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Arc Length from Diameter (Formula & Examples)

Calculate arc length when a diagram gives diameter instead of radius. Conversion steps, L = (θ/360°) × πd, and worked examples included.

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Blueprint-style circular sector diagram for arc length guides

Quick Answer

r = d/2, then L = (θ/360°) × 2πr. Equivalent: L = (θ/360°) × πd without finding radius first.

Formula

  • r = d / 2
  • L = (θ / 360°) × πd
  • Same result either path

Introduction

Manufacturing drawings and architectural plans often label diameter because it spans the full width of a circular feature. Arc length formulas, however, are usually written with radius.

You can convert once with r = d/2 or skip the conversion entirely by using L = (θ/360°) × πd in degree measure.

Enter diameter directly in the Arc Length Calculator when that is what the plan shows.

Main Content

Why diameter appears on plans

Diameter is easy to measure with calipers across a full circular cross section. Radius requires locating the center, which may be off the sheet or buried inside a solid model.

Pipe schedules, manhole tables, and gear catalogs frequently list diameter first. Converting mentally saves time when you only need a short arc on a large circle.

Both conversion paths belong to the same family as the standard arc length formula; you are only swapping d for 2r in the circumference factor.

After converting, compare your result to the practice set in arc length examples, which includes a quarter-circle case starting from diameter.

Worked examples

Example A: d = 12 m, θ = 30°. Using L = (θ/360°) × πd gives L = (30/360) × 12π = π ≈ 3.142 m.

Example B: d = 8 m, θ = 90°. Radius is 4 m. L = (90/360) × 2π(4) ≈ 6.283 m. Direct diameter form: (90/360) × π(8) ≈ 6.283 m.

Example C: d = 20 m, θ = 45°. L = (45/360) × π(20) = 0.125 × 20π ≈ 7.854 m for a gentle bend on a large culvert.

FAQ

Must I always convert to radius?
No. The πd form is equivalent when θ is in degrees.
What if only radius is given?
Use the radius formulas directly. Diameter conversion is unnecessary.

Conclusion

Diameter is twice the radius. Pick one form, substitute carefully, and keep θ in degrees unless you switch to L = rθ with radians.

The calculator accepts either radius or diameter so you can mirror the plan labels exactly.

Use diameter in the tool