Land Area Calculator

Use our Land Area Calculators to compute plot area with six common shapes

Land Area Formulas for Common Field Shapes

This section lists the standard area formulas used in land measurement for irregular or geometric plot shapes.

• Irregular Polygon: Area = ½ × |Σ(xᵢyᵢ₊₁ − xᵢ₊₁yᵢ)| — uses the shoelace method for coordinates.
• Fan-Shaped Lot: Area = ½ × r² × θ — r is radius, θ is central angle in radians.
• Arc Segment: Area = ½ × r² × (θ − sinθ) — r is radius, θ is angle in radians.
• Kite Shape: Area = ½ × d₁ × d₂ — d₁ and d₂ are diagonals.
• Pie-Shaped Wedge: Area = (θ / 360) × π × r² — θ in degrees, r is radius.

Jump to Shape Calculator

• Irregular Polygon
• Fan-Shaped Lot
• Arc Segment
• Kite Shape
• Pie Wedge
• GPS Plot

Use case from the field: When measuring a rectangular lot for subdivision, I relied on the land area calculator to calculate a 145 × 90 ft plot — came out to 13,050 square feet. For irregular zones with diagonals and curves, I used the area calculator, which supports common shapes like trapezoids, triangles, and circles.

Formula for Irregular Polygon

The area of an irregular polygon can be estimated using the shoelace formula: A = ½ × |Σ(xᵢyᵢ₊₁ - xᵢ₊₁yᵢ)| for all vertices in order. Coordinates are plotted and processed geometrically. Using the calculator with points (0,0), (4,0), (4,3), and (0,4), the result is A = ½ × |(0×0 + 4×3 + 4×4 + 0×0) - (4×0 + 4×0 + 0×3 + 0×4)| = ½ × |0 + 12 + 16 + 0 - (0 + 0 + 0 + 0)| = ½ × 28 = 14 units².

Formula for Fan-Shaped Lot

A fan-shaped lot is modeled as a circular sector with area A = (θ / 360) × π × r², where θ is the angle and r is the radius. For a fan-shaped lot with θ = 60° and r = 20 m, the calculator returns A = (60 / 360) × π × 20² = ⅙ × π × 400 ≈ 209.44 m².

Formula for Arc Segment

The area of a circular segment is A = (r² / 2) × (θ - sinθ), where θ is in radians. It measures the area between a chord and the arc. For r = 10 m and θ = 2 radians, A = (100 / 2) × (2 - sin2) ≈ 50 × (2 - 0.9093) ≈ 50 × 1.0907 ≈ 54.53 m² using the calculator.

Formula for Kite Shape

The area of a kite is A = (d₁ × d₂) / 2, where d₁ and d₂ are the diagonals. For diagonals of 8 m and 6 m, the calculator gives A = (8 × 6) / 2 = 48 / 2 = 24 m².

Formula for Pie-Shaped Lot

The area of a pie-shaped lot is calculated as a sector: A = (θ / 360) × π × r². For θ = 45° and r = 25 ft, use the calculator to get A = (45 / 360) × π × 625 = ⅛ × π × 625 ≈ 245.04 ft².

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