How a horizontal sundial works
A sundial tells time from the direction of the sun's shadow. The shadow-casting edge – the gnomon or style – must be parallel to the Earth's axis. On a horizontal dial that means it points to the celestial pole and rises at an angle equal to your latitude. Because the sun moves 15° per hour around that axis, the hour lines on a flat dial are not evenly spaced: they are bunched near noon and spread out toward morning and evening.
Hour line angle θ = arctan( sin(latitude) × tan(15° × hours from noon) )
Hour line angles at common latitudes
| Hour from noon | 30° (Houston, Cairo) | 40° (New York, Madrid) | 51.5° (London) |
|---|
| 1 h (11 AM / 1 PM) | 7.6° | 9.8° | 11.9° |
| 2 h | 16.1° | 20.4° | 24.3° |
| 3 h | 26.6° | 32.7° | 38.0° |
| 4 h | 40.9° | 48.1° | 53.6° |
| 5 h | 61.8° | 67.4° | 71.1° |
| 6 h (6 AM / 6 PM) | 90° | 90° | 90° |
Why your sundial disagrees with your watch
1. Longitude
Clocks use standard time for a whole time zone, centered on a meridian every 15°. A sundial shows local solar time. For every degree you are west of your zone's central meridian, the sundial runs 4 minutes behind your watch; east of it, ahead.
2. Daylight saving time
When clocks spring forward, add one hour to the sundial reading.
3. The equation of time
Because the Earth's orbit is elliptical and its axis is tilted, the sun runs up to about 16 minutes fast (early November) or 14 minutes slow (mid-February) relative to an evenly ticking clock. Many sundials carry a small table or graph of this correction.
Installing a garden sundial
- Choose a spot that receives sun for most of the day, away from trees and buildings.
- Mount the dial on a stable pedestal and level it carefully.
- Align the noon line with true north (in the northern hemisphere) using a map or GPS – a compass points to magnetic north, which can be many degrees off.
- Alternatively, at local solar noon (clock noon plus the corrections above) turn the dial until the shadow falls on the 12 line.
- Buy a dial made for your latitude, or one with an adjustable gnomon.
Frequently asked questions
What angle should a sundial gnomon be?
Equal to your latitude. In London (51.5° N) the gnomon rises at 51.5°; in New York at about 40.7°.
Which way should a sundial face?
The gnomon and noon line must point to true north in the northern hemisphere and true south in the southern hemisphere.
Why is my sundial wrong?
Usually because of longitude within the time zone, daylight saving time and the equation of time, which together can add up to more than an hour.
Will a sundial made for another latitude work?
Not accurately. The gnomon angle and hour lines depend on latitude; a mismatch of a few degrees causes noticeable errors.
Can I use a compass to align a sundial?
Only if you correct for magnetic declination, which varies by location. A map or GPS bearing to true north is easier.
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