HalfLife Calculator
The following tools can generate any one of the values from the other three in the halflife formula for a substance undergoing decay to decrease by half.
HalfLife Calculator
Result
quantity remains, N_{t} = 90.572366426391
HalfLife, Mean Lifetime, and Decay Constant Conversion
Please provide any one of the following to get the other two.
Definition and Formula
Halflife is defined as the amount of time it takes a given quantity to decrease to half of its initial value. The term is most commonly used in relation to atoms undergoing radioactive decay, but can be used to describe other types of decay, whether exponential or not. One of the most wellknown applications of halflife is carbon14 dating. The halflife of carbon14 is approximately 5,730 years, and it can be reliably used to measure dates up to around 50,000 years ago. The process of carbon14 dating was developed by William Libby, and is based on the fact that carbon14 is constantly being made in the atmosphere. It is incorporated into plants through photosynthesis, and then into animals when they consume plants. The carbon14 undergoes radioactive decay once the plant or animal dies, and measuring the amount of carbon14 in a sample conveys information about when the plant or animal died.
Below are shown three equivalent formulas describing exponential decay:

where
N_{0} is the initial quantity
N_{t} is the remaining quantity after time, t
t_{1/2} is the halflife
τ is the mean lifetime
λ is the decay constant
If an archaeologist found a fossil sample that contained 25% carbon14 in comparison to a living sample, the time of the fossil sample's death could be determined by rearranging equation 1, since N_{t}, N_{0}, and t_{1/2} are known.
This means that the fossil is 11,460 years old.
Derivation of the Relationship Between HalfLife Constants
Using the above equations, it is also possible for a relationship to be derived between t_{1/2}, τ, and λ. This relationship enables the determination of all values, as long as at least one is known.