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Hour Angle from Local Solar Time

Converts local solar time into the hour angle used in sun-position and sundial calculations.

Written by the Vorzep Team

AstronomySolar PositionPractical

Hour Angle from Local Solar Time Calculator

H = 15° · ( LSThours − 12 )
Solve for H (degrees), LST (hours), or 15° (constant)
H ⟷LSThours, 15°
deg
hr
deg/hr
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Result —
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Hour Angle vs. Local Solar Time H(LST) = k · (LST − 12)
H(LST) for fixed k Computed point
LST in hours (0–24) • k = 15°/hr (Earth's rotation rate) • H in degrees

Variables

SymbolQuantityUnit
HHour angledeg
LST_hoursLocal solar timehours (24h format)

What it means

The hour angle H is the angular distance of the Sun from the local meridian, measured in hours (15° per hour). It is derived from local solar time. A positive hour angle means the Sun is west of the meridian (afternoon), negative means east (morning). This is used in the solar altitude formula and in telescope pointing (hour angle system). It is essential for tracking the Sun’s position for solar energy, heliostats, and for planning astronomical observations. Understanding this helps in converting time to angle for practical applications.

Worked example

Hour Angle from Local Solar Time – Two Detailed Examples

Real‑World
Scenario: An observer at a location where the local solar time (LST_hours) is 9:00 AM (9 hours) wants to find the hour angle H of the Sun. Using H = 15° × (LST_hours - 12), they get H = 15° × (9 - 12) = 15° × (-3) = -45°. This means the Sun is 45° east of the meridian (since negative hour angle indicates east). This is useful for calculating solar position and predicting shadows.
ParameterValue
LST_hours (h)9
1H = 15 × (9 - 12) = 15 × (-3) = -45°
Result -45° ✓ Hour angle (east)
Scenario: At 3:00 PM (15 hours), the hour angle is H = 15° × (15 - 12) = 45°. This positive angle means the Sun is 45° west of the meridian. This information is used in solar energy applications to determine the sun's position and optimise panel orientation for maximum output.
ParameterValue
LST_hours15
1H = 15 × (15 - 12) = 45°
Result 45° ✓ Hour angle (west)
Insight: The hour angle is the angular distance of the Sun from the local meridian, measured westward. It increases at a rate of 15° per hour. Negative values indicate morning.

Common mistakes

  • Hour angle: H = 15° × (LST_hours − 12) – in degrees.
  • LST_hours: Local Sidereal Time in hours (0‑24).
  • Result: Hour angle in degrees (negative before meridian, positive after).
  • Conversion: 15° per hour – the Earth rotates 15° in 1 hour.
  • Used in: Telescope pointing and coordinate transformations.

Applications

The hour angle, H = 15° × (LST_hours − 12), relates local sidereal time to the hour angle of an object. The hour angle is used in telescope pointing to determine when an object is on the meridian and to calculate its altitude. It is also used in timekeeping and in understanding the daily motion of celestial objects. By computing the hour angle, observers can schedule observations and align telescopes. This formula is essential for practical astronomy and navigation.

  • Telescope pointing and tracking using hour angle
  • Determination of optimal observation times (when target transits)
  • Calculation of solar altitude for energy applications
  • Educational understanding of celestial coordinate systems
  • Navigation and timekeeping (solar vs. sidereal time)