How to Calculate Area (Every Common Shape)

Area measures the amount of two-dimensional space a shape occupies. Whether you are ordering flooring for a renovation, estimating paint for a bedroom wall, buying sod for a lawn, or sizing a concrete slab, you need an accurate area calculation before you spend a dollar.

This guide walks through the area formulas for every shape you will encounter in daily life, with worked examples and unit conversions. For quick results, use our Free Area Calculator.

Rectangle and Square

The rectangle is the most frequently calculated shape. Rooms, walls, decks, driveways, and garden beds are typically rectangular.

Formula:

$A = length \times width$

For a square, both sides are equal, so the formula simplifies to side squared.

$A = s^2$

Example: A bedroom measures 14 feet by 12 feet. How much carpet do you need?

• Area = 14 x 12 = 168 sq ft
• With 10% waste factor: 168 x 1.10 = 184.8 sq ft (round up to 185 sq ft)

Example: A square patio measures 9 feet on each side.

• Area = 9 x 9 = 81 sq ft

Triangle

Triangles appear in gable walls, roof sections, oddly-shaped lots, and decorative features.

Formula:

$A = \frac{1}{2} \times base \times height$

The height must be perpendicular to the base, not the length of a sloped side.

Example: A triangular gable wall has a base of 24 feet and a peak height of 8 feet.

• Area = 0.5 x 24 x 8 = 96 sq ft

If you only know the three side lengths (a, b, c), use Heron’s formula:

$s = \frac{a + b + c}{2}$

$A = \sqrt{s(s-a)(s-b)(s-c)}$

Example: A triangular garden plot has sides of 5 m, 7 m, and 8 m.

• Semi-perimeter: s = (5 + 7 + 8) / 2 = 10
• Area = sqrt(10 x 5 x 3 x 2) = sqrt(300) = 17.32 sq m

Circle

Circular areas come up with ponds, round tables, fire pits, pizza stones, irrigation coverage, and pipe cross-sections.

Formula:

$A = \pi r^2$

Where r is the radius (half the diameter). Use 3.14159 for pi.

Example: A circular patio has a diameter of 16 feet. What is the area?

• Radius = 16 / 2 = 8 feet
• Area = 3.14159 x 8 x 8 = 201.06 sq ft

Half circle (semicircle):

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

A semicircular window with a 3-foot diameter: A = (3.14159 x 1.5 x 1.5) / 2 = 3.53 sq ft

Trapezoid

Trapezoids appear in retaining walls, lot shapes, tabletops, and architectural features. A trapezoid has two parallel sides of different lengths.

Formula:

$A = \frac{(a + b)}{2} \times h$

Where a and b are the two parallel sides, and h is the perpendicular height between them.

Example: A garden bed is shaped like a trapezoid with parallel sides of 10 feet and 6 feet, and a height of 4 feet.

• Area = ((10 + 6) / 2) x 4 = 8 x 4 = 32 sq ft

Parallelogram

A parallelogram has two pairs of parallel sides. Think of a diamond-shaped tile pattern or a slanted wall section.

Formula:

$A = base \times height$

The height is the perpendicular distance between the base and the opposite side, not the slant side length.

Example: A parallelogram-shaped planter has a base of 5 feet and a perpendicular height of 3 feet.

• Area = 5 x 3 = 15 sq ft

Ellipse (Oval)

Ellipses show up in oval pools, racetrack designs, and decorative landscaping features.

Formula:

$A = \pi \times a \times b$

Where a is the semi-major axis (half the longest diameter) and b is the semi-minor axis (half the shortest diameter).

Example: An oval swimming pool measures 30 feet long and 18 feet wide.

• a = 30 / 2 = 15, b = 18 / 2 = 9
• Area = 3.14159 x 15 x 9 = 424.12 sq ft

Composite Shapes

Most real-world spaces aren’t perfect geometric shapes. An L-shaped room, a house footprint with a garage bump-out, or an irregular lot all require the composite method.

