Land Area Calculator

This land area calculator determines the area of geometric field shapes like irregular polygons, fan-shaped lots, arc segments, kite shapes, and pie-shaped wedges. It supports both common and irregular land formats, using standard survey geometry formulas. Scroll down to choose a shape-specific calculator and view input-based results.

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.