Square Footage Calculator: Calculate Area for Any Shape
A square footage calculator is an essential measurement tool that accurately computes the area of various geometric shapes including rectangles, circles, triangles, trapezoids, parallelograms, rings, borders, and sectors measured in square feet or square meters. By inputting specific dimensions for each shape, this calculator determines precise area measurements—helping homeowners, contractors, designers, real estate professionals, and students calculate flooring, painting, landscaping, room sizes, and property measurements for accurate material estimation, cost calculation, and spatial planning in construction, renovation, and educational mathematics applications.
📐 Interactive Square Footage Calculator
Select shape and calculate area
Rectangle Area Calculator
For rooms, floors, walls, yards, and rectangular spaces
Rectangle Border/Frame Area Calculator
Calculate border area between outer and inner rectangles
Circle Area Calculator
For circular rooms, patios, pools, or round spaces
Ring (Annulus) Area Calculator
Area between two concentric circles
Triangle Area Calculator (Using Edge Lengths)
Uses Heron's formula when all three sides are known
Triangle Area Calculator (Base × Height)
Standard triangle formula with base and height
Trapezoid Area Calculator
Quadrilateral with one pair of parallel sides
Circular Sector Area Calculator
Portion of a circle (like a pie slice)
Parallelogram Area Calculator
Quadrilateral with opposite sides parallel
Understanding Area Formulas
Area represents the amount of space inside a two-dimensional shape, measured in square units (square feet, square meters, etc.). Different shapes require specific formulas based on their geometric properties.
Rectangle Area Formula
Rectangle Area:
\[ A = L \times W \]
Where:
\[ A = \text{Area (square feet)}, \quad L = \text{Length}, \quad W = \text{Width} \]
Rectangle Example:
Room dimensions: 12 feet × 10 feet
\[ A = 12 \times 10 = 120 \text{ square feet} \]
Rectangle Border Area Formula
Border/Frame Area:
\[ A_{\text{border}} = (L_{\text{outer}} \times W_{\text{outer}}) - (L_{\text{inner}} \times W_{\text{inner}}) \]
Subtract inner rectangle from outer rectangle
Border Example:
Outer: 12' × 10', Inner: 8' × 6'
\[ A = (12 \times 10) - (8 \times 6) = 120 - 48 = 72 \text{ sq ft} \]
Circle Area Formula
Circle Area (using radius):
\[ A = \pi r^2 \]
Circle Area (using diameter):
\[ A = \frac{\pi d^2}{4} \]
Where:
\[ r = \text{Radius}, \quad d = \text{Diameter} = 2r, \quad \pi \approx 3.14159 \]
Circle Example:
Circular patio: 5-foot radius (10-foot diameter)
\[ A = \pi \times 5^2 = 3.14159 \times 25 = 78.54 \text{ square feet} \]
Ring (Annulus) Area Formula
Ring Area:
\[ A = \pi R^2 - \pi r^2 = \pi(R^2 - r^2) \]
Where:
\[ R = \text{Outer radius}, \quad r = \text{Inner radius} \]
Ring Example:
Ring dimensions: Outer radius 8', Inner radius 5'
\[ A = \pi(8^2 - 5^2) = 3.14159(64 - 25) = 3.14159 \times 39 = 122.52 \text{ sq ft} \]
Triangle Formulas
Triangle with Base and Height
Standard Triangle Area:
\[ A = \frac{1}{2} \times b \times h \]
Where:
\[ b = \text{Base length}, \quad h = \text{Height (perpendicular to base)} \]
Triangle with Three Side Lengths (Heron's Formula)
Heron's Formula:
\[ A = \sqrt{s(s-a)(s-b)(s-c)} \]
Where:
\[ s = \frac{a + b + c}{2} \quad \text{(semi-perimeter)} \]
\[ a, b, c = \text{Three side lengths} \]
Heron's Formula Example:
Triangle sides: a = 5', b = 6', c = 7'
Step 1: Calculate semi-perimeter:
\[ s = \frac{5 + 6 + 7}{2} = \frac{18}{2} = 9 \]
Step 2: Calculate area:
\[ A = \sqrt{9(9-5)(9-6)(9-7)} = \sqrt{9 \times 4 \times 3 \times 2} \]
\[ A = \sqrt{216} = 14.70 \text{ square feet} \]
Trapezoid Area Formula
Trapezoid Area:
\[ A = \frac{(b_1 + b_2) \times h}{2} \]
Where:
\[ b_1, b_2 = \text{Two parallel bases}, \quad h = \text{Height (perpendicular distance)} \]
Trapezoid Example:
Dimensions: Base 1 = 12', Base 2 = 8', Height = 5'
\[ A = \frac{(12 + 8) \times 5}{2} = \frac{20 \times 5}{2} = \frac{100}{2} = 50 \text{ sq ft} \]
Circular Sector Area Formula
Sector Area (angle in degrees):
\[ A = \frac{\theta}{360} \times \pi r^2 \]
Sector Area (angle in radians):
\[ A = \frac{1}{2} r^2 \theta \]
Where:
\[ r = \text{Radius}, \quad \theta = \text{Central angle} \]
Sector Example:
Pizza slice: 10-foot radius, 90-degree angle
\[ A = \frac{90}{360} \times \pi \times 10^2 = \frac{1}{4} \times 3.14159 \times 100 = 78.54 \text{ sq ft} \]
Parallelogram Area Formula
Parallelogram Area:
\[ A = b \times h \]
Where:
\[ b = \text{Base length}, \quad h = \text{Height (perpendicular to base)} \]
Note: Height is NOT the slanted side length
Parallelogram Example:
Dimensions: Base = 12', Height = 8'
\[ A = 12 \times 8 = 96 \text{ square feet} \]
