1. What is Chord Height?

The chord height (or sagitta) is the perpendicular distance from the chord to the circumference of the circle. It represents how "deep" the chord is within the circle.

2. How Does the Calculator Work?

The calculator uses the chord height formula:

Where:

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

Explanation: The formula calculates how much the chord "sags" from the circle's circumference by using the Pythagorean theorem on the right triangle formed by the radius, half-chord, and radius minus height.

3. Applications of Chord Height

Details: Chord height calculations are used in architecture (arch design), engineering (circular structures), astronomy (measuring apparent sizes), and various geometric applications.

4. Using the Calculator

Tips: Enter both radius and chord length in meters. Both values must be positive numbers. The chord length must be less than or equal to the diameter (2 × radius).

5. Frequently Asked Questions (FAQ)

Q1: What if my chord length is greater than the diameter?
A: The chord length cannot exceed the diameter (2 × radius) of the circle. Such input would be invalid.

Q2: Can I use different units?
A: Yes, as long as both radius and chord use the same units. The result will be in those same units.

Q3: What's the maximum possible chord height?
A: The maximum height equals the radius, which occurs when the chord length approaches zero.

Q4: How is this related to circular segment area?
A: The chord height is crucial for calculating the area of a circular segment (the region between the chord and the arc).

Q5: Is there an inverse formula to find radius from height and chord?
A: Yes: \( r = \frac{h}{2} + \frac{c^2}{8h} \)