Chord Length in Feet Calculator
Calculate the length of a chord in a circle by entering the radius and central angle. Get instant results with our interactive calculator.
Calculator
Please enter a valid radius greater than 0
Please enter a valid angle between 0 and 360
Result
Chord Length: 0 feet
Need to convert units?
Unit Converter
Interactive Visualization
This visualization shows how the chord length changes as you adjust the radius and central angle.
Blue line: Radius of the circle
Red line: Chord length
Green arc: Central angle
Chord Length Formula
The formula to calculate the chord length is:
c = 2r × sin(θ/2)
Where:
- c = chord length (feet)
- r = radius of the circle (feet)
- θ = central angle (radians, converted from degrees)
How to Calculate Chord Length
- Measure the radius of the circle in feet
- Determine the central angle in degrees
- Convert the central angle from degrees to radians (multiply by π/180)
- Apply the formula: c = 2r × sin(θ/2)
Note: The central angle must be measured in radians for the formula to work correctly. Our calculator automatically handles this conversion.
Practical Applications
Architecture
Architects use chord length calculations for designing arched windows, doorways, and circular structures. Knowing the chord length helps determine material requirements for curved elements.
Construction
Construction workers use chord measurements to build circular or semi-circular components like domes, arches, and curved walls. Precise chord measurements ensure proper fitting of materials.
Engineering
Engineers use chord length in designing circular bridges, tunnels, and circular water tanks. It helps in calculating material quantities and structural stability.
Landscaping
Landscape architects use chord measurements to design circular garden beds, pathways, and water features. It helps in accurate layout planning and material estimation.
Example Calculation
Problem: Find the chord length in a circle with radius 10 feet and a central angle of 60 degrees.
Step 1: Convert 60 degrees to radians: 60 × (π/180) = π/3 radians
Step 2: Apply the formula: c = 2 × 10 × sin(π/6) = 20 × 0.5 = 10 feet
Answer: The chord length is 10 feet.
Common Questions About Chord Length
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 of a circle, passing through the center.
What’s the difference between an arc and a chord?
An arc is a portion of the circumference of a circle, while a chord is a straight line connecting two points on the circumference. The chord creates a “shortcut” across the circle.
How is chord length related to the central angle?
As the central angle increases (for a fixed radius), the chord length increases until the angle reaches 180 degrees, at which point the chord becomes the diameter. Beyond 180 degrees, the chord length decreases.
Can I calculate the central angle if I know the chord length and radius?
Yes, you can rearrange the chord length formula to find the central angle: θ = 2 × arcsin(c/(2r)), where c is the chord length and r is the radius.
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