37 Degree Angle

At 37°, this angle is acute, meaning it is narrower than the corner of a square. It is less than half of a right angle, and its complement (the angle that makes 90° with it) is 53°.

37° is 37/360 of a full circle, or 37π/180 radians. If you face north and turn 37° clockwise, you end up facing between NNE and NE (closest to northeast (NE)).

37° angle facts

Trigonometric values of 37°

37° on a protractor

How to draw a 37° 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 37° 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 37°.

Drawing it a 37° 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 7.54 inches (about 7 9/16″) up that line and make a mark.
4. Join the mark to the vertex. The angle at the vertex is 37°, because tan 37° ≈ 0.7536.

Where you see 37° angles

• Stairs built to the maximum US residential code (7¾-inch risers, 10-inch treads) are about 37.8° steep.
• A 9/12 roof pitch is 36.87°, very close to 37°.
• A board sloped at 37° rises about 90.4 inches over a 10-foot (120-inch) run.
• 37° of latitude on Earth spans roughly 2,555 miles north to south.
• The Earth turns 37° on its axis in about 2 h 28 min.

Related angles

• Complement: 53°
• Supplement: 143°
• Explement: 323°
• Double: 74°
• 30°
• 45°
• 60°
• 90°
• 120°