%. The pattern continues exponentially.
What formula does this calculator use?
It uses N(t) = N0 times (1/2)^(t / halfLife), which is equivalent to N(t) = N0 times e^(-k t) where the decay constant k equals ln(2) divided by the half-life.
What is the decay constant and the mean lifetime?
The decay constant k is the instantaneous decay rate per unit time, equal to ln(2) divided by the half-life. The mean lifetime tau is the average time a particle survives and equals 1 divided by k, which works out to about 1.4427 half-lives.
Can the remaining amount be greater than the initial amount?
No. Half-life describes decay, so the remaining amount must be smaller than the starting amount. If you enter a larger remaining value the calculator rejects the input.
What can I use this for besides radioactive decay?
Drug pharmacokinetics (how long a medication stays active in the body), carbon-14 dating, capacitor discharge, biological clearance rates, and any other process that decays by a fixed fraction per unit time.