Half-Life Calculator

How to Calculate Half-Life

Calculating the half-life of a substance can be done with the following variables:

• Quantity


• Half-life time


• Total elapsed time

Then you can apply them in the formula for calculating the remaining quantity of a substance: Where:

• QR = Quantity remaining


• T = Half-life time


• IQ = Initial quantity


• ET = Elapsed time

Understanding Your Results

When you use this tool you will get three different results. First, you will see the remaining quantity of the substance based on your specified situation. Then, you will see the decay constant. This is the rate at which the substance is decaying at based on the unit of measurement selected. By default, this is shown as per second but can be changed to many other intervals. Finally, you will get your mean lifetime. This refers to the average time it takes for particles in a radioactive sample to decay. It is a statistical measure that provides insight into the average duration of a particle's existence before decaying. It will always be larger than the half-life time.

How to Use the Half-Life Calculator

This tool simplifies the process of determining the remaining quantity of a substance after a specified time. To use it:

1. Enter the initial quantity of the substance.


2. Specify the half-life time and its unit.


3. Provide the total elapsed time and its unit.


4. Click calculate to get your results.

Calculation Example

For example, if a substance starts with a quantity of 100 units, has a half-life of 2 hours, and 6 hours have elapsed, the remaining quantity can be calculated as follows:

• Remaining Quantity = 100 * (1/2)^{(Elapsed Time / Half-Life)}


• Remaining Quantity = 100 * (1/2)^(6 / 2) = 100 * 1/8 = 12.5 units

You will also learn that the decay constant is .3466 per hour, or .0058 per minute. The mean lifetime is equal to about 2.8854 hours, or 173.1234 minutes.