Quarter Circle Perimeter Calculator
Find the total perimeter of a quarter circle — the two straight radial edges plus the curved arc — given the radius.
P = 2r + πr/2 (two straight sides + arc)
- 1
Arc length = πr ÷ 2
π × 6 ÷ 2 = 9.4248 - 2
Straight sides = 2r
2 × 6 = 12 - 3
Perimeter = arc + straight sides
9.4248 + 12 = 21.4248The perimeter includes both straight radial edges plus the curved arc.
How does this calculator work?
Quarter circle perimeter = 2r + πr/2, where 2r is the two straight radial edges and πr/2 is the arc. Written as a multiple: P = r × (2 + π/2) ≈ r × 3.5708. For radius 6 that gives P ≈ 21.42. The arc alone is πr/2; the perimeter includes both straight sides too.
Formula
How this is calculated
The perimeter of a quarter circle is the total length of its boundary, which consists of three parts: two straight radial edges and one curved arc. Each straight edge has length r (the radius), so together they contribute 2r. The arc is one-quarter of the full circumference 2πr, giving arc length = 2πr/4 = πr/2. Adding all three gives P = 2r + πr/2, which can also be written as r × (2 + π/2) ≈ r × 3.5708.
For a radius of 6, for example: arc = π × 6 / 2 ≈ 9.425, straight sides = 12, total P ≈ 21.425. This is useful in construction when estimating trim or formwork length around a quarter-circle window, curved corner slab, or decorative arch — all three edges of the shape need measuring.
Note that "perimeter" means the complete outer boundary of the solid quarter-circle shape. If you only need the curved portion — for instance the length of a road curve or pipe bend — use just the arc length πr/2. To also compute the area or centroid of the quarter circle, see the full quarter-circle calculator.
Frequently asked questions
P = 2 × 10 + π × 10 / 2 = 20 + 5π ≈ 35.708 units. The arc contributes about 44% of the total perimeter; the two straight sides contribute the remaining 56%.
"Circumference" usually refers only to the curved arc: πr/2 (one-quarter of the full circle circumference 2πr). The perimeter is the complete boundary including the two straight radial edges: 2r + πr/2.
Solve P = r × (2 + π/2) for r: r = P ÷ (2 + π/2) ≈ P ÷ 3.5708. For example, if P = 35.708 then r ≈ 10.
Also known as
TG we-Calculate Editorial Team. (2026). Quarter Circle Perimeter Calculator [Online calculator]. TG we-Calculate. https://we-calculate.com/calculator/quarter-circle-perimeter-calculator
TG we-Calculate Editorial Team. "Quarter Circle Perimeter Calculator." TG we-Calculate. 2026. https://we-calculate.com/calculator/quarter-circle-perimeter-calculator.
TG we-Calculate Editorial Team, "Quarter Circle Perimeter Calculator," TG we-Calculate, 2026. [Online]. Available: https://we-calculate.com/calculator/quarter-circle-perimeter-calculator
@misc{wecalculate_quarter_circle_perimeter_calculator, title = {Quarter Circle Perimeter Calculator}, author = {{TG we-Calculate Editorial Team}}, howpublished = {\url{https://we-calculate.com/calculator/quarter-circle-perimeter-calculator}}, year = {2026}, note = {TG we-Calculate} }
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