When to use this calculator
Use this to model repeated proportional losses, such as retained material through successive processes.
Explore the algebra & number calculators for other questions in this topic. For a related calculation, use the Factor Calculator: List all positive integer divisors of a whole number.
PUTTING IT INTO PRACTICE
Exponential Decay: a worked example
The values below are an illustrative example, not a recommendation. Replace them with measurements or assumptions that match your question.
| Input | Example value |
|---|---|
| Initial amount | 100 |
| Reduction each period (%) | 50 |
| Periods (integer) | 3 |
| Result | 12.5 |
- Check the input labels and enter the example values above.
- Apply the relationship: Remaining amount = initial × (1 − reduction/100)^periods.
- The result is 12.5 , rounded for display.
How to interpret your result
Assumes the same fractional reduction each period, not the same absolute reduction.
Identify whether the question asks for one term, a total or a count of possible selections. Sequences use a fixed difference or ratio. In counting problems, order and replacement determine the correct model.
Frequently asked questions
Do combinations and permutations count the same thing?
No. Combinations ignore the order of selection; permutations count different orders separately.
When is the exponential decay calculator useful?
Use this to model repeated proportional losses, such as retained material through successive processes.
How do I use the exponential decay calculator?
Enter initial amount, reduction each period (%), periods (integer). The result updates automatically. Use the units shown beside each input; the example values illustrate the method.
Which formula does this calculator use?
Remaining amount = initial × (1 − reduction/100)^periods.
What should I check before using the result?
Assumes the same fractional reduction each period, not the same absolute reduction.
How are results rounded?
Scalar numbers display up to six decimal places, with scientific notation for very large or small values. Text, fraction, date and schedule outputs use the format described on the tool. Intermediate calculations use JavaScript floating-point arithmetic. Keep sensible precision for your measurements.
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