Half Life Calculator

Enter the initial quantity, final quantity, and total time passed to calculate the half life. Half life is defined as the amount of time it takes for a value to decrease by half. This is most often used in nuclear physics.

Half Life Formula

So, how to do you calculate half life? Half life is calculated through the use of the exponential decay formulas as show below.

{\displaystyle {\begin{aligned}N(t)&=N_{0}\left({\frac {1}{2}}\right)^{\frac {t}{t_{1/2}}}\\N(t)&=N_{0}e^{-{\frac {t}{\tau }}}\\N(t)&=N_{0}e^{-\lambda t}\end{aligned}}}

Where N0 is the intital quantity

N(t) is the quantity remaining after some time

t1/2 is the half-life and t is time.

This can be further simplified into the following to calculate half life.

{\displaystyle t_{1/2}={\frac {\ln(2)}{\lambda }}=\tau \ln(2)}

What is half life?

Half life is a term that is mostly used in nuclear physics to describe the rate of decay or radioactive substances. As a result, the formula above includes the decay constant of material. However, half life can also be calculated simply though time passed, initial quantity, and final quantity by re-arranging the very first equation above.

The idea of half life is that since it’s exponential decay, it starts off losing a lot of mass to start, then slowly slows down. In fact, it will never actually reach absolute 0. Yet, of course it would eventually approach an amount that is considered negligible.

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