Arc Length Calculator

Arc Length Formula

Worked Example

A circle of radius 6 with a 120° central angle:

1. s = rθ with θ in radians
2. θ = 2.0943951 rad
3. s = 6 × 2.0943951 = 12.56637061

Chord length 2r·sin(θ/2): 10.39230485 · Angle in radians: 2.094395102 · Angle in degrees: 120 · Fraction of the full circle: 0.3333333333

Test-day tip

SAT answers are often left in terms of π. Divide the decimal by π (12.566 ÷ π = 4) to match a choice like 4π.

More Geometry and Trigonometry Calculators

• Circle Equation Calculator

  (x − h)² + (y − k)² = r²

  from x² + y² + Dx + Ey + F = 0: h = −D/2, k = −E/2, r² = h² + k² − F

  Example: The circle x² + y² − 4x + 6y − 12 = 0: Center and radius: center (2, -3), r = 5.

  Open the circle equation calculator →

• Unit Circle Calculator

  (cos θ, sin θ) on x² + y² = 1

  tan θ = sin θ / cos θ; signs follow the quadrant (ASTC)

  Example: The angle 150°: Point on the unit circle (cos θ, sin θ) = (−√3/2, 1/2).

  Open the unit circle calculator →

• Distance Formula Calculator

  d = √[(x₂ − x₁)² + (y₂ − y₁)²]

  the Pythagorean theorem on the coordinate plane

  Example: The points (1, 2) and (7, 10): Distance d = 10.

  Open the distance formula calculator →

• Midpoint Calculator

  M = ((x₁ + x₂)/2, (y₁ + y₂)/2)

  endpoint: x₂ = 2Mx − x₁, y₂ = 2My − y₁

  Example: The segment from (−2, 3) to (6, −5): Midpoint = (2, -1).

  Open the midpoint calculator →

Frequently asked questions

Sources

Last reviewed: 2026-10-15. Factors are stored exactly and computed with 50-digit decimal arithmetic. See how we verify conversion factors.