Apparent Solar Time Calculator

Apparent solar time, also called true solar time or sundial time, is the measure of time based on the actual position of the Sun in the sky. When the Sun crosses the meridian (the imaginary north-south line passing directly overhead), a sundial reads exactly 12:00 — solar noon. Before and after that crossing, the sundial counts hours and minutes based on how far the Sun is from its noon position.

This differs from the clock time most people use daily. Standard clock time (also called mean solar time) uses a fictitious "mean sun" that moves at a perfectly uniform speed throughout the year, smoothing out the real Sun's irregular motion. Because Earth's orbit is elliptical — not circular — and because the axis is tilted relative to the orbital plane, the real Sun's apparent speed varies throughout the year. The result is that a sundial can read up to about 16 minutes ahead of or behind a clock, depending on the time of year.

This calculator computes Local Apparent Solar Time (LAST), Local Mean Solar Time (LMST), the Equation of Time, the solar hour angle, solar declination, and the exact time of solar noon for any date, location, and time zone you enter. It is useful for sundial calibration, solar panel optimization, astronomical observation planning, and navigation.

The time correction factor applied by this calculator accounts for both the Equation of Time (the orbital/tilt correction) and the longitude correction (how far your location is from the standard time zone meridian). Together these two corrections give you the precise local solar time for your position on Earth.

The Local Apparent Solar Time (LAST) is derived from standard clock time by applying two corrections: a longitude offset and the Equation of Time. The Time Correction Factor (TC) combines both.

The Equation of Time (EoT) captures the total accumulated difference between apparent and mean solar time caused by two independent effects: the eccentricity of Earth's orbit and the obliquity of the ecliptic (Earth's axial tilt). Each effect contributes a sinusoidal variation with a period of one year; because they have different phase offsets, their sum creates a more complex curve with two maxima and two minima per year.

The EoT reaches its positive peak of about +16.4 minutes in early November (sundial fast) and its negative peak of about -14.3 minutes in mid-February (sundial slow). At four dates each year — approximately February 12, May 14, July 26, and November 1 — the Equation of Time equals zero, meaning sundial time and clock time briefly agree.

This calculator uses the NOAA Fourier series approximation for the EoT, which achieves accuracy within 0.5 minutes throughout the year. The formula expresses EoT as a sum of sinusoidal terms weighted by empirically fitted coefficients, taking the fractional year angle γ as input.

The solar hour angle (HRA) measures how far the Sun is from its noon position, expressed in degrees. At solar noon HRA = 0. Each hour of time corresponds to 15 degrees of hour angle (since 360 degrees / 24 hours = 15 degrees per hour). Before noon the hour angle is negative; after noon it is positive.

The hour angle is a key input for computing the Sun's altitude and azimuth: knowing HRA, your latitude, and the solar declination, you can solve the spherical triangle of celestial navigation to pinpoint the Sun's exact position in the sky at any moment. This is the basis of solar altitude calculations used in energy modeling, architecture, and navigation.

HRA = 15 × (LAST − 12), where LAST is in decimal hours. A positive HRA means it is afternoon (Sun has passed noon); negative means it is morning. At sunset and sunrise the Sun's altitude equals zero, and the corresponding HRA at those moments determines day length.

Standard time zones are set to a reference meridian (e.g., UTC+5 uses 75° E as its standard meridian, since 15 × 5 = 75). If you are located east of that meridian your local solar time is ahead; west of it, your solar time is behind. The correction is 4 minutes per degree of longitude difference.

A location at 80° E in the UTC+5 zone is 5 degrees east of its standard meridian, adding 5 × 4 = 20 minutes to clock time to get mean solar time. Combined with the Equation of Time, the total correction can place apparent solar noon more than 30 minutes away from 12:00 clock time at certain locations and dates.

This is why solar panels should not assume noon is 12:00 on the clock — the actual solar maximum for charging depends on both the longitude correction and the Equation of Time on that day. This calculator gives you the exact solar noon time for optimal fixed-tilt panel orientation.