Exponential Decay Calculator
Use our exponential decay calculator to find reduction in value over time.
Final Value:
Joe is the creator of Inch Calculator and has over 20 years of experience in engineering and construction. He holds several degrees and certifications.
Aditya holds a PhD in electrical engineering from Stanford University and specializes in signal processing, algorithms, and machine learning.
How to Calculate Exponential Decay
Exponential decay is the reduction in a value by the same percentage over a period of time, where the percentage of decay during each period includes the effect of decay accumulated over previous periods.
Exponential decay is the mechanism behind things such as half-life decay.
Exponential decay is the inverse of exponential growth, and you can calculate it using a formula.
Exponential Decay Formula
The formula to find a value after exponential decay is:
The final value xt is equal to the initial value x0 times 1 plus the decay rate r raised to the power of the number of time periods t. In the case of exponential decay, the rate r < 0.
For example, let’s calculate the decay in a value of 250 over 5 time periods given a decay rate of 12%.
So, an initial value of 250 that decays at a rate of 12% over 5 time periods will have a final value of 131.93.