Area Calculator

Strategic Applications of Area

Area calculations drive decisions in home improvement, construction, real estate, and material ordering. Trusted by students and educators for geometry homework and project planning. These cards explain why accurate area matters and how to use your result. All calculations run locally.

Strategic Applications

Home Improvement

Get net area for flooring, paint, or turf and add a 10% waste buffer. Reduces mid-project shortages and return trips to suppliers.

Construction Accuracy

Precision in area directly prevents over-ordering. A 5% error on a large project can waste thousands in excess materials.

Real Estate & Land

Gross area includes walls and common space; usable square footage is livable space that drives value. Use the right measure for the context.

Material Optimization

Compare cost per square unit and multiply area by unit cost to get total project cost for informed budgeting.

Area Calculator: Free Online Tool for Common Shapes

Free area calculator: how to calculate area of a rectangle, circle, triangle, trapezoid. Square footage calculator, area of a room, area formula for flooring and projects. Multiple units, instant results. Trusted by students and educators. No sign-up—all calculations run locally.

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

An area calculator is a tool that finds the size of a two-dimensional region in square units (e.g. m², ft²). How do you calculate area? It depends on the shape: for a rectangle, area = length × width; for a circle, area = π × radius²; for a triangle, area = ½ × base × height. To calculate area of a room for flooring or paint, measure length and width (or break the room into rectangles) and multiply; that gives you square footage. A square footage calculator does the same for feet and inches. This area calculator supports squares, rectangles, circles, triangles, trapezoids, and more, with multiple units and instant results—useful as an area calculator for flooring, landscaping, and construction. All calculations run in your browser; no data is sent to servers.

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

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.

? 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.

Shape & Dimensions