Circular Arc Calculator
Compute Radius, Chord, Height, Arc Length & Angle
Arc Diagram
Calculation Results
How to Use the Circular Arc Calculator
This calculator helps you determine the properties of a circular arc when you know at least two of the following measurements: radius, chord length, arc height (sagitta), arc length, or central angle.
Step-by-Step Instructions
- Select your preferred units (Imperial or Metric) using the toggle buttons.
- Enter any two known values in the input fields.
- Click the "Calculate" button to compute all other arc properties.
- View the results in the output section and see the visual representation in the diagram.
Input Variables Explained
- Radius (R): The distance from the center of the circle to any point on the arc.
- Chord (C): The straight line distance between the two endpoints of the arc.
- Height/Sagitta (S): The vertical distance from the midpoint of the chord to the arc.
- Arc Length: The distance along the curved line of the arc.
- Central Angle (θ): The angle subtended by the arc at the center of the circle.
Formulas Used
Chord from Radius and Angle: C = 2R × sin(θ/2)
Sagitta from Radius and Chord: S = R - √(R² - (C/2)²)
Arc Length from Radius and Angle: L = R × θ (θ in radians)
Central Angle from Arc Length and Radius: θ = L / R (in radians)
Real-World Use Cases
Architecture & Construction
Calculate arch dimensions for doorways, windows, and structural elements in buildings and bridges.
Woodworking & Carpentry
Determine the curvature for arched furniture, cabinetry, decorative elements, and handrails.
Metalworking & Pipe Bending
Calculate bend angles and arc lengths for pipes, tubes, and metal fabrication projects.
Landscaping & Hardscaping
Design curved pathways, garden beds, and other landscape features with precise arc measurements.
Frequently Asked Questions
The sagitta (also called the versine) is the height of an arc, measured as the perpendicular distance from the midpoint of the chord to the arc itself. It represents how much the arc "rises" above its chord.
Use the formula: R = (C² + 4S²) / (8S), where C is the chord length and S is the sagitta (height). Our calculator automatically computes this when you enter the chord and height values.
A minor arc is the shorter arc between two points on a circle, with a central angle less than 180°. A major arc is the longer arc between two points, with a central angle greater than 180°. This calculator focuses on minor arcs by default.
Yes! Use the Advanced Options tab to input diameter instead of radius. The calculator will automatically convert between radius and diameter (Diameter = 2 × Radius).
You can use both Imperial (inches, feet) and Metric (millimeters, centimeters, meters) units for length measurements. For angles, you can choose between degrees and radians.