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THE FEUTEX TOOLKIT

Exponential Relaxation Rate from Two Observations

Infer a first-order relaxation constant from a starting offset and a later offset from equilibrium.

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01 Your input
02 Your result
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FormulaRate = -log((end-equilibrium)/(start-equilibrium))/time; Time Constant = -time/log((end-equilibrium)/(start-equilibrium))
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  • Infer a first-order relaxation constant from a starting offset and a later offset from equilibrium.
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Worked example

Inputs

Initial value
80 number
Later value
50 number
Equilibrium value
20 number
Elapsed time
10 number

Expected results

Rate
0.06931471806 1/time
Time Constant
14.42695041 time

Load the example in the workspace to reproduce these results. Display rounding does not change the underlying calculation.

How to use this tool

  1. Enter initial value, later value, equilibrium value, elapsed time.
  2. Use the displayed units and confirm the model assumptions.
  3. Calculate and compare the outputs against your input scenario.

Try this example

{
  "start": 80,
  "end": 50,
  "equilibrium": 20,
  "time": 10
}

Accuracy and scope

Constant equilibrium and a single first-order decay mode; not valid for overshoot or changing environment.

Is my data uploaded?

This tool runs locally in your browser. Input and output are not sent to a processing server. Copy or download your result before leaving the page.