Solar Time vs Clock Time Calculator
Convert standard clock time to true solar time for any location and date. Useful for astronomers, sundial builders, and anyone tracking solar noon or sunrise/sunset times precisely.
About this calculator
Solar time differs from clock time because time zones assign a single offset to large geographic areas, while the sun's position depends on your exact longitude. Every 15° of longitude equals one hour of solar time difference. An additional correction called the Equation of Time accounts for Earth's elliptical orbit and axial tilt, causing the sun to run up to ~16 minutes fast or slow throughout the year. The formula used here is: solarTime = (clockHour + clockMinute/60) − (longitude/15) − timeZoneOffset + EoT/60, where EoT (in minutes) = 7.53·cos((dayOfYear−81)·2π/365.25) + 1.5·sin((dayOfYear−81)·4π/365.25). The result gives you the true solar hour, where 12.00 means the sun is exactly at its highest point in the sky.
How to use
Suppose you are in Denver (longitude 104.99°W, time zone UTC−7) on March 21 (day 80) and your clock reads 12:00 (noon). Step 1 — longitude correction: 104.99/15 = 6.999 hours. Step 2 — EoT: 7.53·cos((80−81)·2π/365.25) + 1.5·sin((80−81)·4π/365.25) ≈ 7.53·1.00 + 1.5·(−0.034) ≈ 7.48 minutes. Step 3 — solar time: (12 + 0/60) − 6.999 − (−7) + 7.48/60 = 12 + 0.001 + 0.125 ≈ 12.13. True solar noon in Denver on March 21 is about 12:08 solar time — just 8 minutes ahead of the clock.
Frequently asked questions
Why does solar time differ from standard clock time at my location?
Clock time is set by political time zones that span up to 15° of longitude each, so everywhere within a zone shares the same offset from UTC. Your true solar time, however, depends on your exact longitude: every degree east or west shifts solar noon by 4 minutes. Add the Equation of Time correction for Earth's orbital eccentricity and axial tilt, and the two can diverge by more than half an hour.
What is the Equation of Time and how does it affect solar calculations?
The Equation of Time is the difference between mean (clock) solar time and true apparent solar time. It arises from two effects: Earth moves faster near perihelion (January) and slower near aphelion (July), and the ecliptic plane is tilted relative to the celestial equator. The combined effect swings between about −16 minutes in late October and +14 minutes in mid-February. This calculator incorporates a two-term Fourier approximation of that correction.
How do I find the exact time of solar noon at my longitude?
Solar noon occurs when the sun crosses your local meridian, i.e., when solar time equals exactly 12.00. Using this calculator, enter your longitude, UTC offset, and the day of year, then adjust the clock time until the result reads 12.00. Alternatively, set the clock to 12:00 and subtract the displayed offset from noon — that difference tells you how many minutes before or after 12:00 on your clock the sun will peak.