Segment Height of Circle Calculator

Calculate Segment Height, Radius, or Chord Length

Enter the circle's radius.
Enter the chord length of the segment.
Enter the height of the circular segment.

Note: Please fill in exactly two of the three fields above to calculate the third.

Unlock the geometry of circles with our free Segment Height of Circle Calculator. Quickly determine the height of a circular segment, radius, or chord length by providing two known values. Ideal for students, engineers, and designers needing precise measurements for arcs and segments. Simplify complex calculations instantly!

Formula:

The relationship between Segment Height (h), Radius (R), and Chord Length (c) is derived from geometric principles, typically involving the Pythagorean theorem. You can find any one variable if the other two are known:

  • To find Segment Height (h): h = R - √(R² - (c/2)²)
  • To find Chord Length (c): c = 2 × √(h × (2R - h))
  • To find Radius (R): R = (c² / (8 × h)) + (h / 2)

Where:

  • h = Segment Height (also known as Arc Height or Sagitta)
  • R = Radius of the Circle
  • c = Chord Length of the Circular Segment

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