Half-Life Calculator
Determine how much material remains after any number of half-lives with exponential decay assumptions.
Units cancel; use grams, counts, moles, etc.
Half-lives elapsed
2.4
Remaining amount
18.9465
Fraction remaining
0.1895
How to Use This Calculator
Define the initial quantity
Measure or specify the starting amount of substance before decay begins.
Enter half-life
Use time units appropriate for the isotope or first-order process (seconds, minutes, years, etc.).
Provide elapsed time
Use the same time units as the half-life to maintain consistency.
Interpret the results
Review how much material remains and the fraction relative to the initial amount.
Formula
N = N0 * (1/2)^(t / t1/2)
N0 is the initial amount, t elapsed time, t1/2 the half-life. The ratio N/N0 equals (1/2)^(number of half-lives).
Example
For N0 = 100 g, t1/2 = 5 years, t = 12 years: half-lives = 2.4, fraction = (1/2)^2.4 about 0.19, remaining about 19 g.
Full Description
Half-life calculations apply to nuclear decay, pharmacokinetics, and any first-order decay process. The amount decreases exponentially with time.
Knowing half-lives helps forecast safe handling periods, dosing intervals, and residual concentrations in environmental studies.
Frequently Asked Questions
Is the decay assumed first order?
Yes. The half-life model assumes exponential decay with a constant half-life.
Can the half-life change over time?
Not for true first-order processes. If it changes, use a more detailed kinetic model.
What units should I use?
Any time unit works as long as the half-life and elapsed time units match.
Can I compute elapsed time given a target amount?
This tool focuses on forward calculation. Rearranging the formula or using logarithms lets you solve for time.
Does this handle growth processes?
No. For growth with doubling times, use a similar formula with base 2 but reverse the exponent sign.