HesapHanem

Equation of Time Calculator

Enter the day of the year (1–366).

How it is calculated

You enter the day of the year N, where 1 is 1 January and 44 is 13 February. The tool first finds an angle in degrees, B = 360 × (N − 81) / 365, and then uses the standard approximation EoT = 9.87 sin(2B) − 7.53 cos(B) − 1.5 sin(B), giving minutes. A positive value means the sundial reads ahead of the clock, a negative value means it reads behind. The formula is the same every year, with no leap-year adjustment, and it assumes a 365-day cycle, so the result is a close approximation rather than an astronomical ephemeris value. Days outside 1 to 366 give no result, and a decimal day such as 100.5 is accepted. The value does not include your longitude or daylight saving time.

Worked example

For 13 February, N = 44. The angle is B = 360 × (44 − 81) / 365 = −36.49°. Then 9.87 × sin(−72.99°) = −9.44, −7.53 × cos(−36.49°) = −6.05 and −1.5 × sin(−36.49°) = +0.89. Adding them: −9.44 − 6.05 + 0.89 = −14.60 minutes. The tool shows -14.60 min, and because the sign is negative the sundial is behind the clock, about 14.6 minutes. Around 1 November (N = 305) the sign flips and the sundial runs about 16.4 minutes ahead.

Try this example →

Common mistakes

  • Entering the day of the month instead of the day of the year. 13 February is day 44, not 13, so count from 1 January.
  • Entering the month number or a date such as 2.13. The field takes a single day count between 1 and 366.
  • Reading a negative value as the sundial being ahead. A negative equation of time means the sundial is behind the clock, and a positive one means ahead.
  • Using the result as the full correction for a sundial. It does not include the offset from your time zone meridian or daylight saving time, so a longitude correction must be added separately.
  • Expecting the same value on a given date every year to the second. The tool applies a fixed approximation, so leap years and the exact year are not modelled.

About this calculator

A sundial and a clock rarely agree. The equation of time is the day-by-day difference between apparent solar time (what a sundial shows, based on the sun's actual position) and mean solar time (the uniform 24-hour day that clocks keep), and it swings between roughly −14 and +16 minutes over the course of a year. The discrepancy comes from two effects layered together: Earth's elliptical orbit, which speeds and slows the sun's apparent motion (Kepler's second law), and the tilt of Earth's axis, which skews the sun's path relative to the celestial equator.

Given a day of the year, this calculator returns how many minutes fast or slow the sundial reading is compared to clock time. It's essential for sundial design, where a correction table or analemma curve lets a sundial be read against real clock time, and it's also used in solar energy calculations, where predicting the sun's exact position throughout the year affects tracking-panel angles and solar noon timing.

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Comments (1)

  • Editorial team

    A useful reading is solar noon. Subtract the shown value from 12:00 in local mean time. On day 44 the value is minus 14.60 minutes, so the sun crosses the meridian about 14.6 minutes after clock noon, before any longitude or daylight saving adjustment. A sundial reader still has to add the longitude difference from the centre of the time zone, four minutes per degree. What are you building or checking: a sundial, a solar tracker or a classroom demo?

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