An adjustable equatorial sundial places its polar gnomon parallel to Earth's axis and its hour ring in the equatorial plane. This calculator is an orientation comparison, not a prediction of reading accuracy or civil time.
Universal Sun Dial Interactive Calculator
Enter local latitude magnitude and a signed angular setting offset. The tool reports direct orientation quantities only; it does not calculate a shadow, date, equation of time, longitude correction, alignment error or clock time.
Equation Used
- The base is treated as level for the orientation sketch.
- Latitude is entered as a magnitude from 0 to 70 degrees.
- The polar axis is assumed to lie in the local meridian and point toward the appropriate celestial pole.
- The hour ring is perpendicular to the polar axis and uses 15-degree solar-hour increments.
- Date, solar declination, shadow geometry, longitude, time zone, equation of time, refraction, levelling, azimuth alignment, scale error, thickness and reading uncertainty are omitted.
Equatorial Ring and Polar Gnomon
U.S. Patent 6,871,407 documents an equatorial ring perpendicular to a primary polar gnomon, with hour marks at 15-degree radial increments and a mount adjustable for latitude. The Smithsonian records an eighteenth-century universal equinoctial sundial whose brass setting mechanism covers latitude.
The animation shows this orientation schematically; it is not an optical ray trace.
What This Calculator Represents
The tool adds a signed setting offset to entered latitude magnitude for a set-axis elevation, repeats latitude as the ideal polar-axis elevation, reports the signed offset directly and displays the standard 15-degree-per-solar-hour spacing.
Axis-orientation Comparison
ideal polar-axis elevation = latitude magnitude
signed axis offset = entered offset
equatorial hour spacing = 15° per solar hour
NOAA gives solar hour angle as true solar time divided by four minutes per degree, equivalent to 15 degrees per solar hour. Civil time additionally involves longitude, time zone and equation of time.
Worked Orientation Example
At entered latitude magnitude 50° with a +2° setting offset, the set axis elevation is 52°, the ideal polar-axis elevation is 50° and the signed offset is +2°. Hour divisions remain 15° per solar hour. No minutes-of-time error is inferred.
Model Boundary
- Calculated: direct entered-angle orientation arithmetic.
- Illustrated: generic polar gnomon, perpendicular equatorial ring and level base.
- Not calculated: sun position, shadow, date, declination, equation of time, longitude or time-zone correction, civil time, hemisphere direction, refraction, levelling, north alignment, scale error, accuracy or readability.
Frequently Asked Questions
Why is the hour spacing 15 degrees?
A solar hour corresponds to 15 degrees of solar hour angle.
Does a 2-degree setting offset always cause the same time error?
No.
Does the latitude magnitude specify north or south?
No. Enter the latitude magnitude; the appropriate north or south celestial-pole direction must be established separately.
Is equation of time included?
No.
Does the tool convert sundial time to clock time?
No.
Can it predict a real dial's accuracy?
No.
References
- U.S. Patent 6,871,407, Equatorial sundial with simple time and date interpretation: polar gnomon, perpendicular equatorial ring, latitude adjustment and 15-degree hour increments.
- NOAA Global Monitoring Laboratory, General Solar Position Calculations: true solar time, equation of time, longitude/time-zone offset and solar hour-angle relations.
- Smithsonian National Museum of American History, Universal Equinoctial Sundial: documented 1736 brass instrument adjustable for latitude.
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