The Arc Length Calculator helps you find the curved distance of an arc on a circle or curve — using radius & angle (degrees or radians), or even the chord length.
It also provides the sector area and central angle automatically for complete geometric analysis.

• Supports calculations in degrees, radians, and chord-based modes.
• Instant results for arc length, radius, diameter, sector area, and angle.
• Accurate up to four decimal points with automatic unit conversion (in, ft, cm, m).
• Perfect for geometry, welding, design, architecture, and engineering fields.

The length of an arc represents the curved distance along a circle or curve between two points.
There are several ways to calculate the arc’s length depending on which values are known — angle (in degrees or radians) or chord length.

1. Using Degrees:
s = (θ / 360) × 2πr
where θ is the central angle in degrees and r is the radius.

2. Using Radians:
s = rθ
This is the simplest and most direct form — ideal when the angle is given in radians.

3. Using Chord Length:

θ = 2sin⁻¹(c / 2r) → s = rθ

Here c is the chord connecting the arc’s endpoints — this method allows you to find the arc length even when the angle is unknown.

The arc length and the sector area are closely related — both depend on the circle’s radius and central angle (θ).
While arc length measures the curved distance along the circle’s edge, the sector area measures the surface enclosed by that arc and its radii.

1. Arc Length Formula:

s = (θ / 360) × 2πr   or   s = rθ

2. Sector Area Formula:

A = ½ × r²θ   or   A = (θ / 360) × πr²

This shows that both formulas share the same variables — radius and angle — but differ in how they use them to express distance vs area.

In practical terms, knowing any two values (arc length, angle, or radius) allows you to find the third, as both equations are interdependent in circular geometry.

Here are three practical examples showing how to calculate arc length and sector area under different conditions:

• ① r = 10 in, θ = 60° →
  s = (60 / 360) × 2π × 10 = 10.47 in,
  A = (60 / 360) × π × 10² = 52.36 in²
• ② r = 12 cm, θ = 1.2 rad →
  s = rθ = 12 × 1.2 = 14.4 cm,
  A = ½ × 12² × 1.2 = 86.4 cm²
• ③ r = 20 m, chord c = 18 m →
  θ = 2sin⁻¹(18 / (2×20)) = 1.047 rad →
  s = rθ = 20 × 1.047 = 20.94 m

This table helps visualize how the length of arc and sector area vary with radius and angle across different unit systems — making it useful for geometry, design, and construction work.

This versatile geometry calculator is used across many technical and creative fields to determine the length of an arc and related values.
Whether you’re working in construction, design, or education, precise arc measurements are essential for accuracy and professional results.

• Geometry & Education: Visualize how radius, angle, and arc relate — perfect for teaching circle theorems and trigonometry.
• Welding & Fabrication: Determine arc length in welding to ensure proper current, penetration, and joint precision.
• Design & Architecture: Plan arches, bridges, domes, or curved layouts accurately using radius and arc angle.
• Engineering & CAD: Use for curvature and path design when modeling circular or spiral structures in CAD software.

While calculating arc length or sector area, small input errors can cause large deviations.
Here are the most common mistakes users make — and how to avoid them:

• 🔹 Mixing degrees and radians: Always confirm the angle unit before applying a formula. Using degrees in a radian-based formula will make the arc appear 57× too long.
• 🔹 Using full circumference (2πr) instead of the fractional arc: Remember to multiply by the ratio (θ / 360) or use radians directly.
• 🔹 Incorrect chord vs. arc use: The chord is the straight line between endpoints; the arc is the curved path — don’t substitute one for the other.
• 🔹 Mixing units (inches, cm, meters): Make sure all measurements are in the same unit before calculation to avoid scaling errors.

1) What is arc length?
Arc length is the curved distance along a circle between two points on its circumference. It’s a fraction of the full circumference (2πr) based on the central angle.

2) What is the arc length formula in degrees?
Use s = (θ/360) × 2πr, where θ is in degrees and r is the radius.

3) What is the arc length formula in radians?
Use the direct form s = rθ with θ in radians.

4) How do I find arc length with a chord?
First find the angle via θ = 2·sin⁻¹(c / 2r), then compute s = rθ. Here c is the chord length.

5) What’s the difference between arc length and chord length?
The arc is the curved path; the chord is the straight line connecting the endpoints. The chord is always shorter than its corresponding arc (except when θ → 0).

6) How do I get sector area from arc length?
If you know s and r, then θ = s / r (radians) and A = ½·r²·θ. In degrees: A = (θ/360)·πr².

7) Do I need to convert degrees to radians?
Only when you use the radian formula (s = rθ). The calculator accepts both and converts automatically; just ensure the selected unit matches your input.

The Arc Length Calculator provides accurate results for the length of arc, along with radius, angle, and sector area — all from a single input.
It automatically converts between degrees, radians, and chord-based measurements, giving you the length of the arc and area instantly — ideal for students, engineers, and designers.

Use these related tools to explore other geometry calculations:

• Circle Area Calculator → for perfect circles
• Rectangle Area Calculator → for right angles
• Triangle Area Calculator → for 3-sided shapes
• Trapezoid Area Calculator → for parallel sides

For more details on formulas and derivations, visit

Wikipedia – Arc Length Formula & Geometry
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