📏 Arc Length Calculator
Instantly calculate arc length, sector area, and chord length of a circle.
Formulas (Angle θ in Radians)
- Arc Length = r × θ
- Sector Area = ½ × r² × θ
- Chord Length = 2r × sin(θ/2)
- 1 Radian ≈ 57.2958 Degrees
The Comprehensive Guide to Arc Length Calculator
What is a Arc Length Calculator?
An Arc Length Calculator is a specialized geometric tool used to find the exact distance along the curved edge of a circle (the arc).
By providing the radius of the circle and the central angle (in either degrees or radians), the calculator instantly determines the arc length, the total area of that pie-shaped sector, and the straight "chord" distance connecting the two endpoints of the arc.
The Mathematical Formula
This tool utilize standardized mathematical formulas and logic to calculate precise Arc Length results.
Calculation Example
Let's calculate the Arc Length of a semi-circle (half of a circle). Radius = 10 units, and the Angle = 180 Degrees.
- First, convert 180° to Radians: 180 × (π / 180) = π radians.
- Arc Length = r × θ
- Arc Length = 10 × π
- Arc Length = 10 × 3.14159...
- Arc Length ≈ 31.4159 units
Notice this is exactly half of the standard circumference formula (2πr = 62.8318).
Strategic Use Cases
- Civil Engineering: Designing highway curves and calculating the precise length of banking turns required for safe vehicle traversal at high speeds.
- Manufacturing & Piping: Finding the exact length of material needed to bend a steel pipe or wire into a specific curved shape.
- Astronomy: Measuring the apparent distance between two stars in the night sky based on their angular separation and estimated distance from Earth.
Frequently Asked Questions
What is the difference between Arc Length and Sector Area?
The Arc Length is a 1-dimensional measurement of perimeter—it is the literal distance you would travel if you walked along the curved edge. Sector Area is a 2-dimensional measurement of space—it is the amount of surface area inside the entire 'pizza slice'.
What is a Chord?
A chord is a perfectly straight line segment that connects the two endpoints of an arc. While the arc travels along the curved boundary of the circle, the chord cuts straight through the interior space.
How accurate is this calculator?
Our calculator uses industry-standard formulas to provide the most accurate results possible. However, it should be used for informational purposes only and not as a basis for formal calculations or legal advice.