Area Calculator

About the Area Calculator

This free area calculator finds the area and perimeter (or circumference) of seven common geometric shapes: rectangle, square, circle, triangle, trapezoid, parallelogram, and ellipse. Whether you are measuring a room for new flooring, sizing a garden bed, checking a homework problem, or estimating material for a project, the tool applies the standard geometric formula and shows the formula used alongside every result.

All calculations run locally in your browser. Results are displayed to four decimal places, so you can verify the math by hand or learn how each shape is solved.

How to Use

1. Select a shape from the dropdown menu — the input fields change to match it.
2. Enter the required dimensions as whole numbers or decimals.
3. Click Calculate to see the area, the perimeter or circumference, and the exact formula applied.
4. Click Reset to clear the fields and start over.

Any unit works — inches, feet, meters — as long as every input uses the same unit. The area is then reported in that unit squared: enter feet and the answer is in square feet.

Area Formulas for Common Shapes

Each shape has its own formula. The table below lists the area formula the calculator uses, together with the perimeter or circumference it reports.

• s = side length of the square
• l, w = length and width of the rectangle
• b = base; h = height measured perpendicular to the base
• r = radius of the circle (half the diameter)
• a, b = the two parallel sides of a trapezoid, or the semi-major and semi-minor axes of an ellipse
• c, d = the remaining sides of triangles and trapezoids
• π ≈ 3.14159, the circle constant

The ellipse has no simple exact circumference formula, so the calculator uses the common approximation C ≈ 2π√((a² + b²) / 2); its area A = πab is exact.

Worked Examples

• Square: side s = 7 → A = 7² = 49 square units, perimeter 28.
• Rectangle: length 9, width 4 → A = 9 × 4 = 36 square units, perimeter 26.
• Triangle: base 10, height 6 → A = ½ × 10 × 6 = 30 square units.
• Circle: radius 5 → A = π × 5² ≈ 78.54 square units (the calculator shows 78.5398), circumference ≈ 31.42.
• Trapezoid: parallel sides 6 and 10, height 4 → A = ½ × (6 + 10) × 4 = 32 square units.
• Parallelogram: base 8, height 5 → A = 8 × 5 = 40 square units.
• Ellipse: semi-axes a = 5 and b = 3 → A = π × 5 × 3 ≈ 47.12 square units (the calculator shows 47.1239).

Enter any of these examples in the calculator above — the results match to four decimal places.

Area Unit Conversions

Area is always expressed in square units. The two you will encounter most are square feet (ft²) in the United States and square meters (m²) in most other countries. The key conversion factors are:

These factors come from exact definitions: one foot is exactly 0.3048 m, so 1 m² = 1 ÷ 0.3048² ≈ 10.7639 ft², and one acre is defined as exactly 43,560 ft².

Example: a bedroom measures 4 m × 3 m, so its area is 12 m². In square feet that is 12 × 10.7639 ≈ 129.17 ft². Working the other way, a 1,000 ft² apartment is 1,000 × 0.0929 ≈ 92.9 m², and a half-acre building lot is 0.5 × 43,560 = 21,780 ft².

How to Calculate the Area of Irregular Shapes

Few real-world spaces are perfect rectangles, but almost any irregular shape can be solved by decomposition: split it into simpler pieces whose areas you already know how to find, calculate each piece, and add the results.

1. Sketch the shape and divide it into rectangles, triangles, or circles along straight lines.
2. Measure and label the dimensions of each piece.
3. Compute the area of every piece using the formulas above.
4. Add the pieces together for the total area.

Worked example — an L-shaped room. Suppose a room measures 10 ft × 12 ft overall, with a 4 ft × 6 ft rectangular notch cut out of one corner for a hallway. Split the L into two rectangles: a full-width section of 10 ft × 6 ft = 60 ft², and the remaining leg of 6 ft × 6 ft = 36 ft². The total is 60 + 36 = 96 ft². You can check the answer by subtraction instead: the full bounding rectangle is 10 × 12 = 120 ft² and the missing notch is 4 × 6 = 24 ft², so 120 − 24 = 96 ft² — the same result either way.

The same approach handles T-shaped rooms, driveways with curved ends (treat the curve as a half-circle), and yards with angled corners (use the triangle formula). For whole rooms, apartments, and homes, our square footage calculator automates the process and totals multiple rooms at once.