Area Calculator
What This Tool Does
This calculator finds the area of seven common two-dimensional shapes: rectangle, triangle, trapezoid, circle, sector, ellipse, and parallelogram. Select your shape, enter the required dimensions, and the result appears instantly in your chosen unit — square metres, square feet, acres, or others. It is particularly useful for estimating land area, planning construction, calculating flooring or paint coverage, and solving geometry problems.
You can also use this Pip Calculator.
How It’s Calculated
Each shape uses a specific formula. Below are the formulas, what measurements are needed, and a worked example for each.
Rectangle
Formula: Area = Length × Width
A rectangle has four right angles. When length and width are equal, it becomes a square — the same formula applies.
Worked Example:
A plot of land measures 30 m long and 20 m wide:
Area = 30 × 20 = 600 m²
In land measurement terms, 600 m² is 0.06 hectares or approximately 6,458 sq ft.
Triangle
Formula (Heron’s Formula — when all three sides are known):
s = (a + b + c) ÷ 2
Area = √(s × (s−a) × (s−b) × (s−c))
Where a, b, c are the three side lengths and s is the semi-perimeter.
Worked Example:
A triangular plot with sides 30 m, 45 m, and 50 m:
s = (30 + 45 + 50) ÷ 2 = 62.5
Area = √(62.5 × 32.5 × 17.5 × 12.5) = √445,312.5 ≈ 667.3 m²
If you know the base and height instead: Area = 0.5 × base × height
Trapezoid
Formula: Area = ((b1 + b2) ÷ 2) × h
Where b1 and b2 are the two parallel sides (bases) and h is the perpendicular height between them.
Worked Example:
A trapezoidal piece of land with bases of 30 m and 45 m, height 20 m:
Area = ((30 + 45) ÷ 2) × 20 = 37.5 × 20 = 750 m²
Circle
Formula: Area = π × r²
Where r is the radius (half the diameter) and π ≈ 3.14159.
Worked Example:
A circular plot with radius 30 m:
Area = π × 30² = π × 900 = 2,827.4 m²
That is approximately 0.28 hectares or 0.70 acres.
Sector
A sector is a “slice” of a circle — the region enclosed by two radii and an arc.
Formula:
- If angle θ is in degrees: Area = (θ ÷ 360) × π × r²
- If angle θ is in radians: Area = (θ ÷ 2π) × π × r²
Worked Example:
A 90° sector with radius 30 m:
Area = (90 ÷ 360) × π × 30² = 0.25 × 2,827.4 = 706.9 m²
Ellipse
An ellipse is an oval shape defined by two axes. The semi-major axis (a) is the longer half, the semi-minor axis (b) is the shorter half.
Formula: Area = π × a × b
Worked Example:
An elliptical garden bed with semi-major axis 30 m and semi-minor axis 20 m:
Area = π × 30 × 20 = 1,884.96 m²
Parallelogram
A parallelogram has two pairs of parallel sides. Rectangles, rhombuses, and squares are all special cases of parallelograms.
Formula: Area = base × height
Note: height is the perpendicular distance between the two bases — not the length of the slanted side.
Worked Example:
A parallelogram-shaped plot with base 30 m and perpendicular height 20 m:
Area = 30 × 20 = 600 m²
Irregular Shapes — Breaking Them Down
Most real land plots are not perfect rectangles or triangles. The standard approach for irregular shapes is to divide the area into simpler shapes — rectangles, triangles, and trapezoids — calculate each separately, and add the results together.
For example, an L-shaped plot can be split into two rectangles. A plot with one curved boundary can be approximated by splitting it into a rectangle and a sector. For highly irregular land on a map, GPS-based area measurement tools or Google Maps area calculation tools are more practical than formula-based calculators.
Common Area Units Conversion
| Unit | Equivalent in m² |
|---|---|
| 1 square metre (m²) | 1 (SI base unit) |
| 1 square foot | 0.0929 m² |
| 1 square yard | 0.8361 m² |
| 1 acre | 4,046.9 m² (43,560 sq ft) |
| 1 hectare | 10,000 m² |
| 1 square kilometre | 1,000,000 m² |
| 1 square mile | 2,589,988 m² (640 acres) |
For land area in India, the following local units are also commonly used:
| Unit | Equivalent |
|---|---|
| 1 Bigha | Varies by state (typically 1,337–6,772 m²) |
| 1 Marla | 25.29 m² (272 sq ft) |
| 1 Kanal | 505.857 m² (4,500 sq ft) |
| 1 Guntha | 101.17 m² (1,089 sq ft) |
| 1 Ground | 222.97 m² (2,400 sq ft) |
Edge Cases and Special Rules
Four unequal sides (irregular quadrilateral): The basic rectangle formula does not apply when all four sides are different lengths and no angles are known. The shape must be split into two triangles using a diagonal, each triangle calculated separately, and the areas summed. For agricultural land with four unequal sides, professional surveying or a GPS-based tool gives more reliable results.
Curved boundaries: Natural land boundaries — rivers, roads, contours — rarely follow geometric shapes. For these cases, the trapezoidal rule (averaging successive widths at regular intervals) or software-based mapping tools are more appropriate than hand calculations.
Sloped land: All area formulas calculate horizontal (flat) area projected on a plane. Actual surface area on sloped terrain is larger than the horizontal area — relevant for agricultural yield calculations or material estimations on hillside plots.
Units consistency: All measurements entered must be in the same unit. Mixing metres and feet in a single calculation produces incorrect results. Convert all measurements to a consistent unit before entering values.
Who Uses This
- Landowners and farmers estimating plot size for sale, purchase, or agricultural planning
- Construction and civil engineers calculating floor areas, footings, and site coverage
- Interior designers and contractors working out paint, tile, or flooring quantities
- Students solving geometry problems in school or competitive exams
- Architects and urban planners calculating building footprints and open space ratios
- Anyone using Google Maps area tools who wants to verify or cross-check a measurement with formula-based calculations
FAQ
How do I calculate land area with four different sides?
If you know all four sides but no angles, you cannot calculate the area precisely without at least one diagonal or angle. Measure one diagonal to split the quadrilateral into two triangles, then use Heron’s formula on each triangle and add the results.
How do I convert square metres to square feet?
Multiply square metres by 10.764. For example, 100 m² = 1,076.4 sq ft.
How do I convert square feet to acres?
Divide square feet by 43,560. For example, 21,780 sq ft ÷ 43,560 = 0.5 acres.
What is the formula for the area of a circle?
Area = π × r², where r is the radius. If you know the diameter, divide by 2 to get the radius first. For a circle with diameter 10 m: r = 5, Area = π × 25 ≈ 78.54 m².
Can I use this calculator for agricultural land in India?
Yes for the shape calculations. For conversion to local units like Bigha, Marla, or Kanal, use the area converter tool or apply the relevant conversion factor for your state, since Bigha in particular varies significantly across states.
A Note on Results
All calculations in this tool are based on geometric formulas and the measurements you enter. For land transactions, legal disputes, or construction permits, always verify area measurements through a licensed surveyor, as actual land boundaries may differ from the ideal geometric shapes these formulas assume.