Area Calculator

Area Calculator: Circles, Triangles & Square Footage

A 12 ft × 15 ft room is 180 ft². The same dimensions in meters (3.66 m × 4.57 m) give 16.7 m². Linear conversions square when you switch to area, so 1 m² = 10.76 ft², not 3.28, which is the part most people get wrong.

How it works

Pick a shape, type the lengths you have, and read the result in your chosen unit squared. The page covers classic homework problems (area of a circle, area of a triangle, a rectangle floor plan, a trapezoid from a sketch), floor plans for tile or paint estimates, and rough lot sketches from tape-measure dimensions. Acres and hectares are a unit toggle away when you're working at land scale. For wrapping a box or painting the outside of a solid, use the surface area calculator instead, that's three-dimensional. For irregular yards, decompose the outline into rectangles and triangles, run each piece, and sum the results.

Common Area Formulas Reference

Basic Quadrilaterals

Square:

A = s^2

Rectangle:

A = \ell \times w

Parallelogram:

A = b \times h

Trapezoid:

A = \frac{1}{2}(b_1 + b_2) \times h

Rhombus:

A = s \times h

Kite:

A = \frac{1}{2} d_1 \times d_2

Circular & Curved

Circle:

A = \pi r^2

Semicircle:

A = \frac{1}{2} \pi r^2

Sector:

A = \frac{1}{2} r^2 \theta

(θ in radians)

Ellipse:

A = \pi a b

Annulus (Ring):

A = \pi (R^2 - r^2)

Polygons & Irregular

Triangle:

A = \frac{1}{2} b \times h

Regular Pentagon:

A = \frac{a^2 \sqrt{25+10\sqrt{5}}}{4}

Regular Hexagon:

A = \frac{3\sqrt{3}}{2} a^2

Regular Octagon:

A = 2(1+\sqrt{2}) a^2

Regular Polygon:

A = \frac{n a^2 \cot(\pi/n)}{4}

Irregular Quadrilateral:

A = \frac{1}{2} d_1 d_2 \sin\theta

Common measurement mistakes

Three things go wrong most often. (1) Circles use radius squared, not diameter; a 30-foot-across pond is π × 15² ≈ 707 ft², not π × 30² ≈ 2,827. (2) Triangle height has to be perpendicular to the base you chose, not the slanted side; using a 5-foot hypotenuse instead of the 3-foot perpendicular leg on a 4-foot base prints 10 ft² when the answer is 6. (3) Linear conversions square when you switch to area: 1 m is 3.28 ft, but 1 m² is 10.76 ft², not 3.28. The calculator handles unit conversion automatically; the gotcha shows up when you double-check against a hardware store quote in different units.

Area Calculator FAQ

How do I calculate the area of an Annulus (Ring)?

An Annulus is the area between two concentric circles. Use the formula:

A = \pi (R^2 - r^2)

where R is the outer radius and r is the inner radius. For example, a ring with outer radius 5 m and inner radius 3 m has area ≈ 50.27 m². This is useful for circular walkways, ring-shaped gardens, and donut-shaped areas.

How do I calculate the area of a Sector?

A Sector is a "pie slice" of a circle. Use the formula:

A = \frac{1}{2} r^2 \theta

where θ is in radians. If your angle is in degrees, convert first: θ = degrees × π / 180. For example, a sector with radius 5 m and 60° (≈1.047 rad) has area ≈ 13.09 m². Useful for pie-shaped plots and circular segments.

Why are area units squared (m², ft²)?

Area units are squared because area is two-dimensional. When you multiply length × width, you multiply two linear measurements, resulting in square units. For example, 5 m × 3 m = 15 m². Converting between square units requires squaring the linear conversion factor, e.g., 1 m = 3.28084 ft, so 1 m² = (3.28084)² ≈ 10.764 ft².

Is this the same as a surface area calculator?

Not quite. This page is for flat shapes drawn on a plane (square meters, square feet, acres on the ground when you already know the distances). Surface area is for the outside of a three-dimensional solid like a box or a cylinder. For that job, use our surface area calculator.

Can I use this for GPS land area or a weird-shaped yard?

You can use it whenever you can describe the patch with straight sides or regular curves we support (rectangles, triangles, circles, trapezoids, and more). This tool does not read GPS tracks or draw polygons on a map; you still enter lengths yourself. For odd yards, measure convenient rectangles and triangles, run each piece here, and add the areas. When boundaries are curved or legally precise, a surveyor or mapping software stays the right call.

How do I calculate area for irregular or complex shapes?

Break irregular shapes into regular geometric components (rectangles, triangles, circles) and calculate each separately, then sum the areas. For complex curves, use the trapezoid rule by dividing the shape into narrow trapezoids. For professional accuracy, consider CAD software or surveying tools.

How accurate do my measurements need to be for practical projects?

For home improvement projects (flooring, painting), measurements within ±2% are typically sufficient. For construction and material ordering, aim for ±1% accuracy to prevent costly over-ordering. Always add a 10% waste buffer for materials that require cutting or have irregular coverage.

How do I convert between different square units accurately?

Square unit conversions require squaring the linear conversion factor. Example: 1 m = 3.28084 ft, so 1 m² = (3.28084)² ≈ 10.764 ft². Our calculator handles this automatically. Remember: converting square units is not the same as converting linear units, always square the factor to maintain accuracy.

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