Sizu Riatto
Every Angle · Chapter 5

How Tall Is It?

Similar triangles do the climbing. A stick's shadow, or one angle through a drinking straw, gives the height of anything you can see the top of.

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Opens on the book's house and plot. Change any number to your own and press Calculate. No clinometer yet? Print the paper clinometer: a full-size scale to glue to card, fold over a straw and hang a thread from.

By shadows, at the same moment

By clinometer: one angle, from a measured distance

By clinometer: two angles, when you cannot reach the base

Enter a shadow pair or a distance and an angle, then press Calculate.

The formula

  • Shadows: height = the stick × its shadow's ratio: stick × the tall thing's shadow ÷ the stick's shadow
  • One angle: height = eye height + distance × tan(angle up)
  • Two angles a₁ (far) and a₂ (near), d apart: height = eye + d ÷ (1/tan a₁ − 1/tan a₂)
  • A tree can reach the house if its height is more than its distance from the wall
The book's worked example, Chapter 5. A 1.00 m stick casts 1.25 m while the eaves cast 6.75 m: the eaves stand 5.4 m. The back-garden tree from 15 m out, eye 1.6 m, 39° up: 13.75 m (45.1 ft). It stands 11 m from the back wall, so it could reach the house with 2.75 m to spare. Two angles, 26° then 39° from 10 m closer, give 13.86 m: 0.12 m different.
Check it. Measure the same height both ways. If shadows and clinometer disagree by more than 10%, re-read the angle: one degree near 40° moves a 15 m sighting by about a third of a meter.

Honest limits. A paper clinometer reads to about a degree; level ground is assumed. A tree that could reach the house is a question for an arborist, not a ladder: tree work is a Stop Line. The book's house was worked out on paper from published figures, not surveyed by us: measure your own, and walk your own plot at night. Prices are illustrative US prices from November 2026, shown without a currency sign; put in your own. Everything stays in your browser: no sign-up, nothing stored.

These calculators go with Every Angle (Make It Add Up, Book 2), where every number on this page is worked by hand.