Solar Time Calculator
Convert clock time into apparent solar time and find the solar noon for any place and date.
What it does
A sundial is right about the sun and wrong about the clock, and the difference is what this page calculates. There are two reasons. The first is longitude: the sun crosses each meridian at a slightly different moment, so a place on the west side of its time zone sees noon later than the zone centre. The second is the equation of time, which comes from the tilt of the earth's axis and the shape of its orbit.
NOAA publishes the full set of equations in its solar position calculations, and they are what this tool uses. The equation of time is built from a fractional year angle that depends on the day of the year and the hour, and the correction added to the clock time is the equation of time plus four minutes for every degree of longitude, less sixty minutes for each hour of the time zone offset. NASA explains the same ideas in its note on apparent and mean solar time.
Solar noon is the moment the sun crosses the meridian, and it is not 12:00 by the clock except in the middle of a time zone on two days a year. The formula is 720 minutes, less the longitude correction, less the equation of time, and in New York it lands on 11:53 in late April.
A three term approximation of the equation of time is also in circulation, and the solar time page from PV Education prints it with the B angle form. It agrees with the NOAA equations to within a few seconds, and the difference matters for nothing except the keenest sundial.
The practical uses are a sundial, a solar tracker, an astronomical observation, or working out when a shadow points the right way. Whatever the use, the clock time has to be standard time, so daylight saving has to come off first.
How to use
- Pick the date, which sets the equation of time.
- Enter the clock time in local standard time.
- Enter the longitude of the place, positive east.
- Enter the offset of your time zone from UTC, negative west.
- Read the apparent solar time, which is what a sundial shows.
- Read solar noon, which is when the sun crosses the meridian.
Formula
- E
- Equation of time, the difference between mean solar time and apparent solar time, in minutes.
- Longitude
- Degrees east of Greenwich, negative in the Americas.
- Offset
- Time zone offset from UTC in hours, so UTC minus 5 for Eastern Standard Time.
- N
- Day of the year, with 1 for January 1.
NOAA uses 366 in the denominator in a leap year and 365 otherwise, and this page follows that. The result is a clock reading to the minute, which is the accuracy the source equations carry. The equation of time swings between roughly minus 14 minutes in February and plus 16 minutes in November, so a fixed offset for your longitude is only good near the equinoxes.
Worked example
Example: 30 April at noon in New York
Defaults: 30 April 2026, a clock time of 12:00, a longitude of 74 degrees west and a time zone offset of minus 5 hours.
- 30 April is day 120 of the year.
- The fractional year angle with the hour at noon gives the equation of time: 229.18 x (0.000075 + 0.001868 cos gamma - 0.032077 sin gamma - 0.014615 cos 2 gamma - 0.040849 sin 2 gamma) = 2.9 minutes.
- The longitude correction is 4 x -74 = -296 minutes, and the time zone correction is -60 x -5 = +300 minutes.
- Total offset: 2.9 - 296 + 300 = 6.9 minutes.
- Apparent solar time: 12:00 + 6.9 minutes = 12:07.
- Solar noon by the clock: 720 - 4 x (-74 + 75) - 2.9 = 713.1 minutes, which is 11:53.
- The tool shows 2.9 min, 6.9 min, 12:07 and 11:53.
Reference table
| Date | Equation of time | Total correction | Apparent solar time |
|---|---|---|---|
| 10 January | -6.7 min | -2.7 min | 11:57 |
| 10 April | -1.6 min | +2.4 min | 12:02 |
| 30 April | +2.9 min | +6.9 min | 12:07 |
| 14 June | +0.2 min | +4.2 min | 12:04 |
| 25 December | +0.3 min | +4.3 min | 12:04 |
Limits
- Works on standard time, so daylight saving has to be taken off before you use it.
- Assumes the longitude is known to a fraction of a degree, since four minutes of time is one degree.
- Gives the mean sun, with no correction for the equation of the centre of the sun.
- The longitude correction assumes the time zone offset matches the zone the place is in.
Common mistakes
- Forgetting that the longitude correction is four minutes per degree and not one.
- Using daylight saving time, which shifts the whole answer by an hour.
- Taking the sign of the longitude the wrong way, so the correction is added instead of subtracted.
- Using a three digit longitude for a place in the eastern hemisphere, which needs a positive number.
- Expecting solar noon to be at 12:00, which happens on only two days a year.
Try it yourself
Quick checks. Answers sit tucked under each question.
What is the equation of time on 10 January for a place at 74 degrees west?
The equation of time is -6.7 minutes, and with a time zone offset of minus 5 hours the longitude correction is +4 minutes, so the total correction is -2.7 minutes and the clock time of 12:00 is 11:57 of apparent solar time.
What is the total correction for a place at 74 degrees west in a UTC minus 5 zone?
Four minutes for each degree from the central meridian at 75 degrees west gives +4 minutes, and the equation of time is added to that.
Why is solar noon not at 12:00 in New York?
New York sits 1 degree east of the 75 degree west central meridian of its zone, which puts solar noon four minutes earlier, and the equation of time moves it further. On 30 April it is 11:53 by the clock.
Questions
What is apparent solar time?
The time a sundial shows, which is the clock time corrected for the longitude of your place and for the equation of time.
What is the equation of time?
The difference between mean solar time and apparent solar time, caused by the tilt of the earth and the shape of its orbit. It moves by more than twenty minutes between February and November.
How far off is solar noon?
By up to about 16 minutes in either direction, plus the longitude correction for your place, so the sun can cross your meridian nearly 30 minutes away from 12:00 by the clock.
Does daylight saving change it?
It shifts the clock but not the sun, so every result moves by an hour if you leave daylight saving in. Take it off first.
Why do sundials need a longitude adjustment?
Because the sun crosses each meridian at a different time, four minutes apart for every degree. A sundial set to the local mean time will be right at one longitude and wrong everywhere else.
Can I use this for solar panels?
For a tracker that points at the sun, the panel needs the sun's position rather than the time, so a solar position calculator is the better tool. For a fixed panel aimed by a compass reading, the solar time correction is what you need.
Sources
- NOAA Global Monitoring Laboratory: general solar position calculations
- NASA: apparent solar time and mean solar time
- PV Education: solar time and the equation of time