MM to Degree Calculator – Millimeters to Degrees Converter

Use our mm to degrees calculator designed to convert millimeters in degrees using Degrees = (2 × π × Radius × Arc Length (mm)) × 360 formula.

Let’s say you have a wheel with a diameter of 200 mm, and you want to know what angle corresponds to an arc length of 50 mm on its circumference. The mm to degree converter helps you determine this angle quickly and accurately.

MM to Degree Calculator

Radius (mm)	Arc Length (mm)	Angle (degrees)
50	10	11.46
100	25	14.32
100	50	28.65
120	30	14.32
150	50	19.10
150	75	28.65
200	50	14.32
200	75	21.48
200	100	28.65
250	100	22.92
250	125	28.65
250	150	34.38
300	100	19.10
300	125	23.87
300	150	28.65
400	150	21.09
400	200	28.65
500	200	22.92
500	250	28.65

Explanation of the Data

• Radius (mm): The radius of the circular object.
• Arc Length (mm): The length of the arc measured in millimeters.
• Angle (degrees): The angle subtended by the arc at the center of the circle, calculated using the formula θ = (s / r) × (180 / π).

MM to Degree Conversion Formula

The formula used for this conversion is derived from the arc length formula:

θ = (s / r) × (180 / π)

Where:

• θ (theta) is the angle in degrees
• s is the arc length in millimeters
• r is the radius in millimeters
• π (pi) is approximately 3.14159

• Calculate the radius: r = 200 mm / 2 = 100 mm
• Apply the formula: θ = (50 / 100) × (180 / π) ≈ 28.65 degrees

How to Convert mm to Degrees?

Converting millimeters to degrees involves a step-by-step process:

• Measure the arc length in millimeters.
• Determine the radius of the circle or circular segment.
• Apply the conversion formula: θ = (s / r) × (180 / π)
• Calculate the result to obtain the angle in degrees.

Let’s convert 75 mm to degrees on a circle with a radius of 120 mm.

Arc length (s) = 75 mm

Radius (r) = 120 mm

θ = (75 / 120) × (180 / π)

θ ≈ 35.83 degrees

How to Convert Numbers into Degrees?

In most cases, you’re dealing with a fraction of a full circle (360 degrees). Here’s approach:

Determine the total units that represent a full circle.

Divide your number by the total to get a fraction.

Multiply the fraction by 360 to get the equivalent in degrees.

Suppose you have a protractor marked from 0 to 100, and you want to convert the number 25 to degrees.

• Total units = 100
• Fraction = 25 / 100 = 0.25
• Degrees = 0.25 × 360 = 90 degrees

Sources / Reference URLs

• National Institute of Standards and Technology (NIST) – Units and Measurements
• Khan Academy – Radians and Degrees

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