How to Measure an Angle Without a Protractor

1. Use your phone or computer (easiest)

If you have a screen, you have a protractor. The online protractor measures anything on your screen; paste a screenshot under it for diagrams and PDFs. For real objects, lay your phone on the surface and read the tilt with the angle finder, or snap a picture and tap three points in measure angle from photo. No printer? The printable protractor takes a minute.

2. Ruler and calculator: the rise-over-run method

This is the most accurate manual method and works for any angle. It uses the tangent: angle = arctan(rise ÷ run).

1. Measure along one arm. From the vertex, measure a convenient distance along one arm, for example 10 inches, and mark it.
2. Measure straight across to the other arm. From that mark, measure at a right angle (use a carpenter's square or the corner of a sheet of paper) to the other arm. This is the rise.
3. Divide rise by run. Divide the rise by the run. For example 5.77 in ÷ 10 in = 0.577.
4. Take the arctangent. Enter tan⁻¹ (arctan) of that number on a calculator in degree mode. arctan(0.577) = 30°.

No calculator handy? Use this table for a 10-inch run:

For obtuse angles, extend one arm past the vertex, measure the acute angle on the other side, and subtract it from 180°.

3. Tape measure only: the chord method

Measure the same distance r (say 10 inches) from the vertex along each arm and mark both points. Measure the straight distance c between the two marks. Then angle = 2 × arcsin(c ÷ 2r). This is great for inside corners of walls or cabinets, where you cannot fit a square. Example: r = 10 in, c = 7.65 in → 2 × arcsin(0.3825) ≈ 45°.

4. Fold a sheet of paper

• 90°: the corner of any sheet of printer paper. Or fold any piece of paper in half, then fold the folded edge onto itself.
• 45°: fold a square corner so one edge lies along the other. The fold line is at 45°.
• 22.5°: fold the 45° again.
• 30° and 60°: fold a sheet in half lengthwise (long sides together) and unfold it, leaving a crease down the middle. Fold one bottom corner up until the corner touches that crease, with the fold line running through the other bottom corner. The fold line makes a 30° angle with the bottom edge and a 60° angle with the side edge.

Hold the folded template against your angle to check it, or compare using several folds.

5. Compass and straightedge

Classic geometry constructions produce exact angles: an equilateral triangle gives 60°, bisecting it gives 30° and 15°, and a perpendicular gives 90° (bisect for 45° and 22.5°). Each angle page shows the construction when one exists. See the 60°, 75° and 105° pages for examples.

6. The 3-4-5 rule for right angles

Builders check square corners with a tape measure: 3 units along one side, 4 along the other, and the diagonal must be exactly 5. Any multiple works (6-8-10, 9-12-15 ft). If the diagonal is longer, the corner is more than 90°; shorter, less than 90°.

7. Estimate with a clock face or your hand

• Clock face: each hour mark is 30° and each minute mark is 6°. Picture the angle as clock hands: hands at 12 and 2 make 60°.
• Your hand at arm's length: a fist covers about 10° of your view, the tip of your little finger about 1°, and a spread hand (thumb to pinkie) about 20°. Handy for estimating slopes and sky angles.

More guides

• How to Use a Protractor
• How to Read a Protractor
• Types of Angles
• Degrees to Radians