How to use the decay rate calculator
Prepare the values for this calculation
Calculate a continuous exponential growth/decay rate from starting value, ending value, and elapsed time. Use the formula below to check that it answers your question. Read the input units before transferring figures from a statement, measurement or dataset.
Enter and check each input
- Starting value: enter a value at least 1e-06. Use the unit named in the label or selected above. Do not leave this required field blank.
- Ending value: enter a value at least 1e-06. Use the unit named in the label or selected above. Do not leave this required field blank.
- Elapsed time: enter a value at least 1e-06. Use the unit named in the label or selected above. Do not leave this required field blank.
The input table gives a complete example. Keep units and time periods consistent across related fields.
Calculate and resolve any input error
Choose Calculate after entering the values. Changes also update the answer after a short pause. If an error appears, follow its message, correct the field and calculate again. Reset restores the example values.
Interpret the answer
Check Continuous rate first. With the unchanged example inputs, it is -6.9314718056% per time unit. Compare the additional metrics with the primary result; each has its own label and unit.
Compare and keep a useful result
For a controlled comparison, keep every other example input unchanged and change Starting value from 100 to 110. The resulting Continuous rate is -7.8845736036% per time unit. This illustrates the equation’s response to that input, rather than a forecast of real events.
Read the chart’s axis labels and data table. A scenario curve changes one stated input while holding the others fixed; it does not add external observations. Use Download graph to save an available chart as a PNG.
Use Copy result or Download CSV to keep the answer. Share tool shares the page address without placing your input values in the URL. Recheck inputs and assumptions before using the result for a decision.
Decay Rate Calculator formula
Continuous rate r=ln(end/start)/time.
Inputs and units
| Input | Format / range | Example |
|---|---|---|
| Starting value | minimum 1e-06 | 100 |
| Ending value | minimum 1e-06 | 50 |
| Elapsed time | minimum 1e-06 | 10 |
Worked example
Using the example inputs above, the continuous rate is -6.9314718056% per time unit.
- Continuous rate
- -6.9314718056% per time unit
- Continuous rate
- -0.069314718056
Results and assumptions
The output uses the continuous rate convention and formula shown above. Match the entered units and source assumptions when comparing results.
Fix an input or unexpected result
Starting value is required. Enter starting value using the format and bounds in the input table. Zero and an empty field are different: use zero only if it is allowed and represents your data.
If your answer differs from the example, choose Reset and compare every field, including selected units and options. Check percentage versus decimal entry and whether values describe the same period. Round only the final displayed answer when reproducing the formula.
If a discrepancy remains, report the calculator issue with the page address, non-sensitive example inputs, actual result, expected result and a reference for your calculation.