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What does a neighbouring house to the south do to your light?

A neighbouring house to the south steals winter sun first and summer sun last — settle it with one angle: arctan(height divided by distance), weighed against the sun's height on the date.

The one angle it all comes down to

The question "does the neighbour's house take my sun?" has one precise answer, and it only needs two measurements: how tall the neighbouring house is, and how far away it stands.

The shading angle — how high above the horizon the neighbouring house rises, seen from your window — is found from:

shading angle = arctan(height ÷ distance)

The sun reaches through the window when the sun's height above the horizon is greater than the shading angle. Otherwise it doesn't. That's the entire mechanism.

An example: the neighbour's house stands 8 metres to the ridge and sits 20 metres south of the living-room window. 8 ÷ 20 = 0.4, and arctan(0.4) = 21.8°. So the sun has to sit above 21.8 degrees before it reaches the glass.

The sun's height on the dates that matter

The sun's height at midday is found from 90° − latitude + declination. Declination is −23.4° at the winter solstice, 0° at the equinox and +23.4° at the summer solstice. Look up your latitude on a map, and work the numbers out once:

• 45°N: roughly 22° at the winter solstice, 45° at the equinox, 68° at the summer solstice.
• 50°N: roughly 17°, 40°, 63°.
• 55°N: roughly 11°, 35°, 58°.
• 60°N: roughly 7°, 30°, 53°.

Every degree further north costs a degree of sun height all year round. The rest of this article uses 55°N, where the winter sun sits around 11 degrees above the horizon at midday.

Weighed against the example above, with a shading angle of 21.8°: the living room gets midday sun from a while before the equinox and on through summer, but no midday sun at all in December, January and much of February and November. That's the sort of thing you can't spot at a viewing in May.

How far away does the neighbouring house need to be?

Turn the maths around: the minimum distance that gives clear sun is height ÷ tan(sun height).

For a neighbouring house 8 metres to the ridge:

• Clear midday sun at the winter solstice (11°): 8 ÷ 0.194 = 41 metres
• Clear midday sun at the equinox (35°): 8 ÷ 0.70 = 11 metres
• Clear midday sun at the summer solstice (58°): 8 ÷ 1.60 = 5 metres

The jump from 11 to 41 metres is the whole story of winter light at this kind of latitude. On a typical house plot, those 41 metres to the south are rarely there — so shade from a neighbouring building in the depths of winter is normal, not a flaw in the house. What's worth investigating is how much of the year the shade actually lasts.

Remember to measure from the window, not the boundary line

Two corrections make the maths noticeably more accurate:

• Subtract the window's height above ground from the neighbouring house's height. Looking out from a window whose centre sits 1.5 metres above the ground, only the top 6.5 metres of an 8 metre neighbouring house is above your eye level. The shading angle becomes arctan(6.5 ÷ distance) instead of arctan(8 ÷ distance).
• One floor up changes everything. A first-floor window 4 metres above ground only sees 4 metres of the same neighbouring house: arctan(4 ÷ 20) = 11.3°. That's just barely under the winter sun's 11 degrees at 55°N. The ground floor sits in shade in December; the floor above gets sun. Same house, same neighbour.
• Terrain counts too. If the neighbour's plot sits 1.5 metres higher than yours, that difference is added to the neighbouring house's height. If it sits lower, it's subtracted.

The shade doesn't sit still — it sweeps

The calculations above hold at midday, when the sun sits due south and highest. The rest of the day the sun sits both lower and elsewhere in the sky, and the neighbouring house's shadow sweeps across the plot.

At the winter solstice the sun rises around southeast (azimuth 135°) and sets around southwest (225°). It stays within the southern quarter of the sky all day — the same quarter the neighbouring house sits in. If the house is due south, there can still be sun early and late in the day, once the sun has cleared the house's corners, even with shade at midday. That light is weak, though, because the sun is also at its very lowest then.

At the summer solstice the sun rises around northeast (azimuth 45°) and sets around northwest (315°). Then most of the day's sun doesn't come from the south at all, and a neighbouring house to the south matters almost nothing. That's why a plot can feel sun-drenched in July and shut off in November.

What can you do about it?

• Move the light up. A high-set window, a rooflight or a dormer looks over whatever is casting shade. A rooflight also gets most of its sun precisely in summer and least in winter, so it doesn't solve the winter problem on its own.
• Swap the rooms around. If the home has sun upstairs and shade on the ground floor in winter, it can be worth putting the living room up and the bedroom down.
• Make use of reflected light. When direct sun is scarce, diffuse light matters more. Light-coloured surfaces to the south — a pale terrace, a light-rendered gable, a light fence — send noticeably more daylight through the glass than dark ones.
• Look at what's within your own control. Your own hedges, sheds, carports and trees to the south are often the single biggest shadow, and easier to do something about than the neighbour's house. A hedge 1.8 metres tall casts a 9 metre shadow at the winter solstice; trimmed to 1.2 metres, the shadow shrinks to 6 metres.
• Keep an eye on what could still be built. An empty plot or a low building to the south can become something taller. How high a neighbouring plot is allowed to build is set by local planning rules — check it before you buy, if the light matters to you.

Don't count on shade being something you can complain away. Rules on fences and boundary distances are about heights and setbacks, not a right to sunlight, and an actual dispute with a neighbour is settled by the authorities — not by a calculation. The calculation exists so you know what you're buying.

How to check it before you buy

1. Stand at the window of each living room and look south, southeast and southwest.
2. Estimate the height of what you see — a storey is typically about 3 metres, a pitched roof adds another 2-3 metres.
3. Estimate or measure the distance — pace it out, or measure it on a map.
4. Work out arctan(height ÷ distance) and weigh the figure against the sun's height for your latitude — at 55°N, 11° for December, 35° for the equinox and 58° for June.
5. Take a photo facing south from each room. It's the cheapest record of the horizon you can bring home with you.

If you have the home's floor plan measured and correctly placed on the map, this can be done for every room at once. In HouseSense, sunlight is calculated in the 3D model from the address's location, the house's true north, and a date and time you choose yourself — so you can see the house's December on the same day you're standing in it in August.