Calculator inputs
Enter a due time, Person A arrival window, Person B arrival window, a grace buffer, and a patience limit. The result appears above this form.
Example data table
Use the sample row below to test the calculator quickly and compare your own schedule assumptions.
| Scenario | Due time | Person A window | Person B window | Grace | Patience | Confidence | Use case |
|---|---|---|---|---|---|---|---|
| Morning meeting | 09:00 | 08:40 to 09:20 | 08:50 to 09:30 | 5 min | 15 min | 90% | Estimates late risk and average meeting wait. |
| Pickup handoff | 14:30 | 14:10 to 14:50 | 14:20 to 15:00 | 10 min | 12 min | 85% | Tests buffers when both arrivals vary. |
| Service visit | 16:00 | 15:45 to 16:35 | 15:30 to 16:20 | 8 min | 20 min | 95% | Plans a safer grace target. |
Formula used
The calculator assumes each arrival is uniformly distributed across the entered window. That means every time inside each window is treated as equally likely.
1) Expected arrival for a window
2) Late probability after grace
Let the lateness threshold be due time plus grace. Person A is late only when the arrival time is greater than that threshold.
3) Expected overdue minutes
Overdue minutes are counted only after the threshold. The calculator uses the expected positive excess.
4) Expected waiting time for the first arrival
If both people eventually wait for one another, the first arrival waits exactly the gap between the two arrival times.
5) Patience-limited waiting
When patience is limited, the effective wait is capped.
6) Confidence-based grace
The recommended grace is the extra time after the due time required so the chosen fraction of likely arrivals remains on time.
How to use this calculator
- Enter the target due time.
- Enter Person A arrival start and end times.
- Enter Person B arrival start and end times.
- Add grace minutes if you allow a small delay.
- Add patience minutes for the meeting window.
- Choose a confidence target for a safer grace recommendation.
- Press Calculate now.
- Review the results shown above the form.
- Use CSV or PDF download when you need a record.
FAQs
1) What does this calculator measure?
It measures expected lateness after a due time, the chance of being late, expected waiting between two arrivals, capped waiting with patience, and a suggested grace period for a target confidence level.
2) What is the expected amount of time that the one who arrives first must wait for the other person?
In general, it is E|A − B|, the expected gap between arrival times. If both people have the same uniform window length T and nobody leaves, the expected wait becomes T/3.
3) Why do I need a grace period?
Grace separates minor delay from true lateness. A five-minute grace means arrivals up to five minutes after the due time still count as on time for the calculator’s overdue metric.
4) What does the patience limit change?
It limits how long either person is willing to wait. The calculator then estimates the average effective wait and the chance that both arrivals are close enough for the meeting to happen.
5) Why does the calculator use arrival windows instead of single times?
Real arrivals often vary. Windows capture uncertainty better than one fixed time, so the results reflect likely late risk and waiting patterns rather than only one exact schedule.
6) Can I use this for pickups, meetings, and service calls?
Yes. It works for any same-day event where two independent arrival windows matter and you need a clear estimate of lateness, waiting, or the chance of meeting within a patience threshold.
7) What does the recommended grace value mean?
It is the added time after the due time needed to hit your chosen confidence level. A higher confidence target usually produces a larger recommended grace period.
8) Are the results exact real-world predictions?
No. They are expectation-based estimates under a uniform arrival assumption. They are most useful for planning, comparing scenarios, setting buffers, and discussing timing risk with a consistent method.