How Shadow Length Is Calculated and How to Check It with a Sun Calculator

Updated

Shadow length is the ground distance from the base of an object to the tip of its shadow. For a vertical object on flat ground, it equals the object's height divided by the tangent of the sun's altitude angle: shadow length = height ÷ tan(altitude). The lower the sun sits in the sky, the longer the shadow. You can get this number for any place, date, and time with a sun calculator such as SunCalc.org, which reports "Shadow length [m]" alongside the sun's altitude and azimuth.

The core relationship

Two inputs determine shadow length:

  • Object height — how tall the thing casting the shadow is.
  • Sun altitude — the angle of the sun above the horizon at that moment.

The formula follows from a right triangle: the object is the vertical side, the shadow is the horizontal side, and the sun's altitude is the angle at the shadow's tip.

Sun altitude Shadow length (for a 1 m object)
90° (directly overhead) 0 m
45° 1 m
30° ~1.73 m
10° ~5.67 m
1° ~57.3 m

At very low altitudes the shadow grows without bound, which is why shadows stretch out dramatically near sunrise and sunset.

Shadow direction

Length tells you how far the shadow reaches; azimuth tells you which way it points. The shadow falls on the opposite side of the object from the sun. If the sun's azimuth is due south, the shadow points due north. SunCalc reports azimuth as part of its solar data, so you can pair it with the shadow length to place a shadow on a map or plan.

Getting shadow length from SunCalc

SunCalc.org shows the sun's movement and sunlight phases for a chosen day and place, and its solar data panel includes a Shadow length [m] field.

  1. Set the location — enter latitude and longitude, or use the map to pick a point.
  2. Set the date and time — choose the day and drag the time slider (mouse or arrow keys) to the moment you care about.
  3. Read the solar data — the panel lists dawn, sunrise, culmination, sunset, dusk, daylight duration, distance, altitude, azimuth, and shadow length.
  4. Use the object height field — the panel shows shadow length "at an object level [m]," so you supply the height and the tool returns the corresponding shadow length.
  5. Reverse the calculation if needed — a reverse calculation option lets you work backward from a known shadow to another value.

The time slider also colors the day's sunlight phases, and the yellow curve traces the sun's path, so you can see how altitude changes across the day and how that drives shadow length.

Practical uses

  • Photography — long low-angle shadows near sunrise and sunset create dramatic depth; knowing the length helps you frame a subject.
  • Solar panel siting — panels and nearby structures cast shadows that reduce output; shadow length at low sun angles shows how far shading reaches.
  • Outdoor shade planning — awnings, trees, and buildings cast predictable shadows you can size against a patio or seating area.
  • Architecture and landscaping — checking shadow reach at different seasons helps place windows, overhangs, and plantings.

Limits to keep in mind

The formula assumes flat ground and a vertical object. Real conditions change the result:

  • Sloped terrain shortens or lengthens the visible shadow.
  • A tilted object casts a shadow that no longer matches the simple height ÷ tan(altitude) rule.
  • Obstacles, buildings, and vegetation can block or merge shadows.
  • Atmospheric refraction slightly shifts the sun's apparent position near the horizon.

Treat the calculated value as the ideal-case length, then adjust for the actual site.