Shadow length & overhang calculator

What the shadow length and overhang calculator does

A shadow length calculator finds how far an object's shadow reaches across level ground: shadow length equals height divided by the tangent of the sun's altitude. This tool also gives the direction the shadow points and how far down a wall a horizontal overhang shades, allowing for the angle between the sun and the facade.

Enter an object height, a sun altitude and azimuth, the direction a facade faces and the overhang depth. The results show the ground shadow length, the shadow bearing and the vertical shade line below the overhang, with a simple diagram of the sun triangle.

It works from sun angles you supply. To find altitude and azimuth for a location, date and time, use the sun path diagram generator and read its hourly table.

How to use the shadow length & overhang calculator

1. Choose Imperial or Metric. Heights and depths switch between feet and metres; angles stay in degrees.
2. Enter the object height: a fence, wall, tree or building edge, measured from the level the shadow falls on.
3. Set Sun position to Enter altitude & azimuth and type the sun altitude (between 0.01° and 89.99°) and sun azimuth clockwise from north, or choose From date, time & location and enter the date, local clock time, latitude, longitude and the UTC offset in force that day.
4. For overhang shading, enter the facade outward normal (the compass direction the wall faces, 180° for a south wall) and the overhang depth measured out from the wall.
5. Read the ground shadow length, the shadow bearing and the vertical overhang shade. If the sun is behind the facade, the result says so instead of giving a number. In location mode the derived altitude and azimuth are shown, and a seasonal table lists altitude, azimuth, ground shadow and overhang shade for 21 June, the March equinox and 21 December at 09:00, 12:00 and 15:00.
6. Download a PDF, CSV or the SVG diagram, or copy the result. Save inputs lets you reopen a set of angles later.

Worked example

Imperial: At a 45° sun altitude, an 8 ft object casts an 8 ft ground shadow. A 2 ft overhang shades 2 ft down a directly facing wall.

Metric: At a 45° sun altitude, a 3 m object casts a 3 m ground shadow. A 0.6 m overhang shades 0.6 m down a directly facing wall.

How to calculate shadow length from sun altitude

Shadow length = object height ÷ tan(sun altitude). Because tan(45°) = 1, a 45° sun casts a shadow exactly as long as the object is tall. Below 45° shadows lengthen quickly: at 25° a shadow is 2.14 times the height, and at 10° it is 5.67 times.

The shadow multiplier in the table is 1 ÷ tan(altitude). Multiply any height by it to get the shadow on level ground. The last column uses the same angles for a 2 ft overhang on a wall facing the sun directly, which is covered further down.

Which way does a shadow point?

A shadow points directly away from the sun, so its bearing is the sun azimuth plus 180°. With the sun at 225° (southwest), the shadow falls toward 45° (northeast). The tool reports this as the shadow bearing, measured clockwise from north.

Direction matters as much as length when you are checking a neighbor's garden, a courtyard or a roof. In mid-northern latitudes, winter noon shadows point roughly north and are long. Using the New York December 21 noon altitude of about 25.8°, a 6 ft fence casts a 12.4 ft shadow and a 30 ft building a 61.9 ft shadow. On June 21, at about 72.7°, the same building casts only 9.3 ft.

How overhang shading works: the profile angle

For a wall facing the sun directly, a horizontal overhang of depth D shades the wall down to D × tan(altitude) below its underside. At 45° a 2 ft overhang shades 2 ft of wall; at 60° it shades 3.46 ft.

When the sun is off to one side, what matters is the profile angle, also called the vertical shadow angle: the sun's altitude projected onto a vertical plane at right angles to the wall. tan(profile angle) = tan(altitude) ÷ cos(sun azimuth − facade normal). The tool uses this, so vertical shade = D × tan(altitude) ÷ cos(sun azimuth − facade normal).

An oblique sun shades more of the wall, not less. For a south-facing wall (180°), a sun at 50° altitude and 225° azimuth has a profile angle of about 59.3°, so a 2 ft overhang shades 3.37 ft rather than the 2.38 ft it would with the sun straight ahead. Once the sun is 90° or more away from the facade normal, it is behind the wall and the overhang does nothing for that face.

Horizontal overhangs suit walls that face the equator, where the summer sun is high around midday. East and west walls get low morning and afternoon sun that slips under an overhang, so vertical fins, screens or exterior shades usually do more there. The result also assumes an infinitely wide overhang; at the ends of a real one, oblique sun reaches the glass, so extend overhangs past the window jambs.

Worked example: sizing a south overhang at 40°N

A south-facing window at 40°N latitude is 5 ft tall, with its head 1 ft below the underside of the overhang. The goal is full shade at noon on June 21 and full sun at noon on December 21.

• From the sun path solstice table, noon altitude at 40°N is about 73.4° in June and 26.6° in December. At solar noon the sun is due south, so the azimuth difference is 0° and the profile angle equals the altitude.
• To shade the whole window in June, the shade line must reach 6 ft down (the 1 ft gap plus the 5 ft window). Depth = 6 ÷ tan(73.4°) = 1.78 ft, or about 21 in.
• Check December: a 1.78 ft overhang shades 1.78 × tan(26.6°) = 0.89 ft down the wall. That is less than the 1 ft gap, so the whole window is in sun at winter noon.
• Confirm both results in the calculator: enter 1.78 ft for the depth, 180° for the sun azimuth and the facade normal, then each altitude in turn.
• June 21 noon is the highest sun of the year, so an overhang sized for that moment shades less as the sun drops through late summer. Check several dates and hours, not just one.

Who it is for and when to use it

Method, formulas & assumptions

Ground shadow = height ÷ tan(altitude). For a sun-facing wall, vertical shade = overhang depth × tan(altitude) ÷ cos(sun azimuth − facade normal). In location mode the altitude and azimuth come from SunCalc for the date, clock time, coordinates and UTC offset, and a seasonal table repeats the calculation for 21 June, the March equinox and 21 December at 09:00, 12:00 and 15:00.

Imperial inputs are converted with exact factors (1 ft = 0.3048 m, 1 lb = 0.45359237 kg, 1 US gal = 3.785411784 L) before the calculation runs in SI, then results are converted back.

Common mistakes to avoid

• Using the sun's angle from vertical (the zenith angle) instead of altitude above the horizon. A 30° zenith angle is a 60° altitude, and the shadows differ by a factor of three.
• Entering the direction you face when looking at the wall as the facade normal. The outward normal points away from the building, the way the wall faces.
• Measuring height from the wrong level. On sloping ground or a raised deck, the shadow lands at a different level from the one you measured.
• Sizing a south overhang for the June solstice only. By late summer the noon sun is lower, so more sun gets under an overhang sized just for June 21.
• Relying on a horizontal overhang for east or west glass. Low morning and evening sun passes beneath it.
• Forgetting overhang width. The calculation assumes an infinitely wide overhang, and oblique sun reaches glass past the ends of a real one.

Scope & limits

Flat ground, vertical wall, horizontal overhang, no surrounding obstructions or atmospheric refraction. A sun behind the facade does not create direct overhang shading on that face. Enter the UTC offset in force on the date, including daylight saving.

Frequently asked questions

Further reading

• Solar altitude and azimuth explained
• Solar data by location
• All site & solar tools
• All free architecture & construction tools
• Harth resource library

In this category

• Floor area ratio & site coverage
• Sun-path diagram generator