Area Calculator

Area Calculator: Circles, Triangles & Square Footage

Figure out flat area for circles, triangles, rooms, and other shapes you can name with lengths. Pick units, compare square feet to acres when it helps, and keep the math on your device.

What Is an Area Calculator? How to Calculate Area and Square Footage

This tool estimates how much flat space sits inside a boundary you describe: classic homework like area of a circle or area of a triangle, a rectangle floor plan, or a trapezoid from a sketch. Enter measurements you already have from a tape measure, a diagram, or rough lot dimensions. You can read results in square feet, square meters, or flip to acres and hectares when you are thinking about land-sized patches (still plain geometry from numbers you type, not a map layer). If your question is “how much cardboard wraps a box” or total exterior paint on a solid, you want surface area in three dimensions; use our surface area calculator instead. For messy lawns or irregular plots, break the outline into rectangles and triangles, run each piece here, and add them; GPS polygon apps do something different. Everything runs in your browser.

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

How to Use This Calculator

Select your shape from the dropdown, 15+ shapes are available including square, rectangle, circle, triangle, trapezoid, parallelogram, ellipse, sector, annulus, rhombus, kite, pentagon, hexagon, octagon, and regular polygon. The form updates to show only the fields relevant to your chosen shape: a rectangle needs length and width, a circle needs only a radius, and a triangle needs base and height. Enter your measurements in any supported linear unit (mm, cm, m, in, ft, yd); the result displays in that unit squared (e.g., m² or ft²). The area appears instantly as you type or adjust values. For material projects like flooring, paint, or turf, add a 10% waste buffer to the calculated area to account for cuts and irregular coverage. The formula reference section below the result shows the equation used for your shape, so you can verify the calculation or learn the underlying geometry.

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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