The sun (and the stars) sweep 15 degrees of sky per hour.
360° ÷ 24 h. Your fist at arm’s length spans ~10°, so a sun one fist above the horizon sets in about 40 minutes.
That is the average rate in right ascension, and only near the equator does it correspond to 15° of visible arc per hour. At 55° north the sun's path is tilted, so its altitude changes far more slowly near noon; the equation of time also shifts solar noon by up to 16 minutes across the year.
At 172 the rule says 180° and the exact answer is 179.6° — within half a percent. It holds to within 2% from 52.9 to 286, and drifts outside that.
15° an hour is exact for MEAN solar time, and the real sun does not keep mean solar time. The orbit is elliptical and the axis is tilted, so a sundial runs up to 16 minutes fast in November and 14 slow in February. The rule is perfect twice a year and out by a quarter of a degree the rest of it.
The rule against the exact answer, computed across the range. Inside the shaded band the shortcut is close enough to use; outside it, reach for the calculator.
Estimate with the rule, then check it against the calculator that models it properly.
Open Sun & Moon →The sun (and the stars) sweep 15 degrees of sky per hour. 360° ÷ 24 h.