Exponential Decay Calculator

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

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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:

x_{t}=x_{0} \times \left ( 1 + r \right ) ^{t}

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.

Graphic showing the exponential decay formula.

For example, let’s calculate the decay in a value of 250 over 5 time periods given a decay rate of 12%.

x_{t}=250 \times \left ( 1 + -0.12 \right ) ^{5}
x_{t}=250 \times 0.88^{5}
x_{t}=250 \times 0.5277
x_{t}=131.93

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.