MM to Degree Calculator

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Are you looking to convert arc length or deflection into degrees? This mm-to-degree calculator will help you to calculate the angle by entering the arc length and radius. You can easily switch between different units like mm, cm, feet, and inches. Input your values, hit calculate, and get the results instantly!

How to Convert MM to Degree?

To convert millimeters (mm) to degrees, first calculate the angle subtended by an arc at the center of a circle. It can be found using the arc length and the radius of the circle. The relationship between arc length, radius, and angle (in degrees) follows a simple formula:

Formula:

θ = (L/2πR) × 360

Where:

• θ = Angle in degrees
• L = Arc length in mm
• R = Radius in mm

Example:

Arc length (L): 50 mm

Radius (R): 100 mm

θ = (L/2πR) × 360

θ = (50/2π×100) × 360 = 28.65°

This means a 50 mm arc on a 100 mm radius circle subtends an angle of approximately 28.65 degrees at the center.

How to Convert mm to Degrees (using radians)?

When dealing with circles, angles can also be measured in radians. To convert arc length to degrees, first calculate the angle in radians and then convert it to degrees.

Formula (Radians to Degrees):

θ = L/R

Where:

• θ = Angle in radians
• L = Arc length
• R = Radius

To convert radians to degrees:

θ = θ × 180/π

Example 1:

Arc length (L): 75 mm

Radius (R): 150 mm

Calculate in radians:

θ = 75/150 = 0.5 radians

Convert to degrees:

0.5 × 180/π = 28.65° 

Arc Length (mm)	Radius (mm)	Angle (Degrees)
10	100	5.73°
20	100	11.46°
30	100	17.19°
40	100	22.92°
50	100	28.65°
60	100	34.38°
70	100	40.11°
80	100	45.84°
90	100	51.57°
100	100	57.30°
110	100	63.03°
120	100	68.76°

FAQs:

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