Radioactive Decay Calculator

Calculate the decay constant ($\lambda$) and remaining quantity ($N(t)$).

Core Formulas

Decay Constant ($\lambda$)

$$ \lambda = \frac{\ln 2}{T_{1/2}} $$

Remaining Quantity ($N(t)$)

$$ N(t) = N_0 e^{-\lambda t} $$

Input Parameters

Initial Quantity ($N_0$)

Half-life ($T_{1/2}$)

Elapsed Time ($t$)

Calculation Results

Enter all values and click “Calculate Decay” to see results.

Step-by-Step Substitution

Decay Constant ($\lambda$)

$$ \lambda = \frac{\ln 2}{T_{1/2}} $$

Remaining Quantity ($N(t)$)

$$ N(t) = N_0 e^{-\lambda t} $$

What is Radioactive Decay?

Radioactive decay, also known as nuclear decay or radioactivity, is the process by which an unstable atomic nucleus loses energy by radiation. This loss of energy results in the atom, often called the parent nuclide, transforming into an atom of a different type, called the daughter nuclide. This transformation happens over time, and the rate is characterized by the half-life ($T_{1/2}$), which is the time required for half of the initial quantity of the substance to decay.

The phenomenon is fundamental to fields like nuclear physics and chemistry. Its applications are far-reaching:

Archaeology (Carbon Dating): Using the known half-life of Carbon-14 to determine the age of organic materials.
Geology (Radiometric Dating): Dating rocks and minerals using isotopes like Uranium-Lead to determine the Earth’s age.
Medicine (Nuclear Medicine): Employing radioisotopes (e.g., Iodine-131, Technetium-99m) for diagnosis (imaging) and therapy (cancer treatment).

How to Use the Calculator

1.
Enter Initial Quantity ($N_0$): Input the starting amount of the radioactive substance. This can be in mass (grams, kilograms), number of atoms, or activity (Becquerels, Curies).
2.
Enter Half-life ($T_{1/2}$): Input the time it takes for half of the substance to decay. Ensure that the units for the half-life and the elapsed time are consistent (e.g., both in years, both in hours, etc.).
3.
Enter Elapsed Time ($t$): Input the total time that has passed since the decay process started, using the same unit as the half-life.
4.
Calculate: Click the “Calculate Decay” button. The tool will instantly provide the Decay Constant ($\lambda$) and the Remaining Quantity ($N(t)$), along with the full step-by-step formula substitution below.