Exponential decay calculator
Enter a starting value, the decrease per period in percent and the number of periods. You get the end value, the decay factor, the half-life and the value after every period.
Fill in the fields; the answer appears here straight away.
How it's worked out
How it works
-
Enter the values
Type the numbers or the formula. Decimals may use a point or a comma. No idea? Click Fill in an example.
-
Instant answer
The answer appears as you type, with the most important intermediate values.
-
See the working
Under "How it's worked out" you see the steps, handy for checking your own calculation.
The formula
N(t) = N₀ · gᵗ with the decay factor g = 1 − percentage ÷ 100. A car worth 20,000 that loses 15% of its value per year is worth 20,000 × 0.85⁵ ≈ 8,874 after five years.
Half-life
The half-life is the number of periods after which half is left: log(0.5) ÷ log(g). At 15% per year that is about 4.3 years. Radioactive decay, medicine leaving the body and depreciation all follow this pattern.
The decrease must be between 0% and 100%. For growth, use the exponential growth calculator.
Frequently asked questions
Is the exponential decay free?
Yes. The exponential decay is completely free, with no account, sign-up or usage limit.
How accurate is the result?
The tool calculates with your browser's number precision. For important calculations, always double-check what you entered.
Does it work on my phone?
Yes. The tool works in any modern browser on a phone, tablet or computer.