How to use the average bedtime calculator
- Paste your times into the box, one per line or separated by commas. Use forms like 11:30 pm, 23:30 or 11pm.
- The times can be bedtimes, wake times or any clock times, and they can fall before and after midnight.
- Read the average time, then the earliest and latest of the group and the spread.
- Compare the average with the plain average shown at the bottom to see why the around-the-clock method matters.
Formula
angle = minutes after midnight x 360 / 1440
average angle = atan2(mean of sin(angle), mean of cos(angle))
spread in minutes = sqrt(-2 ln(R)) x 1440 / (2 pi), where R is the length of the mean vector
Each time is a point on a 24 hour circle. The average of the points lies inside the circle, and its direction is the average time. R is 1 when all times are equal and falls toward 0 as they spread around the clock.
A week of late nights
Bedtimes were 11:30 pm, 12:15 am, 11:50 pm, 1:05 am, 11:10 pm, 12:40 am and 11:45 pm. The average time around the clock is 12:02 am. The earliest is 11:10 pm and the latest is 1:05 am, so the span is 1 hour 55 minutes, and the spread is 37.4 minutes.
A plain average of the clock numbers (minutes after midnight, where 12:15 am is 15 and 11:30 pm is 1,410) gives 825, which is 1:45 pm. That is a time nobody went to bed, which is the error this method avoids. A set of times from 10:15 pm to 11:30 pm averages 10:48 pm.
The midnight problem
Clock times wrap around: 11:59 pm and 12:01 am are two minutes apart, not 24 hours. A normal average treats midnight as the start of a number line and gets the answer wrong whenever times fall on both sides of it. Averaging points on a circle fixes that.
What the numbers mean
The span covers every time in the list, and the spread is a standard deviation around the clock. Both are descriptions of the data you entered. They are not health advice or a target. If you plan a sleep schedule, the Sleep Cycle Calculator and the Jet Lag Sleep Shift Planner work from times you choose.
Assumptions and limits
- Times are on a 24 hour circle with no date, so a time is the same each day.
- If the times are spread evenly around the clock, they have no meaningful average, and the page says so.
- The span is the smallest arc that holds every time.
- No recommendation is made about when to sleep.
Frequently asked questions
Why not just add the times and divide?
That works only when no times cross midnight. Around midnight, a simple average lands in the middle of the day, far from any real time on the list.
Which time formats are accepted?
You can use 24 hour times like 23:30, 12 hour times like 11:30 pm or 11 pm, and times without minutes like 7am. Separate entries with new lines, commas or semicolons.
What does it mean when no average exists?
If the times are spread evenly around the clock, such as midnight and noon only, the average point sits at the center and has no direction. Add more times or check your entries.
Can I average wake times too?
Yes. Any clock times work, including meal times or arrival times. The method does not care what the times represent.