4 Degree Angle

At 4°, this angle is acute, meaning it is narrower than the corner of a square. It is a very narrow angle, just 4.4% of a right angle, the kind of small slope you see in drainage, ramps and fine adjustments.

4° is one ninetieth (1/90) of a full circle, or π/45 radians. If you face north and turn 4° clockwise, you end up facing between N and NNE (closest to north (N)).

4° angle facts

Trigonometric values of 4°

4° on a protractor

How to draw a 4° 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 4° 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 4°.

Drawing it a 4° 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 0.7 inches (about 11/16″) up that line and make a mark.
4. Join the mark to the vertex. The angle at the vertex is 4°, because tan 4° ≈ 0.0699.

Where you see 4° angles

• The Leaning Tower of Pisa leans roughly 4° from vertical (about 3.97° since its stabilization work).
• Divide a circle into 90 equal slices and each slice is 4°, e.g. 90 spokes on a wheel or 90 equal pie-chart wedges.
• A 45-sided frame (45-sided polygon) is assembled with 4° miter cuts.
• A board sloped at 4° rises about 8.4 inches over a 10-foot (120-inch) run.
• 4° of latitude on Earth spans roughly 276 miles north to south.
• The Earth turns 4° on its axis in about 16 minutes.

Related angles

• Complement: 86°
• Supplement: 176°
• Explement: 356°
• Half: 2°
• Double: 8°
• 30°
• 45°
• 60°
• 90°