Radioactive Decay Calculator
Radioactive decay follows an exponential law: the number of undecayed nuclei decreases as N(t) = N0 * (1/2)^(t/T), where N0 is the initial count, T is the half-life, and t is the elapsed time. This is equivalent to the continuous form N(t) = N0 * exp(-lambda * t) where the decay constant lambda = ln(2) / T. The same formula applies to activity (decays per second) since activity is proportional to the number of remaining atoms. This calculator works for any combination of time units as long as t and T use the same units. Enter the initial quantity, half-life, and elapsed time to find the remaining quantity and the fraction that has decayed.
Radioactive decay formula
N(t) = N0 * (1/2)^(t / T)
lambda = ln(2) / T
N(t) = N0 * exp(-lambda * t)
T is the half-life, t is elapsed time (same units as T), lambda is the decay constant. Fraction remaining = (1/2)^(t/T). Fraction decayed = 1 - (1/2)^(t/T).
Common isotope half-lives
- Carbon-14: 5,730 years (radiocarbon dating of organic materials).
- Iodine-131: 8.02 days (medical use in thyroid treatment).
- Uranium-238: 4.468 billion years (geological dating).
- Polonium-214: 163.7 microseconds (very short, high alpha activity).
- Tritium (H-3): 12.32 years (used in luminescent signs and fusion research).
Radioactive decay: frequently asked questions
What is radioactive half-life?
The half-life of a radioactive isotope is the time required for exactly half of the atoms in a sample to decay. It is a fixed constant for each isotope, independent of temperature, pressure, or chemical state. Half-lives range from nanoseconds (for highly unstable isotopes) to billions of years (for stable ones like uranium-238, half-life 4.47 billion years).
What is the radioactive decay formula?
N(t) = N0 * (1/2)^(t / T), where N0 is the initial number of atoms, T is the half-life, t is the elapsed time, and N(t) is the remaining number of atoms. Equivalently, N(t) = N0 * e^(-lambda * t) where the decay constant lambda = ln(2) / T.
What are common examples of radioactive decay?
Carbon-14 (half-life 5,730 years) is used in radiocarbon dating of organic materials. Iodine-131 (half-life 8 days) is used in thyroid cancer treatment. Uranium-238 (half-life 4.47 billion years) decays slowly and is used in radiometric dating of rocks.
How many half-lives until a sample is essentially gone?
After 10 half-lives, only 1/1024 (about 0.1%) of the original material remains. After 20 half-lives, about 0.0001% remains. In practice, a sample is considered negligible after about 7 to 10 half-lives depending on the application.
What is the difference between activity and number of atoms?
The activity A = lambda * N is the number of decays per second, measured in becquerels (Bq) where 1 Bq = 1 decay/s. Activity decreases over time at the same rate as the number of atoms: A(t) = A0 * (1/2)^(t/T). The curie (Ci) is an older unit where 1 Ci = 3.7 x 10^10 Bq.
Official sources
- NIST: Nuclear Data.
- OpenStax University Physics Vol. 3: Radioactive Decay.
Reviewed by the CalculatorHub team, edited by James Graham, 15 June 2026. See our methodology.