The Area Calculator computes the area of common 2D shapes — squares, rectangles, triangles, circles, trapezoids, parallelograms, and more — from their defining dimensions. All standard geometric area formulas in one tool for students, engineers, contractors, and everyday calculations.
50
sq units
25
sq units
314.159265
sq units
65
sq units
50
sq units
25
sq units
157.079633
sq units
4.363323
sq units
50
sq units
25
sq units
314.159265
sq units
65
sq units
50
sq units
25
sq units
157.079633
sq units
4.363323
sq units
Area is one of the most frequently calculated quantities in everyday life — flooring, paint coverage, land parcels, fabric, solar panels, and hundreds of other practical problems reduce to finding the area of a shape. The calculator for area covers all common 2D shapes with a single tool, applying the correct geometric formula for each shape and returning the result in any unit.
The most frequently needed area formulas, organized by shape:
Use this online calculator to compute area for any shape from any set of given dimensions. The regular polygon calculator provides extended analysis for n-sided polygons including perimeter and interior angles.
Area formulas assume perfectly regular shapes — real-world surfaces are rarely perfect rectangles or circles. Practical area estimation strategies:
Area units scale as the square of linear units — a common source of calculation errors:
The area conversion calculator handles all unit conversions between area systems. The plane geometry calculators provide detailed analysis for each shape type.
For irregular polygons defined by vertex coordinates (x₁,y₁), (x₂,y₂), ..., (xₙ,yₙ), the Shoelace formula gives the exact area regardless of shape: A = ½|Σ(xᵢyᵢ₊₁ − xᵢ₊₁yᵢ)|. This formula is used in GIS software, CAD systems, and surveying to calculate land areas from GPS coordinates. It works for any non-self-intersecting polygon, concave or convex, making it the general-purpose area calculation method when standard shape formulas do not apply.
Each shape uses a specific formula based on its geometric properties:
Circle: $$A = \pi r^2$$
Rectangle: $$A = l \times w$$
Triangle (base and height): $$A = \frac{1}{2} b h$$
Trapezoid: $$A = \frac{1}{2}(a + b) \times h$$ where $$a$$ and $$b$$ are parallel sides
Ellipse: $$A = \pi a b$$ where $$a$$ and $$b$$ are semi-axes
Parallelogram: $$A = b \times h$$ (base times perpendicular height)
Rhombus (from diagonals): $$A = \frac{1}{2} d_1 d_2$$
Circular Sector: $$A = \frac{1}{2} r^2 \theta$$ where $$\theta$$ is the central angle in radians
The result is the area in square units corresponding to the input units. If you enter dimensions in meters, the area is in square meters (m²); in feet, the area is in square feet (ft²). The formula display shows exactly which formula was applied and how your dimensions were substituted, serving as a verification step. For the trapezoid, dim1 is one parallel side, dim2 is the height, and dim3 (advanced) is the other parallel side.
Inputs
Results
A = π × 10² = 100π ≈ 314.16 square units. Only dim1 (radius) is used for circles.
Inputs
Results
A = ½(6+10) × 4 = ½ × 16 × 4 = 32 square units. dim1=top base (6), dim2=height (4), dim3=bottom base (10).
The calculator works with any consistent unit system. If you enter dimensions in centimeters, the area is in square centimeters (cm²). If you use meters, the result is in square meters (m²). The key requirement is that all dimensions for a single calculation must be in the same unit. The calculator does not perform unit conversions between inputs.
For irregular shapes, you can often decompose them into standard shapes (rectangles, triangles, etc.), calculate each area separately, and add them together. Alternatively, if you have coordinates of the vertices of a polygon, you can use the Shoelace formula: $$A = \frac{1}{2}|\sum_{i=0}^{n-1}(x_i y_{i+1} - x_{i+1} y_i)|$$. For curved boundaries, numerical integration methods may be needed.
Area measures the two-dimensional space enclosed within a shape (in square units), while perimeter measures the total length of the boundary (in linear units). For example, a 3×4 rectangle has area 12 square units but perimeter 14 linear units. Two shapes can have the same perimeter but different areas, and vice versa. A circle has the maximum area for a given perimeter.
This can be proven by dividing a circle into infinitely many thin sectors and rearranging them into a shape approaching a rectangle with width $$\pi r$$ (half the circumference) and height $$r$$, giving area $$\pi r \times r = \pi r^2$$. Archimedes first proved this rigorously. In calculus, it follows from integrating $$\int_0^r 2\pi \rho \, d\rho = \pi r^2$$, summing concentric ring areas.
A sector is a fraction of a circle. If the full circle has area $$\pi r^2$$ and the sector subtends angle $$\theta$$ out of $$2\pi$$ radians, the sector's area is $$\frac{\theta}{2\pi} \times \pi r^2 = \frac{1}{2}r^2\theta$$. Note that $$\theta$$ must be in radians for this formula. For degrees, convert first: $$\theta_{\text{rad}} = \theta_{\text{deg}} \times \frac{\pi}{180}$$.
Among all shapes with a given perimeter, the circle encloses the maximum area. This is known as the isoperimetric inequality: $$A \leq \frac{P^2}{4\pi}$$, with equality only for circles. Among rectangles with a given perimeter, the square has the largest area. Among triangles with a given perimeter, the equilateral triangle maximizes area. This principle appears in nature and optimization problems.
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