Sunlight Hours Affected by a South-Side Building

Enter Calculation

Latitude (degrees, + North)

Longitude (degrees, + East)

Timezone offset (hours from UTC)

Day of year (1-366)

Distance to south building

Unit meters (m) centimeters (cm) feet (ft)

Building height above measuring point

Unit meters (m) centimeters (cm) feet (ft)

Half-width (east-west / 2, 0 = infinite wall)

Unit meters (m) centimeters (cm) feet (ft)

Formula

Show calculation steps (1)

1. Solar Time Correction

   

   Converts apparent solar time to local clock time using the equation of time (EoT) and the difference between the timezone standard meridian and the actual longitude. B is the day-of-year angle.

Results

Residual Sunlight Hours at Home

7.75

hours of direct sun clearing the south building

Daylight length	14.35 h
Hours blocked by building	6.6 h
Critical roofline altitude	38.66 deg
Sunrise (clock time, h)	5.14
Sunset (clock time, h)	19.48
Sun goes behind building (h)	5.14
Sun emerges from building (h)	19.48

What this calculator does

This tool estimates how a building standing to the south of your home (or to the north, in the Southern Hemisphere) blocks direct sunlight. For a chosen date and latitude it traces the sun across the sky minute by minute and finds the window during which the sun is hidden behind the building's roofline, then reports the residual sunlight hours your windows actually receive. The astronomy is universal, so it works at any latitude and longitude.

How to use it

Enter your latitude (positive north), longitude and timezone offset, then the day of year (Jan 1 = 1). Measure the horizontal distance from your window to the south building and the building's height above your measuring point (subtract the sill height if needed). Leave the half-width at 0 to model an infinitely wide wall, or enter half the east-west extent to account for sun slipping past the building's edges. Longitude, timezone and the equation of time convert apparent solar time to your local clock.

The formula explained

The critical altitude the sun must exceed to clear the roof is \(\theta_C = \arctan\!\left(\frac{\text{Height}}{\text{Distance}}\right)\). Solar elevation is \(\sin\alpha = \sin\phi\,\sin\delta + \cos\phi\,\cos\delta\,\cos H\), where \(\delta\) is the solar declination from a sine approximation and \(H\) is the hour angle (15 degrees per hour from solar noon). A minute counts as blocked when the sun is up, lies within the building's azimuth span, and its altitude is below \(\theta_C\). Summing those minutes gives the blocked hours; daylight length minus blocked hours gives residual sunlight.

The sun's altitude angle alpha depends on latitude, solar declination and hour angle.

The critical roofline angle θc is set by the south building's height h and its distance d from your home.

Worked example

Latitude 35 degrees, day 81 (declination 0), distance 10 m, height 8 m, infinite wall.

$$\theta_C = \arctan(0.8) = 38.66^\circ$$

The sun clears the roof only between about 09:19 and 14:41 solar time, so blocked hours are about 6.63 and residual sunlight about 5.37 of the 12-hour day.

FAQ

Why use height above the window? Only the part of the building above your line of sight casts shade onto the window, so use the roof height minus the sill height.

What about the Southern Hemisphere? Enter a negative latitude; the obstruction-bearing direction becomes north (equator-facing), and the equations still hold.

Are clock times exact? They include longitude and equation-of-time corrections, giving close first-order estimates that ignore refraction, terrain and daylight-saving shifts.