how to make a sundial

Point the gnomon, the part that casts the shadow, at true north and tilt it up by your latitude: 40.7° in New York, 41.9° in Chicago, 34.1° in Los Angeles. Tilted like that, it points at the celestial pole, and its shadow falls on the same hour line in every season. Below: the hour-line angles for a flat sundial from 25° to 50° north, what your clock says when the sundial says noon, and a calculator for your own place.

Sundial angle calculator

Enter your latitude and longitude (west is negative), the time zone your clock is on that day, and a date. The calculator gives the gnomon angle, the hour-line angles for a horizontal sundial, and the clock time when the sundial reads noon.

The defaults are New York on January 15, 2027. Hour-line angles are measured on the dial from the noon line.

Why the gnomon angle is your latitude

As the Earth turns, the Sun appears to move 15° across the sky every hour. A rod parallel to the Earth's axis sees that motion evenly, so its shadow also moves 15° an hour, whatever the season. Parallel to the axis means pointing at the celestial pole, and the angle between such a pointer and level ground equals your latitude.

A stick pushed straight into the ground does not work this way: its shadow moves differently in summer and in winter.

The easiest one: an equatorial sundial

• Mark a round dial every 15° and number the lines like a clock face.
• Push a stick through the center at a right angle to the dial.
• Point the stick true north, tilted up by your latitude. The dial then sits at 90° minus your latitude to the ground: 49.3° in New York.
• Set it on a level surface with the noon line pointing north.

From the March equinox to the September equinox the shadow falls on the top of the dial. After the September equinox the Sun is south of the celestial equator and the shadow moves to the underside, so mark both faces.

Horizontal sundial hour-line angles

On a flat sundial the hour lines are not 15° apart. Measured from the noon line, the angle is tan(angle) = sin(latitude) × tan(15° × hours from noon). Near noon the lines are closer than 15°; toward morning and evening they spread out, and the 6 o'clock lines are at a right angle to noon. At 40° north, the 11 and 1 o'clock lines sit 9.8° from noon and the 10 and 2 o'clock lines 20.4°.

The gnomon angle is the latitude itself; the 6 a.m. and 6 p.m. lines are always 90°.

How to find true north for a sundial

At the moment of solar noon, the shadow of a vertical stick points due north. The calculator above gives that moment for your place and date. Mark the shadow's tip then and draw the line to the stick.

South of the Tropic of Cancer (23.4° north) there is an exception. In Honolulu, for instance, the noon Sun stands north of overhead from May 27 to July 15, and the shadow points south instead.

Why a sundial disagrees with your clock

A sundial tells solar time. Your clock is set by your time zone: US Eastern standard time is UTC minus 5 hours, which, at 15° an hour, is the time of the 75° west meridian. If you live west of your zone's meridian, the Sun crosses your meridian later, by 4 minutes for each degree: New York, at 74.0° west, sees solar noon about 4 minutes earlier than the 75° line, and Los Angeles, at 118.2° west, about 7 minutes earlier than 120° west.

The second reason is the Earth itself: its distance from the Sun changes through the year and its axis is tilted, so the Sun runs up to about a quarter of an hour fast or slow against a clock. This difference is called the equation of time. On your zone's meridian, sundial noon comes earliest around November 3, at 11:44 a.m., and latest around February 11, at 12:14 p.m..

Daylight saving time adds an hour. In the US it runs from 2 a.m. on the second Sunday of March to 2 a.m. on the first Sunday of November.

Where Angel Step fits

Angel Step reads only your step count from Apple Health and shows it as one number on a living sky. It does not work out shadows or the time of day; that is this page's job. A sundial is a reason to step outside and check on it.

Sources

• NASA Goddard, From Stargazers to Starships — the sundial: a pointer slanted toward the pole of the celestial sphere, at an angle equal to the latitude. NASA
• Royal Museums Greenwich — sundials: a rod parallel to the Earth's axis, 15° an hour, the equation of time and the longitude correction. RMG
• NOAA Global Monitoring Laboratory — solar calculator glossary: the equation of time and US daylight saving time. NOAA
• 15 U.S.C. § 261 — standard time zones of the United States, defined from UTC. Cornell LII
• 15 U.S.C. § 260a — daylight saving time. Cornell LII

Updated 12 October 2026