How it works
- Gnomon angle = latitude: tilt the gnomon's edge toward true north by your latitude and it lines up with Earth's axis, so the shadow lands on the same hour lines all year.
- Hour lines are measured from the noon line: tan θ = sin(latitude) × tan(hour angle), where the hour angle grows 15° per hour from noon.
- Longitude correction: “Match clock time” adds (longitude − zone meridian) to the hour angle. New York sits about 1° east of 75°W, so its lines turn by about 4 minutes; Detroit, 8° west, by 32 minutes.
- Equation of time: Earth's elliptical orbit and tilted axis make a sundial up to about 16 minutes fast or 14 minutes slow depending on the date. Today's value comes from NOAA's solar calculator formulas.
New York sundial hour-line angles
| Time | Solar time (textbook) | Clock time (longitude corrected) |
|---|---|---|
| 6 AM | −90.0° | −88.5° |
| 7 AM | −67.7° | −66.3° |
| 8 AM | −48.5° | −47.4° |
| 9 AM | −33.1° | −32.2° |
| 10 AM | −20.6° | −19.9° |
| 11 AM | −9.9° | −9.2° |
| 12 PM | 0.0° | +0.6° |
| 1 PM | +9.9° | +10.6° |
| 2 PM | +20.6° | +21.4° |
| 3 PM | +33.1° | +34.0° |
| 4 PM | +48.5° | +49.6° |
| 5 PM | +67.7° | +69.1° |
| 6 PM | +90.0° | +91.5° |
Angles from the noon line (true north). − is left of noon (west, morning), + is right (east, afternoon). New York 40.71°N, 74.01°W, Eastern time meridian 75°W.
Frequently asked questions
What angle should the gnomon be?
Tilt the gnomon's sloping edge at an angle equal to your latitude and point it due north. That makes it parallel to Earth's axis, so the shadow falls on the same hour lines all year. New York needs about 40.7°, Chicago 41.9°, Denver 39.7°, Los Angeles 34.1° and Miami about 25.8°.
How do I work out the hour-line angles?
On a horizontal dial, each hour line sits at an angle θ from the noon line where tan θ = sin(latitude) × tan(15° × hours from noon). In New York (40.7°N), the 1 PM and 11 AM lines are 9.9° from noon, the 3 PM and 9 AM lines 33.1°, and the 6 AM and 6 PM lines exactly 90°.
Why doesn't my sundial match my watch?
Three reasons. Clocks follow the time zone's standard meridian (75°W for Eastern, 90°W for Central and so on), so a city west of it sees the Sun later. Choose “Match clock time” and the hour lines are rotated to compensate. The equation of time makes a sundial up to about 16 minutes fast or 14 minutes slow depending on the date; today's value is shown in the results. And during daylight saving time, add one hour to the dial reading.
How do I find true north?
The easiest way is to watch the shadow of a vertical stick at your local solar noon; at that moment it points exactly north. A compass points to magnetic north, which is several degrees off in most of the US, so don't use it as is. Today's solar noon is shown in the results.
How do I print it?
Press “Print dial & gnomon” below the results to print just the dial face and the gnomon template on one page. Line the bold noon line up with true north, copy the template onto card stock, cut it out and stand it on the noon line with the sloping edge rising toward the north.
For solar noon and the Sun's noon height on any date, see the Solar Noon Calculator.