Radioactive Decay and Half-Life Calculator: Amount Left, Age, Decay Constant and Carbon Dating
Work out how much is left after a time and how old a sample is from the half-life.
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How this calculator works
Choose the amount left, the time to decay, or the half-life from two measurements.
Enter the half-life and the unit of time (carbon-14 is 5730 years), then the starting amount and the time or the fraction left.
The calculator gives the decay constant, the mean life, the number of half-lives and the answer.
Formulas used
- N = N_0\left(\tfrac12\right)^{t/t_{1/2}} = N_0e^{-\lambda t}
- \lambda = \frac{\ln2}{t_{1/2}}
- \tau = \frac{1}{\lambda}
- t = \frac{t_{1/2}}{\ln2}\ln\frac{N_0}{N}
Worked example
With the default numbers in the calculator above:
- Decay constant: 0.00012097 per year
- Mean life (the average lifetime of a nucleus): 8266.64 years
- Number of half-lives that have passed: 2.00
- Amount left: 25.00 (25.00 percent of the start)
- Amount that has decayed: 75.00
Change the numbers in the calculator to see the full working, every step, for your own case.
A second worked example
A different case, with these numbers: What do you want? The time to decay to a fraction (the age).
- Decay constant: 0.00012097 per year
- Mean life (the average lifetime of a nucleus): 8266.64 years
- Time for the amount to fall to that fraction (the age of the sample): 11460.00 years (2.00 half-lives)
Common questions
What is a half-life?
The time for half of the radioactive nuclei in a sample to decay. After two half-lives a quarter is left, after three an eighth.
How does carbon dating work?
Living things take in carbon-14, which decays with a half-life of 5730 years once they die. The fraction left tells you how long ago they died.
What is the decay constant?
The probability per unit time that a nucleus decays. It equals ln 2 divided by the half-life.
What is the difference between half-life and mean life?
The mean life is the average lifetime of a nucleus and is 1.44 times the half-life.
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Got a question about this? Ask an engineering question and get a plain-language answer with references.
Further reading: Any first-year physics text (radioactivity).
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