Seasonal (unequal) hours

History

The Byzantines kept the Roman way of counting hours. Daylight, from sunrise to sunset, was divided into 12 equal hours. Night, from sunset to sunrise, was divided into another 12. Day and night change length through the year, so the hours did too. They are called seasonal, unequal or temporal hours (ὧραι καιρικαί).

At the latitude of Constantinople (about 41° N):

Date	Daylight	One day-hour	One night-hour
Summer solstice	≈ 15 h 05 min	≈ 75 min	≈ 45 min
Equinoxes	≈ 12 h	≈ 60 min	≈ 60 min
Winter solstice	≈ 9 h 15 min	≈ 46 min	≈ 74 min

A few hours had fixed meanings in daily and liturgical life:

1st hour: just after sunrise (the office of Prime, Ὥρα Αʹ).
3rd hour: mid-morning (Terce).
6th hour: the hour that contains noon (Sext).
9th hour: mid-afternoon (None).
12th hour: the hour ending at sunset.

Night watches

The night was also split into four watches (φυλακαί), a military custom that also appears in the Gospels. Each watch covers three night hours:

Watch	Night hours
1st	1 – 3
2nd	4 – 6
3rd	7 – 9
4th	10 – 12

How bdate computes it

Sunrise and sunset are calculated for the given latitude and longitude with the Almanac for Computers (US Naval Observatory, 1990) algorithm. It uses the official zenith of 90.833°, which allows for atmospheric refraction and the size of the solar disc.
bdate finds the sunrise/sunset pair around the given moment. This is the current day if the sun is up, or last sunset to next sunrise if it is night.

It works out how far through that period the moment is:

fraction = (now − period_start) / (period_end − period_start)
hour     = min(12, floor(fraction × 12) + 1)
watch    = (hour − 1) // 3 + 1           # night only

The --json output includes the period start and end, so you can see how long the hours are on that day:

$ bdate -d 2026-10-10T12:00+03:00 --json
...
  "seasonal": {
    "period": "day",
    "hour": 6,
    "watch": null,
    "start": "2026-10-10T07:09+03:00",
    "end": "2026-10-10T18:32+03:00"
  }

On that day each day-hour is (18:32 − 07:09) / 12 ≈ 57 minutes.

Location

By default bdate uses Constantinople (Hagia Sophia, 41.0086° N, 28.9802° E). The algorithm takes east longitude as positive. To use a different place, pass --lat/--lon:

bdate --lat 37.98 --lon 23.73    # Athens
bdate --lat 40.64 --lon 22.94    # Thessaloniki

Caveats

Expect errors of a few minutes. The algorithm ignores elevation, local horizon and changes in refraction. Near an hour boundary, the hour shown may be off by one.
At polar latitudes, where the sun does not rise or set on some days, there are no seasonal hours, and bdate leaves the hour out.
Byzantine timekeepers used sundials, water clocks and the church office, so the hours they actually observed were never this precise.

Seasonal hours