Timed Decay Equation

t = -(T1/2/0.693) * ln(A/Ao)

Use this equation to find out how long it will take for a given initial activity of radioactive material to decay to a given final activity.

To use the equation:
The information required by the equation is the initial activity (Ao), the final activity (A), and the half-life of the isotope (T1/2).

  1. Select the isotope from the list at the top of the page; this provides the equation with the isotope's half-life. If your isotope is not on the list, you can still use the equation if you manually enter the half-life in the Half-life textbox at the top of the page.
  2. Enter the initial activity. It is not necessary to worry about units here as long as the units for the final activity are the same.
  3. Enter the final activity.
  4. Click the Calculate button and the decay time is displayed. The time unit will always be the same as the half-life unit.

An example:
You purchase 9.25 MBq of P-32. How long will it take to decay to 2.0 MBq?

  1. Select Phosphorus 32 from the isotope list. 14.26 and d show up in the Half-life and Half-life time unit textboxes.
  2. Enter 9.25 in the Initial activity (Ao) textbox.
  3. Enter 2.0 in the Final activity (A) textbox.
  4. Click the Calculate button and the answer 31.5068... d is received.
  5. You can then use the time calculator to find out the date 32 days from now.

If you enter the activities in the wrong order, the answer received will be 0.