SunnypatchHow long is a fence's shadow?
At midday, a 1.8 m (6 ft) fence at the latitude of New York or Madrid casts a shadow about 0.5 m (1.8 ft) long in midsummer and 3.6 m (12 ft) long in midwinter. Around London and Berlin the same fence casts about 1 m and 6.9 m. The table has the figure for your latitude, and the calculator below it works out any height.
Midday shadow of a 1.8 m (6 ft) fence
| Latitude | 21 June | 20 March | 21 December |
|---|---|---|---|
| 25° Miami, Dubai, Taipei | under 0.1 m 0.2 ft | 0.9 m 2.9 ft | 2.0 m 6.8 ft |
| 30° Houston, New Orleans, Cairo | 0.2 m 0.7 ft | 1.1 m 3.5 ft | 2.4 m 8.1 ft |
| 35° Los Angeles, Tokyo, Charlotte | 0.4 m 1.2 ft | 1.3 m 4.3 ft | 2.9 m 9.8 ft |
| 40° New York, Madrid, Denver, Beijing | 0.5 m 1.8 ft | 1.5 m 5.1 ft | 3.6 m 12.0 ft |
| 45° Portland, Minneapolis, Montreal, Milan | 0.7 m 2.4 ft | 1.8 m 6.1 ft | 4.6 m 15.2 ft |
| 50° Vancouver, Frankfurt, Prague, Kyiv | 0.9 m 3.0 ft | 2.2 m 7.3 ft | 6.0 m 20.2 ft |
| 52° London, Amsterdam, Berlin, Warsaw | 1.0 m 3.3 ft | 2.3 m 7.8 ft | 6.9 m 23.1 ft |
| 55° Edinburgh, Copenhagen, Moscow | 1.1 m 3.7 ft | 2.6 m 8.7 ft | 8.8 m 29.3 ft |
| 60° Oslo, Stockholm, Helsinki | 1.3 m 4.4 ft | 3.2 m 10.6 ft | 15.6 m 52.0 ft |
Late September is the same as 20 March. South of the equator, swap the June and December columns: Sydney and Cape Town are close to 35°, and Melbourne and Auckland are a little further from the equator, at about 37°.
Midday here means solar noon, when the sun is at its highest. That is rarely 12:00 on the clock. It is often close to 13:00 during summer time, and later still in places that sit far west in their time zone, such as Spain.
For any other height
A shadow's length goes up in step with the height of whatever casts it. So multiply the height by the figure for your latitude. A 2.4 m wall at 45° in midwinter casts 2.4 × 2.53 = 6.1 m of shadow at midday. The same figures work in feet.
| Latitude | 21 June | 20 March | 21 December |
|---|---|---|---|
| 25° | 0.03 | 0.48 | 1.13 |
| 30° | 0.11 | 0.59 | 1.35 |
| 35° | 0.20 | 0.71 | 1.63 |
| 40° | 0.30 | 0.85 | 2.00 |
| 45° | 0.39 | 1.02 | 2.53 |
| 50° | 0.50 | 1.21 | 3.36 |
| 52° | 0.54 | 1.30 | 3.84 |
| 55° | 0.61 | 1.45 | 4.88 |
| 60° | 0.74 | 1.76 | 8.67 |
Shadow length calculator
Type a height and your latitude. A map app shows the latitude of any place: it is the first of the two numbers in its coordinates.
How it is worked out
On level ground, a shadow's length is the height divided by the tangent of the sun's angle above the horizon.
At solar noon that angle is 90° minus your latitude, plus the sun's declination: about +23.4° on 21 June, 0° at the equinoxes and −23.4° on 21 December. At 40° north in midwinter the sun is 90 − 40 − 23.4 = 26.6° up, and 1.8 ÷ tan 26.6° = 3.6 m.
Midday is the shortest shadow of the day
The lower the sun, the longer the shadow. At 40° north on 21 December, a shadow is 2.0 times the height at solar noon, 2.6 times two hours either side of it, 4.0 times three hours either side, and more than 10 times four hours either side, soon after sunrise and just before sunset. On 21 June the same hours give 0.3, 0.6, 0.9 and 1.3 times the height.
Length is not the same as reach
A shadow points away from the sun, so how far the shade reaches out from a fence depends on which way the fence runs.
- A fence running east to west throws its whole midday shadow straight out from one side: the north side if you are north of the equator. The tables above give how far it reaches.
- A fence running north to south throws almost no shade at midday, because the shadow lies along the fence. Its shade falls to the west in the morning and to the east in the afternoon.
For the strip on the shaded side of an east to west fence, the season matters a great deal. In London, a spot 1 m north of a 1.8 m fence is clear of the midday shadow only from early June to early July. A spot 2.5 m out is clear of it from the middle of March to the end of September.
Check a real spot through the whole year
A real spot has more than one fence around it, and plants care about the whole day, not only midday. Sunnypatch lets you draw the fences and walls around a spot on a satellite map, then adds up its hours of direct sun for every day of the year. It is free, with no sign-up.