Skip to content
Rebuilding civilization

Geometry and measurement

Height from shadows

Height of a tree, building or tower by comparing its shadow with that of a vertical stick.

m

From the base of the object (or its centre, for a tree) to the tip of the shadow.

m

The part above the ground; make it plumb.

m

Measure it at the same time as the object's shadow.

Result

Object height
— m
Sun's altitude above the horizon
— °

How it is calculated

Sun rays arrive parallel, so the object and the stick form similar triangles: height = stick height × object's shadow ÷ stick's shadow.

Example: a 1.5 m stick casts a 2 m shadow and a tree a 12 m one → 1.5 × 12 ÷ 2 = 9 m.

Keep in mind

  • Measure both shadows within 5 minutes: shadows change length as the sun moves, especially at sunrise and sunset.
  • The ground must be level. Without sun, use the stick method: step back until, holding at arm's length a stick as long as that arm's length, its tip covers the treetop; the height is roughly your distance to the tree plus your eye height.

See also

More tools in “Geometry and measurement”