GeometryFormula

Arc Length Practice Problems

15 arc length problems with full worked solutions, graded from warm-up to stretch — plus an unlimited supply you can generate yourself. Every answer is computed by the same verified function that powers the arc length explorer, so the solutions cannot disagree with the formulas. Free, no account, nothing to install.

Formulas you need

  • Arc length (degrees): L=θ360⋅2πrL = \dfrac{\theta}{360}\cdot 2\pi r
  • Arc length (radians): L=rθL = r\theta

where r = radius, θ = central angle (degrees), L = arc length

Generate a new problem

Pick a difficulty, work it out, then check your answer. Every press gives a new question — the numbers are drawn fresh each time, so you can keep going.

Warm-up

  1. A circle of radius r = 1 has a central angle of 180°. Find the arc length (L).

    Answer & working

    3.14 units

    L = (θ/360) · 2πr = (180/360) · 2π · 1 ≈ 3.14

  2. A circle of radius r = 4 has a central angle of 120°. Find the arc length (L).

    Answer & working

    8.38 units

    L = (θ/360) · 2πr = (120/360) · 2π · 4 ≈ 8.38

  3. A circle of radius r = 5 has a central angle of 45°. Find the arc length (L).

    Answer & working

    3.93 units

    L = (θ/360) · 2πr = (45/360) · 2π · 5 ≈ 3.93

  4. A circle of radius r = 5 has a central angle of 150°. Find the arc length (L).

    Answer & working

    13.09 units

    L = (θ/360) · 2πr = (150/360) · 2π · 5 ≈ 13.09

  5. A circle of radius r = 2 has a central angle of 30°. Find the arc length (L).

    Answer & working

    1.05 units

    L = (θ/360) · 2πr = (30/360) · 2π · 2 ≈ 1.05

Core practice

  1. A circle of radius r = 9 has a central angle of 135°. Find the arc length (L).

    Answer & working

    21.21 units

    L = (θ/360) · 2πr = (135/360) · 2π · 9 ≈ 21.21

  2. A circle of radius r = 5 has a central angle of 210°. Find the arc length (L).

    Answer & working

    18.33 units

    L = (θ/360) · 2πr = (210/360) · 2π · 5 ≈ 18.33

  3. A circle of radius r = 4 has a central angle of 30°. Find the arc length (L).

    Answer & working

    2.09 units

    L = (θ/360) · 2πr = (30/360) · 2π · 4 ≈ 2.09

  4. A circle of radius r = 6 has a central angle of 150°. Find the arc length (L).

    Answer & working

    15.71 units

    L = (θ/360) · 2πr = (150/360) · 2π · 6 ≈ 15.71

  5. A circle of radius r = 9 has a central angle of 270°. Find the arc length (L).

    Answer & working

    42.41 units

    L = (θ/360) · 2πr = (270/360) · 2π · 9 ≈ 42.41

Stretch

  1. A circle of radius r = 9.5 has a central angle of 270°. Find the arc length (L).

    Answer & working

    44.77 units

    L = (θ/360) · 2πr = (270/360) · 2π · 9.5 ≈ 44.77

  2. A circle of radius r = 5.5 has a central angle of 30°. Find the arc length (L).

    Answer & working

    2.88 units

    L = (θ/360) · 2πr = (30/360) · 2π · 5.5 ≈ 2.88

  3. A circle of radius r = 8.5 has a central angle of 60°. Find the arc length (L).

    Answer & working

    8.9 units

    L = (θ/360) · 2πr = (60/360) · 2π · 8.5 ≈ 8.9

  4. A circle of radius r = 10 has a central angle of 300°. Find the arc length (L).

    Answer & working

    52.36 units

    L = (θ/360) · 2πr = (300/360) · 2π · 10 ≈ 52.36

  5. A circle of radius r = 5.5 has a central angle of 135°. Find the arc length (L).

    Answer & working

    12.96 units

    L = (θ/360) · 2πr = (135/360) · 2π · 5.5 ≈ 12.96

Answers are recomputed from the verified arc length function every time this page is built, and every printed line is checked to evaluate correctly. Content last reviewed August 2026. Found a mistake? Tell us — we correct and republish.

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