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- Finds how much of a substance remains after a given time.
- Can also find the half-life, the time elapsed or the starting amount.
- Shows the decay constant and mean lifetime.
- Lists the amount left after each half-life.
How to use the half-life calculator
Choose what to find
Amount remaining, half-life, time elapsed or initial amount.
Enter the values you know
For example 100 g, a half-life of 5,730 years and 10,000 years elapsed.
Keep the time units the same
Use years, days or seconds for both the half-life and the time.
Read the result
With the percentage remaining and the number of half-lives.
What is half-life?
Half-life is the time it takes for half of a substance to decay or be removed. After one half-life 50% remains, after two 25%, after three 12.5%, and so on. It is used for radioactive isotopes, medicines in the body and any process that decays exponentially.
Half-life formulas
N = N₀ × (½)^(t ÷ T½)
T½ = t × ln 2 ÷ ln(N₀ ÷ N)
Decay constant λ = ln 2 ÷ T½
Example 1: carbon-14 after 10,000 years
100 g with a half-life of 5,730 years.
- Half-lives elapsed 1.7452
- Amount remaining 29.83 g (29.83%)
- Decay constant 0.000120968 per year
Example 2: carbon dating
A sample has 25% of its carbon-14 left.
- Time elapsed 11,460 years (2 half-lives)
Example 3: finding the half-life
100 g decays to 12.5 g in 30 days.
- Half-life 10 days (3 half-lives)
Where half-life is used
Nuclear physics
Decay of radioactive isotopes.
Carbon dating
Estimate the age of fossils and artifacts.
Medicine
How long a drug stays in the body.
Chemistry
First-order reaction rates.
For general growth and decay problems, use the exponential growth calculator. Work with logarithms in the log calculator.
Half-life calculator FAQ
What is the half-life formula?
N = N₀ × (½)^(t ÷ T½), where N₀ is the starting amount, t the time and T½ the half-life.
How much is left after 3 half-lives?
12.5%, because ½ × ½ × ½ = 1/8.
What is the half-life of carbon-14?
About 5,730 years.
How do you calculate half-life from two amounts?
T½ = t × ln 2 ÷ ln(N₀ ÷ N). If 100 g becomes 12.5 g in 30 days, the half-life is 10 days.
What is the decay constant?
λ = ln 2 ÷ T½. It is the fraction that decays per unit of time.
Does half-life change with the amount?
No. It is the same no matter how much of the substance you have.