A sundial reads apparent solar time, which differs from clock time through seasonal and longitude effects. Convert its reading to local mean and zone-standard time using the equation of time and a separate longitude correction.
Solar-to-Standard Time Conversion
Enter day of year, an apparent sundial reading, east-positive longitude and the standard UTC offset. The result applies equation-of-time and longitude corrections only; daylight saving and physical dial errors are excluded.
Equation Used
- The apparent reading comes from a correctly constructed and aligned sundial.
- The selected UTC offset is standard time, not a daylight-saving offset.
- The annual approximation uses 365 days and noon-like fractional year; sub-minute ephemeris precision is not claimed.
The equation of time supplies the seasonal correction, and longitude relates local mean time to the selected standard zone. The conversion excludes daylight saving and errors in the physical dial or its reading.
Apparent, local mean and zone-standard time
USNO defines equation of time E as apparent solar time minus mean solar time. Therefore local mean solar time is the sundial reading minus E. Civil standard time also uses a zone meridian, so longitude supplies a separate fixed correction.
A historical mean-time dial may embody a date correction in its geometry. The animation instead shows the documented numerical correction chain and annual E curve; it does not claim to solve a particular dial plate.
A bounded conversion screen
Use the calculator to understand the sign and separation of the seasonal and longitude corrections. It cannot certify a sundial, create an engraving, account for daylight saving, or replace an ephemeris.
NOAA approximation and time conversion
With longitude lambda positive east and standard-zone offset z in hours from UTC: LMST=AST-E and standard time=LMST+60z-4lambda, with minute quantities divided by 60 for hour output.
Arithmetic example
For day 307, an apparent reading of 12.25 h, longitude 120 degrees west and UTC-8 standard time, the zone-longitude correction is zero because the site lies on the zone meridian. NOAA's approximation gives E about +16.4 minutes, so local mean and zone-standard time are about 11.98 h.
Accuracy and physical-dial limits
Actual reading accuracy depends on the instrument, site, date, alignment, refraction, interpretation and timekeeping convention.
Mean-time sundial questions
Why subtract E?
Because this page follows USNO: E=apparent minus mean.
Why is longitude separate?
Local mean solar time varies continuously with longitude, while standard time is shared across a zone.
Does the output include daylight saving?
No. Add any legally applicable seasonal offset separately.
Institutional references
- US Naval Observatory, The Equation of Time: definition, magnitude, longitude relationship and analemma.
- NOAA, General Solar Position Calculations: annual approximation and longitude/time-zone convention.
- Royal Museums Greenwich, Equinoctial dial AST0368: historical analemma dial displaying mean time at midday.
- NBS Letter Circular 265, Sundials: historical corrections added to sundial readings to obtain mean solar time.
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