Arch Arc Length Calculator
The Arch Arc Length Calculator finds the curved length of an arch from its radius and the angle it spans. The formula used is: Arc Length = r × θ, where θ is the central angle in radians (degrees × π/180).
Formula
Arc Length = r × θ (radians)
- The Arch Arc Length Calculator updates instantly as you change the radius or angle.
- Formula: Arc Length = r × θ, where θ is in radians
- Input definitions: • Radius: the radius of the arch's circular curve • Angle: the central angle the arch spans, in degrees
- The angle is converted to radians (degrees × π/180) before multiplying by the radius.
- Arc length uses the same unit as the radius (e.g. meters in, meters out).
- For a semicircular arch, the angle is 180°; for a quarter arch, 90°.
Example Calculation
Inputs
- Radius: 5
- Angle (degrees): 60
For a radius of 5 spanning 60°: θ = 60 × π/180 ≈ 1.0472 rad, so arc length = 5 × 1.0472 ≈ 5.24.
Frequently asked questions
How is the arch's arc length found?
Multiply the radius by the central angle in radians: arc length = r × θ. Degrees are first converted with × π/180.
What angle do I enter for a semicircular arch?
Use 180°, since a semicircle spans half of a full 360° circle.
What units does the result use?
The arc length is in the same unit as the radius you enter, whether feet or meters.
How do I find the radius if I know the span and rise?
For a circular arch, radius = (span²/4 + rise²) ÷ (2 × rise). Then use that radius here.
Is this the straight span or the curved length?
It is the curved length along the arch, which is longer than the straight horizontal span.