Math Playground
Activities

Estimate How Far Away

Thumb-trick triangulation — guess distance to a tree.

How far is that tree? Hold your thumb up at arm's length. Close one eye, then the other. The thumb appears to jump sideways. The bigger the jump, the closer the object.

Try this
3
distance to object ≈ 10 × the size of the jump (rule of thumb) = 30

Why ×10?

Your arm is roughly 10 times longer than the gap between your eyes. When you blink from eye to eye, your thumb shifts against the background by an angle that, multiplied by that 10×, gives the distance — geometry calls it parallax.

Astronomers measure distances to nearby stars the exact same way: they look from one side of Earth's orbit, then the other six months later, and watch how far the star 'jumps'.

Quick check

Your thumb appears to jump across about 4 fence posts that are 3 m apart. Roughly how far is the fence?

Rule of thumb (literally)

The distance to an object ≈ 10 × the size of its sideways jump (in the same units). It's not exact, but it's a fast field estimate.

Surveyors and snipers use a more precise version called parallax. Astronomers measure distances to stars the same way.