Radioactive Decay Calculator

This Radioactive Decay Calculator allows users to compute the remaining amount, decay constant, and decay percentages of a radioactive material based on its initial amount, half-life, elapsed time, and respective time units.

Use Our Radioactive Decay Calculator

Step-by-Step Guide to Using the Radioactive Decay Calculator

Understanding the Calculator’s Purpose

The Radioactive Decay Calculator is designed to help you determine various properties related to the decay of radioactive materials over time. It calculates the remaining amount of material, the decayed amount, the percents remaining and decayed, and the number of half-lives elapsed during the time period specified.

Step 1: Input the Initial Amount

Start by entering the initial amount of radioactive material into the “Initial Amount (N₀)” field. This is a required field, and the value must be greater than or equal to 1e-06. This represents the quantity of substance you begin with before any decay occurs.

Step 2: Define the Half-life

Next, input the half-life value of the substance into the “Half-life (t₁/₂)” field. This is also a required field, and the value must be at least 1e-06. The half-life is the time it takes for half of the radioactive substance to decay.

Step 3: Select the Half-life Time Unit

Choose the appropriate time unit for the half-life from the “Half-life Time Unit” dropdown menu. Options include seconds, minutes, hours, days, and years. Selecting the correct unit is crucial for accurate calculations.

Step 4: Input the Elapsed Time

Enter the elapsed time for which you want to calculate the radioactive decay into the “Elapsed Time (t)” field. The value must be a non-negative number. This is the duration over which decay is observed.

Step 5: Select the Elapsed Time Unit

Choose the appropriate unit for the elapsed time from the “Elapsed Time Unit” dropdown menu. As with the half-life, options include seconds, minutes, hours, days, and years. Ensuring correct unit selection is essential to maintain calculation accuracy.

Step 6: View the Results

Once all required fields are filled and options selected, the calculator will provide the following results:

  • Decay Constant (λ): This is calculated using the formula 0.693147 / halfLife and is displayed to six decimal places.
  • Remaining Amount (N): Calculated as initialAmount * pow(2.718281828, (-0.693147 * elapsedTime) / halfLife), this value gives you the remaining quantity of the material, displayed to six decimal places.
  • Decayed Amount: This is the difference between the initial and remaining amounts and is displayed to six decimal places.
  • Percent Remaining: Displayed as a percentage to two decimal places, calculated using (remainingAmount / initialAmount) * 100.
  • Percent Decayed: Also shown as a percentage to two decimal places, computed as ((initialAmount - remainingAmount) / initialAmount) * 100.
  • Number of Half-lives Elapsed: This is determined by the formula elapsedTime / halfLife and presented to two decimal places.

These results will help you understand the decay process of the radioactive material over your specified time period, providing insights into how much material remains and how much has decayed.