How Do You Calculate Shadow Length?

The short answer

Shadow length = object height ÷ tan(sun elevation angle). With the sun 45° above the horizon, the shadow is exactly as long as the object is tall - a 6 ft (1.8 m) post casts a 6 ft shadow; raise the sun to 50° and the shadow shrinks to about 5 ft (1.5 m), drop it to 20° and it stretches to about 16.5 ft (5 m).

You need exactly two numbers:

1. Object height - the fence, tree, wall or house whose shadow you care about.
2. Sun elevation angle - how many degrees the sun sits above the horizon at your location, date and time of day.

Divide the height by the tangent of the elevation and you have the shadow’s length on level ground. The trigonometry is exact; the only work is finding the elevation angle, and there’s a calculator for that below.

Shadow length by sun angle

The tangent makes shadows brutally sensitive to a low sun. Handy multipliers (shadow = height × multiplier - the multiplier is unit-free, so it works in feet or meters alike):

Each multiplier is 1 ÷ tan(elevation). Notice the blow-up at the bottom of the sky: from 10° down to 5° the shadow doubles, and it heads toward infinity at sunrise and sunset. That’s why anything below about 10° is a “long shadows, weak light” zone rather than a number you’d plan a garden bed around.

How to find the sun’s elevation angle

The elevation depends on your latitude, the date and the clock time. Three ways to get it:

1. Look it up exactly. A solar-position calculator computes it from your coordinates using the NOAA solar algorithm (Jean Meeus, Astronomical Algorithms) - accurate to a fraction of a degree.
2. The noon shortcut. At solar noon, elevation ≈ 90° - your latitude + solar declination. Declination is where the sun sits over the year: +23.44° at the June solstice, 0° at the equinoxes, -23.44° at the December solstice. Near 40° N (New York, Denver, Madrid) that puts the noon sun at about 73° in June, 50° at the equinoxes and 27° in December.
3. Measure it with a stick - see below.

Worked example: a 6 ft fence at 40° N

How long is the fence’s noon shadow on the shortest day of the year (Dec 21)?

1. Noon elevation = 90° - 40° - 23.4° = 26.6°
2. tan(26.6°) ≈ 0.50
3. Shadow = 6 ÷ 0.50 = 12 ft (3.7 m)

Same fence at the June solstice: 90° - 40° + 23.4° = 73.4°, tan(73.4°) ≈ 3.35, so 6 ÷ 3.35 = 1.8 ft (0.5 m).

That’s the whole story of winter shade in two lines: the same fence throws a noon shadow nearly 7 times longer in December than in June. A bed that basks in sun all July can sit in fence shadow all winter. Useful rule of thumb at 40° N: winter noon shadows run about twice the object’s height (tan 26.6° ≈ 0.5).

👉 The Sun Angle & Shadow Calculator does all of this from your location, date and clock time - the sun’s elevation and compass bearing, the exact shadow for any object height, plus sunrise, sunset, solar noon and day length. Tap “Use my location” and it reads the current sky for your spot.

Reverse it: measure the sun with a stick

The same triangle runs backwards: elevation = arctan(height ÷ shadow length). Stand a 3 ft (0.9 m) stick upright on level ground and measure its shadow. If the shadow is 4 ft (1.2 m), the sun is at arctan(3 ÷ 4) = 36.9°. Two tape-measure readings and you’ve measured the sky - handy for checking a spot where you’re planning a patio or panels.

Watch-outs

• The formula assumes level ground. On a downhill slope the shadow stretches farther; uphill it lands short. For a wall or fence line, sketch the worst case.
• Length is only half the answer - direction is the other half. The shadow falls directly opposite the sun’s azimuth (compass bearing, 0° = north, 90° = east, 180° = south). In the Northern Hemisphere the noon sun is due south, so noon shadows point due north.
• Solar noon is not 12:00 on your clock. Your position inside the time zone, the equation of time and daylight saving all shift it - often by 30 to 60 minutes. The calculator works in real clock time, so you don’t have to correct for any of it.
• Don’t trust low-sun numbers to the inch. Below about 10° elevation a fraction of a degree swings the length by feet, and atmospheric refraction makes the sun appear slightly higher than it truly is near the horizon (the calculator corrects for this).

Related

• Sun Angle & Shadow Calculator - elevation, azimuth, shadow length, sunrise and sunset for any spot, date and time.
• Landscaping tools - the full landscaping toolset.
• What slope do you need for patio drainage - the other number to check before pouring a patio in that sunny spot.
• How far can a 2x8 deck joist span - sizing the deck that shadow will fall on.
• How to measure roof pitch - another angle you can read with the same rise-over-run trigonometry.