How to calculate the radius chord offset

Updated March 23, 2017

Civil engineers use the geometric properties of circles to measure and construct smooth curves. Circles encompass all the points in a plane equidistant from a central point. A line extending from the centre of the circle to any point on the circle is called the radius. Any line not passing through the centre while connecting two points on a circle is called a chord. Engineers can determine the dimensions of a curve by stretching a string across two tangent points, marking the midpoint of the chord and calculating the offset of the chord from the midpoint to the arc using basic trigonometry.

Connect two tangent points along an arc and measure the total distance between the two. Record the distance and make note of the unit of measurement. Divide the total distance in half and mark the chord connecting the two tangent points at the midpoint.

Measure from the centre point through the midpoint to the arc. The total distance along that line is the radius of the arc.

Draw a line the length of the radius between each tangent point and the centre point of the arc.

Calculate the length of the line between the midpoint of the chord and the centre point of the arc using the Pythagorean theorem. (See Resources for an explanation of the Pythagorean theorem.) Find the square root of the difference between the square of the radius and the square of half the length of the chord.

Subtract the length of the line between the midpoint of the chord and the centre point of the arc from the total length of the radius. The difference between the two is the radius chord offset.

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Sean Butner has been writing news articles, blog entries and feature pieces since 2005. His articles have appeared on the cover of "The Richland Sandstorm" and "The Palimpsest Files." He is completing graduate coursework in accounting through Texas A&M University-Commerce. He currently advises families on their insurance and financial planning needs.