Half Life Calculator
A half life is the time it takes for half of a sample to decay. Three quantities describe the whole process, and any two of them fix the third.
Amount remaining
12.5
- Fraction of the original remaining
- 12.50%
- Half lives elapsed
- 3
- Decay constant
- 0.0866
Values update as you type. This calculator covers the single scenario its formula assumes — see Common Mistakes for what it leaves out.
The formula this calculator uses
N = N0 x (1/2)^(t / t1/2)
- N
- Amount remaining after the elapsed time
- N0
- Starting amount of the substance
- t
- Elapsed time
- t1/2
- Half life of the substance
- lambda
- Decay constant, equal to ln 2 divided by the half life
How to check the result by hand
- 1
Write down the starting amount and the half life
Both must use consistent time units. An 8 day half life with a 24 day elapsed time is straightforward; mixing days and hours is not, and the conversion has to happen before anything else.
- 2
Divide the elapsed time by the half life
Twenty-four days divided by 8 days is 3, so three half lives have passed. The division removes the units, which is why the half life and the elapsed time must match.
- 3
Raise one half to that power
One half cubed is one eighth, or 0.125. Each whole half life halves the fraction, so the exponent is simply how many halvings have happened. A fractional exponent handles times that fall between whole half lives.
- 4
Multiply by the starting amount
One eighth of 100 milligrams is 12.5 milligrams. If you would rather have a percentage, the fraction on its own is the answer: 0.125, or 12.5 percent of the original.
- 5
Work out the decay constant if you need a rate
Divide the natural logarithm of two, which is 0.6931471805599453, by the half life. For 8 days that gives 0.08664339756999316 per day, the fraction of the sample that decays each day in the continuous model.
For worked examples, common mistakes and the limits of this formula, read the full How To Calculate Half Life page.