Measure Angles Without Tools (Degrees)

Summary

An angle is a turn between two directions. Modern tools measure angles in degrees:

• A full turn is 360°
• A half turn is 180°
• A right angle is 90°

At low tech, you usually do not need “exact” degrees. What you do need is a way to reproduce a few reference angles reliably (90°, 60°, 45°, 30°) and describe other angles as “between” those references.

Prerequisites

• None (Level 0).

Tools and materials (natural / Level 0)

• A straight stick (for a straightedge)
• A pointed stick or sharp stone edge (to scratch lines)
• Flat ground, sand, clay, or a flat board/stone surface you can mark

Optional but helpful:

• A flexible strip (bark strip, fiber strand) to use as a “compass” radius

Reference angles and how to make them

90° (right angle): 3-4-5 triangle

This makes a right angle using only lengths.

1. Mark a point A on the ground.
2. From A, mark a point B at 4 handspans (or any consistent unit).
3. From A in a different direction, mark a point C at 3 handspans.
4. Move point C until the distance BC is exactly 5 handspans.
5. Draw lines AB and AC. The angle at A is 90°.

Any scaled version works (3-4-5, 6-8-10, 9-12-15). Use whatever size is easiest to measure.

60° (and 120°): equilateral triangle

1. Draw a baseline AB (any length you choose).
2. Using AB as the radius, draw an arc centered at A.
3. Using AB as the radius, draw an arc centered at B so it crosses the first arc at C.
4. Connect A-C and B-C. Triangle ABC has all sides equal, and angles of 60°.

If you cannot draw arcs cleanly, you can “step” the same stick length around: AB is the length, then mark C by finding a point that is one AB length from both A and B.

45°: bisect a 90° angle

1. Make a 90° angle using the 3-4-5 method.
2. Mark the angle corner point A and draw a short arc that crosses both legs of the angle at points D and E.
3. From D, draw a small arc.
4. From E, draw a small arc with the same radius so the arcs intersect at F.
5. Draw line A-F. This line splits the right angle into 45° and 45°.

30° and 15°: bisect 60° (and then bisect again)

1. Build a 60° angle using the equilateral triangle method.
2. Use the same bisection steps above to split 60° into 30°.
3. Bisect 30° to get 15°.

Using degrees in early articles (recommended style)

• Prefer descriptions like “shallow / moderate / steep” and “between 45° and 60°”.
• If you include degrees, add a reference like: “(about 60°; see Measure Angles Without Tools).”

Verification

• 3-4-5 triangle: if your measured BC equals 5 units, the angle at A is a right angle.
• Equilateral triangle: if AB, BC, and CA match, all angles are 60°.
• Bisection: the bisector should look symmetric; if you mark equal distances along both legs, the bisector should land in the middle.

Safety

• Scratching lines with sharp stone edges can cut. Keep fingers behind edges and cut away from your body.
• Avoid marking angles on unstable ground where you can slip.

Troubleshooting

• My “right angle” looks off: your length units drifted. Re-measure and make the triangle larger (errors matter less when the triangle is big).
• Arcs don’t intersect cleanly: your radius changed. Use a fixed stick length and keep the pivot point stable.
• Lines are messy: scratch lightly first, then deepen once you are confident.

Variants

• Make an angle template board: scratch a 90° corner and a 60° corner into a flat board or plank so you can reuse it later.