Arc Length in Feet Calculator
Accurately calculate the length of a circular arc with our intuitive geometry calculator
Arc Length Calculator
Enter the radius and angle to calculate the arc length using the formula: s = r × θ (where θ is in radians)
Interactive Visualization
This visual representation shows how the arc changes as you adjust the radius and angle values.
Understanding the Visualization
- The blue circle represents the full circle with your specified radius
- The red arc shows the portion of the circle based on your angle
- The green line represents the radius
Understanding Arc Length
The Mathematics Behind Arc Length
Arc length is the distance along a curved line making up a section of a circle. When we know the radius of a circle and the angle subtended by an arc, we can calculate the arc length.
Arc Length Formula
The formula for calculating arc length is:
Where:
- s = arc length
- r = radius of the circle
- θ = angle in radians
Important Note: Converting Degrees to Radians
Since angles are typically measured in degrees, but the formula requires radians, we need to convert:
This conversion is automatically handled by our calculator.
Step-by-Step Calculation
-
Measure the radius (r)
The radius is the distance from the center of the circle to any point on its circumference, measured in feet.
-
Determine the angle (θ) in degrees
This is the angle subtended by the arc at the center of the circle.
-
Convert the angle to radians
Multiply the angle in degrees by π/180.
-
Apply the formula
Multiply the radius by the angle in radians to get the arc length.
Example Calculation
For a circle with a radius of 5 feet and an arc that subtends an angle of 60 degrees:
- Radius (r) = 5 feet
- Angle (θ) = 60 degrees = 60 × (π/180) = π/3 radians
- Arc Length (s) = r × θ = 5 × (π/3) ≈ 5.24 feet
Practical Applications of Arc Length Calculation
Construction & Architecture
- Designing archways and curved structural elements
- Calculating material needs for curved walls
- Planning circular staircases and railings
- Creating accurate dimensions for arched doorways and windows
Civil Engineering
- Designing curved road sections and highway ramps
- Planning railway curves and determining proper banking
- Creating accurate layouts for curved bridges
- Calculating material requirements for circular infrastructure
Landscape Design
- Designing curved garden paths and borders
- Planning circular water features and fountains
- Creating arched trellises and garden structures
- Calculating material needs for curved retaining walls
Additional Real-World Applications
Manufacturing
In manufacturing, arc length calculations are essential for creating curved components, determining material requirements for circular products, and designing specialized tooling for curved surfaces.
Astronomy
Astronomers use arc length calculations to measure angular distances between celestial objects and to determine the size of features on planetary surfaces.
Navigation
Sailors and pilots use arc length calculations to determine distances along great circle routes, which are the shortest paths between two points on a sphere like Earth.
Optics
Lens designers use arc length calculations to design curved optical surfaces that focus light correctly for cameras, telescopes, and other optical instruments.
Related Geometry & Trigonometry Calculators
Diagonal Length Calculator
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Right Triangle Hypotenuse
Find the hypotenuse of a right triangle using the Pythagorean theorem with sides measured in feet.
Arc Length Calculator
Calculate the length of an arc based on radius and angle measurements in feet.
Chord Length Calculator
Determine the length of a chord in a circle based on radius and angle in feet.
Sector Area Calculator
Calculate the area of a sector of a circle in square feet based on radius and angle.
Polygon Perimeter Calculator
Find the perimeter of regular and irregular polygons with sides measured in feet.
Circle Circumference
Calculate the circumference of a circle in feet using radius or diameter measurements.
Cone Surface Area
Calculate the total surface area of a cone in square feet using radius and height.
Pyramid Surface Area
Find the total surface area of a pyramid in square feet based on base dimensions and height.
Slope Length Calculator
Calculate the length of a slope in feet using horizontal distance and height difference.