Chord Length Calculator
Calculate the length of a chord in a circle based on radius and central angle.
Chord Calculation Results
Chord Length:
Formula Used:
Calculation:
About Our Chord Length Calculator
Our Chord Length Calculator is a precise tool designed to calculate the length of a chord in a circle based on the circle's radius and the central angle. This tool is essential for geometry problems, engineering applications, and various real-world scenarios involving circular structures.
What Is a Chord?
In geometry, a chord is a straight line segment whose endpoints both lie on a circle. The diameter is the longest chord in a circle, passing through the center. Any other chord is shorter than the diameter and does not pass through the center of the circle.
The Chord Length Formula
The formula for calculating the length of a chord is:
Chord Length = 2 × r × sin(θ/2)
Where:
- r is the radius of the circle
- θ is the central angle in radians (the angle formed at the center of the circle by the two radii connecting to the chord endpoints)
Key Features:
- Calculate chord length using radius and central angle
- See the step-by-step calculation with formula breakdown
- User-friendly interface for quick geometric calculations
- Accurate results for all valid input values
How to Use:
- Enter the radius of the circle
- Enter the central angle in degrees
- Click "Calculate Chord Length" to see the results
Real-World Applications:
Architecture: Calculate chord lengths for designing arched structures or circular elements.
Engineering: Determine measurements for circular components in mechanical designs.
Construction: Plan and implement curved structural elements accurately.
Astronomy: Calculate chord lengths related to celestial observations and orbital mechanics.
Landscaping: Design circular garden features with precise measurements.
Circle Geometry Relationships
Understanding chord length is part of a broader set of relationships in circle geometry:
- Diameter: A special chord that passes through the center of the circle and is equal to twice the radius.
- Arc: The portion of the circle's circumference between the two endpoints of a chord.
- Sagitta: The perpendicular distance from the midpoint of a chord to the arc it subtends.
- Sector: The region bounded by two radii and the arc between their endpoints.
Our calculator focuses specifically on finding the chord length based on radius and central angle information.
Ideal for students, teachers, engineers, architects, or anyone working with circular designs and geometric calculations. Start calculating chord lengths today!
Frequently Asked Questions
What is the relationship between chord length and arc length?
Chord length and arc length are related but different measurements. While the chord is a straight line connecting two points on a circle, the arc is the curved portion of the circle's circumference between those same points. For small angles, the chord length approaches the arc length, but as the angle increases, the difference becomes more pronounced. The arc length is calculated using the formula: Arc Length = r × θ, where r is the radius and θ is the central angle in radians.
Can I calculate the central angle if I know the chord length and radius?
Yes, you can derive the central angle if you know the chord length (c) and radius (r) using the formula: θ = 2 × arcsin(c/(2r)), where θ is the central angle in radians. To convert to degrees, multiply by 180/π. This is essentially the reverse of the chord length calculation and is useful when working with known physical measurements to determine angles.
What happens if the central angle is 180 degrees?
When the central angle is 180 degrees (π radians), the chord becomes a diameter of the circle. In this case, the chord length equals twice the radius of the circle. This is because sin(180°/2) = sin(90°) = 1, so the formula gives: Chord Length = 2 × r × sin(180°/2) = 2 × r × 1 = 2r, which is the diameter of the circle.