Plane Angle Conversion Calculator

The formula for plane angle is:

θ = s / r

Where:

θ is the angle in radians. s is the arc length of the sector. r is the radius of the circle.

Alternatively, we can use the formula:

θ = L / (2πr)

Where:

• θ is the angle in radians
• L is the length of the arc
• r is the radius of the circle
• π is the mathematical constant pi, approximately equal to 3.14159.

To convert an angle to a length, you need to know the radius of the circle and the measure of the angle in radians.

• Once you have these two values, you can use the formula:

Length of arc = radius × angle in radians

• For example, if you have a circle with a radius of 5 units and an angle of 60 degrees, you would first convert the angle to radians:

60 degrees × (π/180) = 1.047 radians

• Then, you can use the formula to find the length of the arc:

Length of arc = 5 × 1.047 = 5.236 units

So the length of the arc is approximately 5.236 units.

• To convert a number to an angle in degrees, you need to know the relationship between degrees and radians. One full circle is 360 degrees or 2π radians. Therefore, we can use the following formula to convert from radians to degrees:

Angle in degrees = Angle in radians × (180/π)

• So to convert a given number to an angle in degrees, follow these steps:

1. Determine whether the given number is in radians or some other unit of measure.

2. If the given number is in radians, multiply it by (180/π) to convert it to degrees.

• For example, let's say we have an angle of 2.5 radians that we want to convert to degrees:

Angle in degrees = 2.5 radians × (180/π) = 143.24 degrees

Therefore, an angle of 2.5 radians is equivalent to 143.24 degrees.