# Exponential Decay Calculator

Use our exponential decay calculator to find reduction in value over time.

## Final Value:

_{t}=

## 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 *x _{t}* is equal to the initial value

*x*times 1 plus the decay rate

_{0}*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.