Degrees To MM Calculator – Convert Degree to MM

Use our degrees to mm calculator to convert angular measurements in degrees to linear measurements in millimeters (mm).

For example…

• 30 degrees to mm: If we have a circle with a radius of 100 mm, and we want to know the length of an arc that spans 30 degrees, the calculator would help us determine that it’s approximately 52.36 mm.
• 90 degrees to mm: Using the same circle (radius 100 mm), a 90-degree arc would be about 157.08 mm long.
• 180 degrees to mm: Half of the circle’s circumference, represented by 180 degrees, would measure roughly 314.16 mm.

Degrees To MM Calculator

Angle (degrees)	Radius (mm)	Result (mm)	Conversion Equation	Usage Purpose
30	100	52.36	mm = (2 π 100 * 30) / 360	Calculating arc length for gear tooth design
45	50	39.27	mm = (2 π 50 * 45) / 360	Determining material length for curved molding
90	75	117.81	mm = (2 π 75 * 90) / 360	Measuring quarter-circle pipe bend length
120	200	418.88	mm = (2 π 200 * 120) / 360	Calculating fan blade sweep distance
180	150	471.24	mm = (2 π 150 * 180) / 360	Determining semicircle cutting path length
270	80	376.99	mm = (2 π 80 * 270) / 360	Measuring three-quarter circle track length
360	100	628.32	mm = (2 π 100 * 360) / 360	Calculating full circumference of a wheel

Degrees to MM Formula

The general formula is:

mm = (2 π r * θ) / 360

Where:

• mm is the length in millimeters
• π (pi) is approximately 3.14159
• r is the radius of the circle in millimeters
• θ (theta) is the angle in degrees

This formula essentially calculates the length of an arc on a circle’s circumference based on the given angle and radius.

Let’s break down the formula with a few examples:

Example 1:

Convert 45 degrees to mm for a circle with a radius of 50 mm.

mm = (2 π 50 * 45) / 360

mm ≈ 39.27 mm

Example 2:

Find the mm equivalent of 120 degrees on a circle with a radius of 75 mm.

mm = (2 π 75 * 120) / 360

mm ≈ 157.08 mm

Example 3:

Calculate the mm length for a full rotation (360 degrees) on a circle with a radius of 100 mm.

mm = (2 π 100 * 360) / 360

mm ≈ 628.32 mm (which is the full circumference of the circle)

How to convert degree into mm?

Here’s a detailed explanation of how to perform this conversion:

1. Determine the radius: First, you need to know the radius of the circle or arc you’re working with. This is crucial because the same angle will result in different linear measurements depending on the circle’s size.
2. Identify the angle: Clarify the angle in degrees that you want to convert. This could be any value from 0 to 360 degrees (or even beyond for multiple rotations).
3. Apply the formula: Use the formula mm = (2 π r * θ) / 360. Here’s what each part means:
4. Multiply 2 by π (pi) and the radius (r) to get the circle’s circumference.
5. Multiply this by the angle in degrees (θ).
6. Divide the result by 360 to get the proportion of the circumference that corresponds to your angle.
7. Calculate: Plug in your values and perform the calculation. Be sure to use a calculator for precise results, especially when dealing with π.
8. Round appropriately: Depending on your application, you may need to round the result to a certain number of decimal places. In engineering and manufacturing, it’s common to work with tolerances, so be mindful of the required precision.
9. Check units: Ensure that your radius is in millimeters to get a result in millimeters. If your radius is in another unit, convert it to mm first.
10. Verify reasonableness: As a quick check, remember that a full circle (360 degrees) should equal the circumference (2πr). Use this to gauge whether your result makes sense.

How many degrees is 1 mm?

To find out how many degrees 1 mm represents, we need to rearrange our conversion formula:

θ = (360 mm) / (2 π * r)

Where:

• θ is the angle in degrees
• mm is 1 (since we’re asking about 1 mm)
• r is the radius of the circle in millimeters

Let’s explore this with a few examples to illustrate how the result changes based on the circle’s radius:

1. For a circle with a radius of 10 mm:

θ = (360 1) / (2 π 10) ≈ *5.73 degrees

1. For a circle with a radius of 100 mm:

θ = (360 1) / (2 π 100) ≈ *0.573 degrees

1. For a circle with a radius of 1000 mm:

θ = (360 1) / (2 π 1000) ≈ *0.0573 degrees

1 Degree to MM Conversion

To convert 1 degree to mm, we use our formula:

mm = (2 π r * θ) / 360

In this case, θ (theta) is always 1, as we’re converting 1 degree. Let’s break down the process:

1. Set up the equation: mm = (2 π r * 1) / 360
2. Simplify: mm = (π * r) / 180

This simplified form shows us that the mm length for 1 degree is directly proportional to the radius of the circle. Let’s look at some examples:

1. For a circle with a radius of 50 mm:

mm = (π 50) / 180 ≈ *0.873 mm

1. For a circle with a radius of 100 mm:

mm = (π 100) / 180 ≈ *1.745 mm

1. For a circle with a radius of 1000 mm:

mm = (π 1000) / 180 ≈ *17.45 mm

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