This all-in-one online Exponential Decay Calculator evaluates the continuous exponential decay function. The parameters describing this function are: initial and final amount of something subject to decay, decay rate and time elapsed since the beginning of the observation. You can enter the values of any three parameters in the input fields of this calculator and find the missing parameter.
Note, that this online tool can also be used as Exponential Growth Calculator and even Half-Life Calculator.
Exponential decay formula
The exponential decay process can be expressed by the following formula:
$$A(t)=A(0) { e }^{ -rt }$$
where \(A(t)\) and \(A(0)\) are amounts of some quantity at time \(t\) and \(0\) respectively, \(r\) is the decay rate and \(t\) is the time elapsed.
The exponential decay is found in processes where amount of something decreases at a rate proportional to its current value. Exponential decay occurs in a wide variety of cases that mostly fall into the domain of the natural sciences. The most famous example is radioactive decay. But this phenomenon can also be found in chemical reactions, pharmacology and toxicology, physical optics, electrostatics, luminescence and many more.
A more intuitive characteristic of exponential decay and measure of decay rate is called the half-life. It’s the amount of time it takes a given quantity to decrease to half of its initial value.
The concept of half-life is widely used in nuclear physics in the study of radioactive elements. It is also used in chemistry, biology and pharmacology to describe any kind of exponential decay. For example, they say about the biological half-life of metabolites.
It is easy to show that the half-life and decay rate are related by the following equation for half-life:
$$t_{1/2} = \frac{ln(2)}{r},$$
where \(t_{1/2}\) is the half-life.
Our Exponential Decay Calculator can also be used as a half-life calculator. For this you just need to enter in the input fields of this calculator “2” for Initial Amount and “1” for Final Amount along with the Decay Rate and in the field Elapsed Time you will get the half-time.
However, for full-fledged work with everything related to half-life, we recommend using our Half-Life Calculator.
Note, that the decay rate can also be a negative number. In this case we have a process of exponential growth. Thus, this online exponential decay calculator can be used as exponential growth calculator as well.
There are numerous real-world phenomena where the exponential growth model is applicable. For example, population growth of various living organisms (from microorganisms to humans), deposit compound interest growth, economic growth, etc. In all these cases, you can use this handy online tool.
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