Radioactive Decay Calculator
Enter a half-life and the number of radioactive nuclei. You get the decay constant per second, the activity in Bq and Ci, the mean lifetime, and the activity after a chosen time.
Updated
Report a problem
Formula
- Decay constant:
λ = ln 2 / T½(T½ in seconds) - Activity:
A = λ × Nin becquerel (decays per second);1 Ci = 3.7 × 10^10 Bq - Mean lifetime:
τ = T½ / ln 2 - Activity later:
A(t) = A × (1/2)^(t / T½)
A year is taken as 365.25 days (31,557,600 s).
Worked example
Carbon-14 has T½ = 5730 years = 1.8082 × 10^11 s. For 1 × 10^12 nuclei:
- λ = 0.693147 / 1.8082 × 10^11 = 3.8332 × 10^-12 per second
- A = λN = 3.8332 Bq, which is 1.0360 × 10^-10 Ci
- τ = 5730 / 0.693147 = 8266.64 years
- After one half-life (5730 years) the activity is 1.9166 Bq
Frequently asked questions
How do I get the decay constant from the half-life?
λ = ln 2 / T½, with T½ in seconds. For carbon-14, T½ = 5730 years = 1.808 × 10^11 s, so λ = 0.6931 / 1.808 × 10^11 = 3.833 × 10^-12 per second.
What is the difference between becquerel and curie?
One becquerel is one decay per second. One curie is defined as exactly 3.7 × 10^10 Bq. A sample with 1 × 10^15 iodine-131 nuclei (T½ = 8 days) has A = λN = 1.003 × 10^9 Bq, which is 0.0271 Ci.
What is mean lifetime and how does it differ from half-life?
The mean lifetime is τ = 1 / λ = T½ / ln 2, about 1.4427 times the half-life. It is the average time a nucleus survives. For T½ = 10 minutes, τ = 14.43 minutes.
How does activity fall over time?
Activity halves every half-life: A(t) = A0 × (1/2)^(t / T½). After two half-lives of 8 days each, 1.003 × 10^9 Bq becomes 2.507 × 10^8 Bq. This tool is for study and estimates, not for radiation safety decisions.