1. What is the Chord Length Equation?

The chord length equation calculates the straight-line distance between two points on a circle's circumference when you know the circle's radius and the perpendicular height from the chord to the circle's center.

2. How Does the Calculator Work?

The calculator uses the chord length equation:

Where:

• \( c \) — Chord length
• \( r \) — Radius of the circle
• \( h \) — Perpendicular height from chord to center

Explanation: The equation is derived from the Pythagorean theorem applied to the right triangle formed by the radius, half the chord, and the perpendicular height.

3. Importance of Chord Length Calculation

Details: Chord length calculations are essential in geometry, engineering, and architecture for designing circular structures, calculating segment areas, and solving various geometric problems involving circles.

4. Using the Calculator

Tips: Enter the radius and height in the same units. The height must be less than the radius for a valid chord length. All values must be positive numbers.

5. Frequently Asked Questions (FAQ)

Q1: What if the height equals the radius?
A: When h = r, the chord length becomes zero, which means the "chord" is actually just a single point on the circle's circumference.

Q2: Can the height be greater than the radius?
A: No, the height cannot exceed the radius as that would place the chord outside the circle, which is geometrically impossible.

Q3: What units should I use?
A: You can use any units (cm, m, inches, etc.) as long as both radius and height are in the same units.

Q4: How is this related to circular segments?
A: The chord length is needed to calculate the area of a circular segment, along with the radius and central angle.

Q5: Can this calculate arc length?
A: No, this calculates chord length (straight-line distance). Arc length requires different calculations involving the central angle.