How to Calculate the Arc Length, Central Angle, and Circumference of a Circle

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Calculating a circle's arc length, central angle, and circumference are not just tasks, but essential skills for geometry, trigonometry and beyond. The arc length is the measure of a given section of a circle's circumference; a central angle has a vertex at the center of the circle and the sides that pass through two points on the circle; and circumference is the distance around the circle. The vertex is the center of the circle. Calculating each of these is easy if you have the right tools and you're using the proper formulas.

How to Calculate the Arc Length, Central Angle, and Circumference of a Circle
(Kelly Lawrence/Demand Media)

Things You'll Need

  • Protractor
  • Ruler
  • Calculator

Calculating the Central Angle

Step 1:

Place the origin of the protractor on the angle's vertex.

Kelly Lawrence/Demand Media
Step 2:

Place the base line of the protractor on one of the angle's sides.

Kelly Lawrence/Demand Media
Step 3:

Record the number on the protractor where the second side of the angle passes through the edge of the protractor. If the angle is larger than 90 degrees, record the top number; if the angle is smaller than 90 degrees, record the lower number. This is the measurement of your central angle.

Kelly Lawrence/Demand Media

Calculating Circumference

Step 1:

Measure from a point on the circle to the central angle's vertex to determine the radius of the circle.

Kelly Lawrence/Demand Media
Step 2:

Multiply the radius by pi, a constant that is equal to approximately 3.14.

Kelly Lawrence/Demand Media
Step 3:

Multiply the result by 2 to complete the circumference calculation.

Kelly Lawrence/Demand Media

Calculating Arc Length

Step 1:

Calculate the circle's circumference.

Kelly Lawrence/Demand Media
Step 2:

Calculate the central angle of your circle, using the protractor, then represent this angle as a fraction. As there are 360 degrees in all circles, make 360 the denominator of the fraction. The angle measurement is the numerator.

Kelly Lawrence/Demand Media
Step 3:

Divide the numerator by the denominator to place the number in decimal form.

Kelly Lawrence/Demand Media
Step 4:

Multiply the circumference by the decimal to learn the arc length of that section of the circle.

Kelly Lawrence/Demand Media

References

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