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Equation of Time & Sundial Correction Calculator

Civilian clocks run on mean solar time — they assume the sun crosses the meridian at exactly the same moment every day. The real sun doesn't cooperate. Earth's orbit is elliptical (it moves faster in January, slower in July) and its axis is tilted (so the projection of solar motion onto the equator is not uniform). The combined effect is the Equation of Time (EoT), an annual oscillation between roughly +16 minutes (sundial fast, around November 3) and −14 minutes (sundial slow, around February 11), crossing zero four times a year (mid-April, mid-June, early September, late December). This tool uses the standard astronomical fit EoT ≈ 9.87 sin(2B) − 7.53 cos(B) − 1.5 sin(B) where B = 360°·(N − 81)/365 and N is the day of year. Combined with the longitude offset from your timezone meridian (4 minutes per degree of longitude east of the meridian), it gives the true local apparent solar noon and the sundial correction sheet you need to actually read a sundial against your wristwatch.

—
Day of year
233
B angle
149.92°
Equation of Time
−2m 48s
Longitude correction
−32m 00s
Total correction (EoT + longitude)
−34m 48s
Local apparent solar noon
12:34:48
Sundial reads BEHIND clock by: −2m 48s
Equation of Time over the year
-15-10-551015JanFebMarAprMayJunJulAugSepOctNovDecmin
Notable dates (this year)
Sign convention: positive EoT = sundial AHEAD of mean clock time (sundial reads ~12:16 when clock is at 12:00). Negative = sundial behind. Longitude correction is +4 min for every degree EAST of your timezone's reference meridian.

How to use

  1. Pick a date — the day-of-year drives the entire calculation.
  2. Set your longitude in degrees (east positive, west negative — e.g. Seoul +127°, New York −74°, London 0°).
  3. Set your timezone offset from UTC (e.g. UTC+9 for KST, UTC+1 for CET, UTC−5 for EST).
  4. Read the Equation of Time, the longitude correction, and the actual local apparent solar noon on the clock.
  5. Use the year-long chart to find days when the sundial agrees with the clock — those are the dates EoT crosses zero.

Frequently asked questions

Why does the EoT exist at all?
Two reasons combine. Eccentricity: Earth's orbit isn't circular — it's at perihelion (closest to the Sun) around January 3 and aphelion around July 4. By Kepler's second law it moves fastest at perihelion, so the Sun appears to drift east against the stars faster in January, slower in July. Obliquity: Earth's spin axis is tilted 23.44° relative to its orbit, so the Sun's motion along the ecliptic doesn't project uniformly onto the celestial equator. The two effects each contribute about ±9 minutes; they sometimes add (peak ±16 min) and sometimes partially cancel (zero crossings).
Why is there a longitude correction separate from the EoT?
Time zones are 1-hour bands centered roughly every 15° of longitude. Seoul is at 127° E but Korea Standard Time uses the 135° E meridian — so Seoul's mean solar noon is 32 minutes after KST noon (longitude correction = 4 min/° × (135 − 127) = +32 min). The EoT is the same everywhere on Earth on a given date; the longitude correction depends on where you stand relative to the timezone's reference meridian.
How accurate is the formula?
The 9.87/7.53/1.5 formula is accurate to about ±15 seconds for any year in the current epoch. Modern astronomical libraries use a longer Fourier series that's accurate to fractions of a second. For sundial design or rough astronomy this fit is more than enough; for a high-precision ephemeris use the JPL DE files or Skyfield/NOVAS implementations.
Why does my sundial read a different time than my watch even when EoT = 0?
Because of the longitude correction. EoT = 0 means the apparent Sun crosses your local meridian at exactly 12:00 mean local time. If you're not on your timezone's reference meridian, that 12:00 mean local time is not 12:00 wristwatch time. Add the longitude correction (this tool's 'longitude correction' field) to get the wristwatch time of true solar noon. Add then EoT for any other date.

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