Calculadora de Decaimento Radioativo
- Created by
- Renato Passos, Eng. de Software
- Reviewed by
- Renato Passos, Eng. de Software
Last updated: Apr 18, 2026
Formula
N(t) = N₀·e^(−λt) ; A(t) = A₀·e^(−λt)
About this calculator
The Radioactive Decay Calculator is a tool that determines the remaining amount of a radioactive substance after a given time period. It uses the exponential decay law, where the initial quantity N₀ decays at a constant rate λ, resulting in N(t) = N₀·e^(−λt). The half-life (t₁/₂) is a key parameter, related to λ by λ = ln(2)/t₁/₂. The calculator also computes the activity A(t) = A₀·e^(−λt), which measures the number of disintegrations per second.
To use the calculator, you need to provide the initial quantity (or initial activity), the elapsed time, and the half-life of the material. With these data, the system automatically calculates the remaining quantity and current activity. It is useful in fields such as nuclear medicine, carbon-14 dating, radioactive waste management, and particle physics. For example, to know how much of a radioisotope remains after a treatment or to estimate the time needed for a sample to become safe.
Important precautions: the formula assumes pure decay, without production of new nuclei (as in decay chains). The half-life must be known accurately and in the same time unit as the interval provided. Additionally, for very old samples or very low activity, measurement errors can be significant. The calculator does not consider effects such as shielding or serial decay. Always verify that the entered data are consistent with the experimental context.
Frequently asked questions
What is half-life and how does it affect the calculation?
Half-life is the time required for half of the radioactive atoms in a sample to decay. The shorter the half-life, the faster the decay. The calculator uses half-life to determine the decay constant λ.
Can I use this calculator for serial decay?
No. The calculator assumes decay of a single isotope without production of new radioactive nuclei. For decay chains, more complex models are needed.
What units should I use for time and half-life?
Use the same time unit for both, e.g., years, days, hours, or seconds. The calculator does not automatically convert units.
Does the calculator consider initial activity?
Yes. You can input the initial activity (A₀) in becquerels or curies, and the calculator will return the activity after the given time.
Can the result be negative?
No. The remaining quantity and activity are always positive, as exponential decay never reaches exactly zero, only approaches it.