Half-Life Calculator
Half-Life Calculator
Calculate any variable in the half-life decay formula by providing the other three.
Formula: N(t) = N₀ * (1/2)^(t / T½)
Exponential Decay and Half-Life
Half-life is a fundamental concept used to describe any process that follows exponential decay. It is defined as the time required for a quantity to reduce to half of its initial value. While it is most famously associated with the radioactive decay of elements in physics and chemistry, the principle of half-life also applies to many other fields, such as pharmacology (describing how quickly a drug is eliminated from the body), environmental science (the degradation of pollutants), and even finance (the depreciation of certain assets). It provides a predictable and consistent way to measure the rate of decay, regardless of the initial amount of the substance.
The key characteristic of half-life is that it is constant for a given substance or process. For example, the half-life of Carbon-14 is approximately 5,730 years. This means that if you start with 100 grams of Carbon-14, after 5,730 years you will have 50 grams left. After another 5,730 years (a total of 11,460 years), you will have half of that amount remaining, which is 25 grams. This predictable, exponential pattern is what makes half-life such a powerful tool. It allows archaeologists to date ancient organic artifacts through radiocarbon dating, and it enables doctors to determine the correct dosing schedule for medications to maintain a therapeutic level in the bloodstream. This calculator is a versatile tool that allows you to explore this relationship by solving for any of the variables in the half-life equation.
The Half-Life Formula
The mathematical relationship for half-life is described by the following formula:
N(t) = N₀ * (1/2)^(t / T½)
Where:
- N(t) is the final quantity of the substance remaining after a certain amount of time.
- N₀ is the initial quantity of the substance.
- t is the total time elapsed.
- T½ is the half-life of the substance.