1 Degree Angle

At 1°, this angle is acute, meaning it is narrower than the corner of a square. It is a very narrow angle, just 1.1% of a right angle, the kind of small slope you see in drainage, ramps and fine adjustments.

1° is one three hundred sixtieth (1/360) of a full circle, or π/180 radians. If you face north and turn 1° clockwise, you end up facing between N and NNE (closest to north (N)).

1° angle facts

Trigonometric values of 1°

1° on a protractor

How to draw a 1° angle with a protractor

1. Draw a straight line with a ruler. This is the first arm; mark the vertex at one end.
2. Place the center mark of the protractor exactly on the vertex and line up the 0° baseline with your line.
3. Find 1° on the row of numbers that reads 0° on your line (protractors have two rows running in opposite directions) and make a small dot at the edge.
4. Remove the protractor and draw a line from the vertex through the dot. Mark the angle with an arc and label it 1°.

Drawing it a 1° angle without a protractor (rise and run method)

1. Draw a straight baseline and measure exactly 10 inches along it from the vertex.
2. At the 10-inch mark, draw a short line straight up at 90° (use a carpenter's square or the corner of a sheet of paper).
3. Measure 0.17 inches (about 3/16″) up that line and make a mark.
4. Join the mark to the vertex. The angle at the vertex is 1°, because tan 1° ≈ 0.0175.

Where you see 1° angles

• Plumbing drain lines are usually sloped ¼ inch per foot, which works out to about 1.2°. Just a little more than 1°.
• A 1° aiming error over a 100-foot chalk line puts the far end about 1¾ feet off target.
• A board sloped at 1° rises about 2.1 inches over a 10-foot (120-inch) run.
• 1° of latitude on Earth spans roughly 69 miles north to south.
• The Earth turns 1° on its axis in about 4 minutes.

Related angles

• Complement: 89°
• Supplement: 179°
• Explement: 359°
• Double: 2°
• 30°
• 45°
• 60°
• 90°
• 120°