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Exponential Decay Calculator

Enter a starting amount, a decay rate per period and a number of periods.

%

The share lost in each period, from just above 0 to below 100.

Can be a decimal, for example 2.5 years.

This result is an estimate only. Double-check important figures before relying on them.

How it is calculated

  • Remaining = starting amount × (1 − rate ÷ 100)^periods
  • Amount lost = starting amount − remaining
  • Half-life = ln(0.5) ÷ ln(1 − rate ÷ 100)

For radioactive decay with a known half-life, use the half-life calculator.

Worked example

1,000 losing 10% each period for 5 periods:

  • Remaining = 1,000 × 0.9⁵ = 590.49
  • Lost = 409.51, and the half-life is 6.58 periods

Why your number may differ

Continuous decay (with e) uses a slightly different rate from a percentage-per-period decay. This calculator uses the percentage-per-period form.

Frequently asked questions

What is exponential decay?

A quantity that falls by the same percentage each period, so it drops fast at first and more slowly later. Examples are a cooling drink, a drug in the body and asset value.

What is the formula?

Remaining = start × (1 − rate)^t, with the rate as a decimal.

How is the half-life found?

Half-life = ln(0.5) ÷ ln(1 − rate), the number of periods for the amount to fall to half.

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