1. Measure radius
Measure from circle center to edge in feet.
What is sector square footage?
A circular sector square footage equals the central angle divided by 360, times pi, times radius squared. Apply Area = (angle ÷ 360) × π × r². A 90° sector with a 10 ft (3.05 m) radius has 78.54 sq ft (7.30 m²). For a full round area, use the circle calculator.
Getting started
How to Calculate Sector Square Footage
To calculate sector square footage, measure the radius (from circle center to edge) and the central angle in degrees. Apply Area = (angle ÷ 360) × π × r². A 90° sector covers one quarter of a full circle.
2. Measure central angle
Measure the central angle of the sector in degrees.
3. Apply sector formula
Sector area = (angle ÷ 360) × π × r². A 90° sector with 10 ft radius has 78.54 sq ft.
Quick reference
Reference
1 acre = 43,560 square feet
1 square yard = 9 square feet
1 square meter = 10.764 square feet
1 square inch = 0.00064516 square feet
Material pricing
Calculate Cost of Materials
Sector area times price per unit equals material cost. Apply to pie-slice patios, rounded garden corners, and fan-shaped pavings.
There are 2 steps to calculate material cost:
- Enter the price per square foot of pavers, concrete, or sod covering the sector area.
- The Square Foot Calculator multiplies sector area by the unit price for material total.
Sector shapes have curved arcs. Add 12-15% extra paving or sod for cuts along the curve.
FAQ
Frequently Asked Questions
How do I calculate the square footage of a sector?
Use the formula: Area = (angle/360) x pi x radius squared. Enter the radius and central angle in the Sector Square Foot Calculator for instant results in multiple units.
What is a sector in geometry?
A sector is a pie-shaped slice of a circle defined by two radii and the arc between them. The central angle determines what fraction of the full circle the sector represents.
How many square feet is a quarter-circle with a 10-foot radius?
A quarter-circle (90-degree sector) with a 10-foot radius is 78.54 square feet because (90/360) x pi x 10 squared = 78.54 sq ft.
How do I calculate a half-circle area?
A half-circle (180-degree sector) area equals pi x radius squared divided by 2. For a 12-foot diameter half-circle patio, the radius is 6 feet, so the area is 3.14159 x 36 / 2 = 56.55 sq ft.
When would I use a sector calculation?
Use sector calculations for curved patios, rounded garden beds, pie-shaped lots, and any wedge-shaped area. It is also useful for calculating material needs for curved walkways and radial landscape features.
Can I calculate a sector if I only know the arc length?
Yes, if you know the arc length and radius, calculate the angle first: angle = (arc length / radius) x (180/pi). Then use the standard sector area formula with that angle.
REFERENCES
Further Reading & References
Trusted external sources and related sections on this site. External links open authoritative references on Wikipedia and government agencies.
Explore this Square Foot Calculator site
Authoritative external references
- WIKICircular sector — Wikipedia
- WIKICircle — Wikipedia
- WIKIArea — Wikipedia