How it works
Independent attempts with constant success probability have expected attempts to first success of 1/p, multiplied by a constant attempt duration. This form solves for expected time to first success; enter the known quantities in Duration per attempt, Success probability per attempt.
Inputs and units
| Input | Example value | What to enter |
|---|---|---|
| Duration per attempt | 2 min | Formula symbol: duration. Required unit: min. Must be greater than zero. |
| Success probability per attempt | 20 % | Formula symbol: p. Enter the percentage as a number: for 15%, enter 15. Must be greater than zero. Allowed range: 0.000001–100. |
Worked example
Show example inputs and results
This example is generated by the same calculation engine using the starting values in the form. Your own inputs produce your own result.
- Duration per attempt
- 2 min
- Success probability per attempt
- 20 %
Complete example results
- Expected time to first success
- 10 min
Reading the result
The result solves for expected time to first success from the entered quantities. Check the result unit and the formula conditions before using it.
Questions and answers
Can I use the example values for my own calculation?
The example values illustrate the calculation. Replace every input with your own information, especially dates, rates and the selected operation.
When can I use the expected time to first success result?
This is a mean, not a maximum or guaranteed duration. Attempts are independent, durations constant and success probability positive; include intervening waits in the duration yourself.
Why are some results rounded?
Results display up to 8 decimal places. Calculations use the unrounded values; very small values use scientific notation. JavaScript floating-point arithmetic can introduce tiny rounding differences.
Are my inputs sent to a server?
The calculator processes inputs in your browser. Its code does not send your values to a server.
Method sources: ocw.mit.edu