Area Calculator
Calculate area for common shapes including rectangles, squares, triangles, circles, trapezoids, parallelograms, and ellipses.
Results
The Area Calculator measures how much two-dimensional space lies inside a selected shape. Choose the correct geometry, enter compatible dimensions, and report the answer in squared units such as ft², m², cm², or in².
Composite and irregular outlines
Each shape has its own formula: rectangle lw, triangle bh/2, circle πr², trapezoid (a+b)h/2, and parallelogram bh. The height in triangle and parallelogram formulas is perpendicular to the base, not a sloping side.
Area depends on shape, such as rectangle A=lw, triangle A=bh/2 and circle A=πr².
Enter the values in their mathematical roles
Identify the shape and sketch the labeled dimensions before entering values. Convert every length to one unit. For composite figures, split the outline into nonoverlapping simple shapes, add their areas, and subtract holes.
The governing relationship
Area depends on shape, such as rectangle A=lw, triangle A=bh/2 and circle A=πr².
A compact example
A rectangle 8 m long and 3 m wide has area 24 m².
Valid inputs and boundary cases
Lengths must be nonnegative and describe the fields requested by the selected formula. Radius is half the diameter. Irregular boundaries may require coordinates, surveying, numerical approximation, or another specialized method.
Read the answer in context
All linear dimensions must use compatible units, and area is reported in squared units.
An independent check
Estimate with a bounding rectangle and confirm the calculated area is plausible. Check scaling: doubling every length multiplies area by four. Keep π unrounded until the final result.
Errors that change the answer
- Using diameter where radius is required
- Using a sloped side as triangle height
- Mixing feet and inches
- Reporting linear instead of square units
- Double-counting overlapping pieces
Continue with a related calculator
Continue with the Quadratic Formula Calculator or Volume Calculator. For everyday arithmetic and order-of-operations checks, use the Basic Calculator.
What this numerical result cannot decide
An area result does not automatically include thickness, waste, slope, or material coverage. Construction and land measurements may use plan area, surface area, net area, or legally surveyed area with different meanings.
A second way to understand the method
Draw division lines that create familiar shapes without overlap. Calculate each signed piece and keep a small table of formulas, dimensions, and units. For curves that are not circular or elliptical, the result may need coordinate geometry or a measured approximation rather than a simple closed formula.
Subtraction handles holes and cutouts
A rectangular plate 10 cm by 8 cm has area 80 cm². If a circular hole of radius 2 cm is removed, the remaining area is 80−4π, approximately 67.43 cm². Keep both shapes in the same unit and subtract only the actual overlap.
Area does not identify a unique shape
A 2-by-8 rectangle and a 4-by-4 square both have area 16 square units, yet their perimeters differ. Knowing area alone therefore cannot recover length and width without another condition. When one dimension is unknown, state the additional relationship—such as a fixed aspect ratio—before solving.
Coordinate area for a polygon
When vertices are known in order, the shoelace formula can find a simple polygon’s signed area from coordinates. It is useful for outlines that do not match one standard shape, but vertex order matters and self-intersecting boundaries require special care. Map coordinates must also use an appropriate projection before treating differences as ordinary planar lengths.
Measurement uncertainty grows into area
Because area depends on two lengths, small dimension errors combine. Record the measurement precision and avoid reporting a long decimal result from rough tape measurements. Material orders should add a separate layout-based allowance rather than hiding uncertainty inside premature rounding.
Area Calculator FAQ
How is rectangle area calculated?
Multiply length by perpendicular width.
Why are area units squared?
The calculation combines two independent length dimensions.
Can perimeter determine area?
Not uniquely; different shapes can share a perimeter but have different areas.
For additional worked mathematics, see the free OpenStax Prealgebra 2e reference.
