How to Calculate the Length of an Arch


Measuring the length of a arch is a fundamental concept that every student must understand as they delve into the increasingly advanced areas of geometry and trigonometry. Outside of schooling, this calculation is useful for architects and builders as they work to construct arches like hallways and doorways within structures. You need to know how to convert degrees into radians to accurately calculate the arch's length.

Things You'll Need

  • Protractor
  • Measuring tape or ruler
  • Measure the length of the arch's radius, the distance from the center of the arch to either edge. This is done by measuring the arch from base to base to determine the circumference and dividing by two. For small arches, use a ruler or yard stick. Larger arches will require a retractable tape measure.

  • Place a marking point at the center of the circumference to indicate the center point of the arch. Place your protractor on this center point and identify the degrees of the arch.

  • Multiply the number of degrees in the arch by 0.01745 to covert the degrees into radians. For example, if the arch is 180 degrees, it measures 3.14 radians.

  • Multiply the radians by the radius to find the the length of the arch. Using the same example, if the radius is 15, multiply 15 by 3.14 for a result of 47.115, which is the length of the arch.

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  • Photo Credit Thomas Northcut/Photodisc/Getty Images
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