Strategy:

1. Break the shape into rectangles, triangles, and circles.
2. Calculate the area of each piece.
3. Add the areas together (or subtract if a piece is cut out).

Example: An L-shaped room measures 20 ft x 15 ft for the main section, with a 10 ft x 8 ft extension.

• Main section: 20 x 15 = 300 sq ft
• Extension: 10 x 8 = 80 sq ft
• Total area = 300 + 80 = 380 sq ft

Example: A rectangular wall (12 ft x 9 ft) has a circular window with a 2-foot diameter.

• Wall: 12 x 9 = 108 sq ft
• Window: 3.14159 x 1 x 1 = 3.14 sq ft
• Paintable area = 108 - 3.14 = 104.86 sq ft

Unit Conversions

Different projects use different units. Here are the conversion factors you will need most often:

From	To	Multiply By
sq ft	sq m	0.0929
sq m	sq ft	10.764
sq ft	sq in	144
sq yd	sq ft	9
sq ft	acres	0.0000229568
acres	sq ft	43,560
sq m	sq cm	10,000

Example: You calculated 380 sq ft for a room and the tile is sold by the square meter.

• 380 x 0.0929 = 35.30 sq m

Example: A 0.25-acre lot in square feet:

• 0.25 x 43,560 = 10,890 sq ft

Practical Applications

Flooring: Measure the room’s length and width. Multiply them for rectangular rooms, or use the composite method for irregular layouts. Add 10% for cuts and waste. Tile, hardwood, laminate, and carpet are all sold by square footage or square meters.

Painting: Calculate wall area (height x width for each wall), subtract doors and windows, and check the paint can for coverage per gallon. Most interior paints cover 350-400 sq ft per gallon.

Landscaping: Measure the lawn area to determine how much seed, fertilizer, or sod to buy. Bag labels specify coverage in square feet. For mulch and gravel, you will also need volume (area x depth).

Concrete: Slab area tells you how much concrete to order once you factor in thickness. A 200 sq ft patio at 4 inches thick requires about 2.5 cubic yards of concrete.

Roofing: Roof area determines how many bundles of shingles you need. One “roofing square” covers 100 sq ft. A 2,000 sq ft roof requires 20 squares.

Skip the Math

Our Area Calculator handles rectangles, triangles, circles, trapezoids, and more. Enter your measurements, pick the shape, and get an instant result with the formula shown.

Frequently Asked Questions

What is the difference between area and perimeter?

Area measures the space inside a shape (in square units). Perimeter measures the distance around the outside (in linear units). A 10 ft x 12 ft room has an area of 120 sq ft and a perimeter of 44 ft. You use area for flooring and paint coverage. You use perimeter for baseboards, fencing, and trim.

How do I calculate the area of an irregular shape?

Break it into familiar shapes. Draw lines to divide the irregular shape into rectangles, triangles, and semicircles. Calculate each piece separately, then add them up. For very irregular shapes like ponds or curved garden beds, use the grid method: overlay a grid of 1-foot squares and count the full squares plus estimate the partial ones.

How many square feet are in a square yard?

One square yard equals 9 square feet (3 ft x 3 ft = 9 sq ft). Carpet is often priced per square yard. To convert square feet to square yards, divide by 9. A 180 sq ft room needs 180 / 9 = 20 sq yd of carpet.

Why should I add 10% extra when buying materials?

Flooring, tile, and other materials require cuts to fit around edges, corners, and obstacles. Some pieces will crack or have defects. The 10% buffer covers these losses so you don’t run short mid-project. For diagonal installations or complex patterns, increase the buffer to 15%.

How do I measure a room that isn’t a perfect rectangle?

Measure the longest length and widest width to get the bounding rectangle. Then measure and subtract any missing sections (like a closet bump-in or angled wall). Alternatively, divide the room into rectangular sections, measure each one, and add the areas together. Sketch the room on paper with dimensions before you start calculating.