Half-Life Calculator
Work with exponential decay in any unit. Provide any three of the starting amount, remaining amount, half-life and elapsed time, and the calculator solves for the missing one and reports the decay constant.
How to use the half-life calculator
- Choose which value you want to solve for.
- Enter the three values you know in consistent units.
- Read the missing value plus the decay constant and number of half-lives.
Examples
Carbon-14 after one half-life
N0 = 100, half-life = 5730 yr, time = 5730 yr
Remaining = 50
Find the elapsed time
N0 = 100, remaining = 25, half-life = 5730 yr
Time = 11460 yr
Frequently asked questions
What is the half-life formula?
The amount remaining is N = N0 times one half raised to the power of time divided by half-life, written N = N0 * (1/2)^(t/T).
What is the decay constant?
The decay constant lambda equals the natural log of 2 divided by the half-life, lambda = ln(2)/T. It is the fractional decay rate per unit time.
Does this work for any units?
Yes. As long as the half-life and elapsed time share the same unit, and the two amounts share the same unit, the result is correct in those units.
Can I use it for things other than radioactivity?
Yes. Any quantity that halves over a fixed period, such as drug concentration or a capacitor discharge, follows the same exponential decay law.
How many half-lives until almost nothing is left?
After 10 half-lives less than 0.1 percent remains. Each half-life cuts the amount in half, so decay slows but never quite reaches zero.
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