1. What is Chord Height (Sagitta)?

The chord height (or sagitta) is the distance from the center of a chord to the circumference of the circle, measured perpendicular to the chord. It represents the "height" of the circular segment formed by the chord.

2. How Does the Calculator Work?

The calculator uses the sagitta formula:

Where:

• \( h \) — Chord height/sagitta (cm)
• \( r \) — Radius of the circle (cm)
• \( c \) — Length of the chord (cm)

Explanation: The formula calculates the perpendicular distance from the chord to the circle's edge by using the Pythagorean theorem on the right triangle formed by the radius, half-chord, and radius-minus-height.

3. Practical Applications

Details: Sagitta calculations are used in engineering (arch design), optics (lens curvature), manufacturing (circular segment measurements), and architecture (dome construction).

4. Using the Calculator

Tips: Enter both radius and chord length in centimeters. Both values must be positive numbers. The chord length cannot exceed the circle's diameter (2×radius).

5. Frequently Asked Questions (FAQ)

Q1: What if my chord is longer than the diameter?
A: The calculator will return an error (NaN) since mathematically, a chord cannot be longer than the diameter of its circle.

Q2: How precise are the results?
A: Results are precise to 4 decimal places, suitable for most engineering and manufacturing applications.

Q3: Can I use this for imperial units?
A: While the calculator displays cm, you can use any consistent unit system (inches, mm, etc.) as long as both inputs use the same units.

Q4: What's the relationship between sagitta and arc height?
A: For small segments, sagitta approximates arc height. For larger segments, they diverge as the arc height becomes greater than the sagitta.

Q5: How is this different from circular segment area?
A: Sagitta is just one dimension of a circular segment. Area calculations require additional geometric relationships.