Plot Area Calculator (8-Sided / Octagonal)
Estimate the area of an 8-sided octagonal plot from its eight side lengths. Cyclic-polygon method.
Construction
Plot Area Calculator (8-Sided / Octagonal)
Generated on April 29, 2026
Plot Shape (8 sides — cyclic polygon, max-area assumption)
Plot Pricing — convert any rate to all others
?What is the Plot Area Calculator (8-Sided / Octagonal)?
An 8-sided (octagonal) plot area calculator estimates the area of an octagonal land parcel from its eight side lengths using the cyclic-polygon method. Octagonal plots, while uncommon, do appear in real estate at four-way intersections where all four corners are chamfered (a classic 'octagon plot' visibility design), in roundabout-adjacent retail/commercial sites, in modernist parametric architectural plots, in agricultural land bounded by multiple natural features, and in landmark properties where octagonal symmetry is intentional (mosques, gardens, decorative pavilions). Since eight side lengths do not uniquely determine an octagon, the calculator returns the cyclic-octagon area — the maximum possible area for those sides — using a numerical circumradius solver.
The Formula
Eight-sided polygons have 5 degrees of geometric freedom beyond the side lengths. The cyclic octagon (all eight vertices on a circle) is the unique maximum-area configuration and is the standard surveying default. The calculator solves numerically for the circumradius R that makes the eight central angles sum to 360°, then sums eight triangle areas. For regular octagons (all sides equal length s), Area = 2 · (1 + √2) · s² ≈ 4.828 · s² — a useful sanity check.
Common Octagonal Plot Areas (cyclic estimate, 272 sq ft Marla)
Sample 8-sided plot configurations with cyclic-octagon area in standard Pakistani units.
| Sides (ft) | Cyclic Sq ft | Marla | Kanal | Acre |
|---|---|---|---|---|
| 20 × 20 × 20 × 20 × 20 × 20 × 20 × 20 (regular) | 1,931 | 7.10 | 0.355 | 0.0443 |
| 30 × 30 × 30 × 30 × 30 × 30 × 30 × 30 (regular) | 4,345 | 15.97 | 0.799 | 0.0998 |
| 40 × 40 × 40 × 40 × 40 × 40 × 40 × 40 (regular) | 7,725 | 28.40 | 1.420 | 0.1774 |
| 50 × 50 × 50 × 50 × 50 × 50 × 50 × 50 (regular) | 12,070 | 44.38 | 2.219 | 0.2772 |
| 60 × 30 × 60 × 30 × 60 × 30 × 60 × 30 | 8,700 | 31.99 | 1.599 | 0.200 |
| 70 × 50 × 70 × 50 × 70 × 50 × 70 × 50 | 14,360 | 52.79 | 2.640 | 0.330 |
| 100 × 80 × 90 × 70 × 100 × 80 × 90 × 70 | 24,140 | 88.75 | 4.438 | 0.554 |
Put It in Perspective
A 30-Marla chamfered octagonal corner plot is prime retail real estate at any urban four-way intersection.
Regular octagonal mosque precincts often fall in the 1–3 Kanal range.
Decorative pavilion octagons (gardens, exhibition halls) are typically 7–15 Marla.
Agricultural octagons over 1 acre are usually canal-belt parcels with multiple natural boundaries.
Practical Examples
A regular octagonal plot with each side 30 ft has area ≈ 4,345 sq ft ≈ 15.97 Marla — a notable retail commercial plot.
A four-way-junction octagon (4 chamfered corners) 60 × 30 × 60 × 30 × 60 × 30 × 60 × 30 ft cyclic area ≈ 8,700 sq ft ≈ 32.0 Marla.
Mosque-precinct octagon 50 × 50 × 50 × 50 × 50 × 50 × 50 × 50 ft (regular) = 12,070 sq ft ≈ 44.4 Marla ≈ 2.22 Kanal.
Agricultural irregular octagon 100 × 80 × 90 × 70 × 100 × 80 × 90 × 70 ft cyclic area ≈ 24,140 sq ft ≈ 0.55 acres.
Decorative pavilion plot 40 × 40 × 40 × 40 × 40 × 40 × 40 × 40 ft = 7,725 sq ft ≈ 28.4 Marla.
Roundabout commercial octagon 70 × 50 × 70 × 50 × 70 × 50 × 70 × 50 ft cyclic area ≈ 14,360 sq ft ≈ 52.8 Marla ≈ 2.64 Kanal.
Frequently Asked Questions
Popular Conversions
Jump to a ready-made conversion — useful for quick reference and sharing: