Geometry

Confusing Arc Length with Sector Area

Students use the arc length formula when they need sector area, or use the sector area formula when they need arc length.

Quick check

Why students make it

Both formulas use the same fraction of the circle, so they can look almost the same. The key difference is that arc length measures distance around the circle, while sector area measures space inside the circle.

The rule done right

Arc length is L=θ360⋅2πrL=\frac{\theta}{360}\cdot 2\pi r for degrees, and it has linear units. Sector area is A=θ360⋅πr2A=\frac{\theta}{360}\cdot \pi r^2, and it has square units.

Related resources

circlesarc-lengthsector-area