Shape Comparison Table
| Shape | Formula | Required Measurements |
|---|---|---|
| Rectangle | \( A = L \times W \) | Length, Width |
| Circle | \( A = \pi r^2 \) | Radius or Diameter |
| Triangle (base) | \( A = \frac{1}{2}bh \) | Base, Height |
| Triangle (sides) | \( A = \sqrt{s(s-a)(s-b)(s-c)} \) | Three side lengths |
| Trapezoid | \( A = \frac{(b_1+b_2)h}{2} \) | Two bases, Height |
| Parallelogram | \( A = b \times h \) | Base, Height |
| Sector | \( A = \frac{\theta}{360}\pi r^2 \) | Radius, Central angle |
| Ring | \( A = \pi(R^2-r^2) \) | Outer radius, Inner radius |
Common Applications
Flooring and Carpeting
- Calculate room area: Measure length and width, multiply for square footage
- Add waste factor: Order 10% extra for cuts and mistakes
- Complex rooms: Divide into rectangles, calculate separately, sum totals
- Circular areas: Use circle formula for round rooms or alcoves
Painting and Wallpaper
- Wall area: Length × height for each wall
- Subtract openings: Deduct doors and windows
- Coverage rates: Paint covers 350-400 sq ft per gallon
- Multiple coats: Multiply total area by number of coats
Landscaping
- Lawn seeding: Calculate yard area for seed quantity
- Sod installation: Measure total grass area needed
- Mulch beds: Irregular shapes divided into manageable sections
- Patio pavers: Calculate area for material ordering
Real Estate and Property
- Home size: Interior square footage for listing
- Lot size: Property area in square feet or acres
- Usable space: Calculate living area vs. total footprint
- Pricing: Cost per square foot calculations
Unit Conversions
Common Area Conversions
| From | To | Multiply By |
|---|---|---|
| Square feet | Square inches | 144 |
| Square feet | Square yards | 0.1111 (÷ 9) |
| Square feet | Square meters | 0.0929 |
| Square feet | Acres | 0.00002296 (÷ 43,560) |
| Square yards | Square feet | 9 |
| Square meters | Square feet | 10.764 |
Tips for Accurate Measurements
Measurement Best Practices:
- Use proper tools: Laser measure for accuracy, tape measure for flexibility
- Measure twice: Verify all dimensions before calculating
- Record measurements: Write down all dimensions immediately
- Draw diagrams: Sketch room/area with labeled dimensions
- Account for irregularities: Measure at multiple points, use average
- Include all areas: Don't forget closets, alcoves, or bump-outs
- Round up: When ordering materials, always round up slightly
Common Mistakes to Avoid
⚠️ Area Calculation Errors
- Mixing units: Using feet and inches without converting
- Forgetting π: Circles and sectors require pi in calculations
- Wrong formula: Using diameter instead of radius in circle formula
- Height confusion: Using slant height instead of perpendicular height
- No waste factor: Ordering exact amount leaves no room for errors
- Incorrect Heron's formula: Not calculating semi-perimeter first
- Border errors: Adding areas instead of subtracting for borders
- Sector angle: Using radians when formula expects degrees
Frequently Asked Questions
How do I calculate square footage of a room?
Measure length and width in feet, multiply together: Length × Width = Square footage. Example: 12' × 10' room = 120 square feet. For L-shaped or irregular rooms, divide into rectangles, calculate each separately, add totals. Always round up when ordering materials and add 10% waste factor.
What's the formula for circle area?
Circle area = πr² where r is radius. If you have diameter, divide by 2 to get radius. Example: 10-foot diameter circle: radius = 5 feet, area = 3.14159 × 5² = 78.54 square feet. Remember π (pi) ≈ 3.14159. Use diameter formula A = πd²/4 as alternative.
How do I calculate triangle area with three sides?
Use Heron's formula: First calculate semi-perimeter s = (a+b+c)/2, then area = √(s(s-a)(s-b)(s-c)). Example: sides 5', 6', 7': s = 9, area = √(9×4×3×2) = √216 = 14.70 sq ft. This works for any triangle when all three side lengths are known.
What's the difference between parallelogram and rectangle area?
Both use base × height, but parallelogram height must be perpendicular to base, not the slanted side length. Rectangle sides are already perpendicular. Example: Parallelogram with 12' base, 10' slanted side, 8' perpendicular height: Area = 12 × 8 = 96 sq ft (not 12 × 10).
How many square feet in an acre?
One acre = 43,560 square feet. To convert: acres × 43,560 = square feet. Example: 0.5 acres = 21,780 sq ft. Reverse: square feet ÷ 43,560 = acres. One acre is roughly 208.7' × 208.7' square. Used primarily for land/property measurements.
How do I calculate trapezoid area?
Trapezoid area = [(base1 + base2) × height] ÷ 2. Add both parallel bases, multiply by perpendicular height, divide by 2. Example: bases 12' and 8', height 5': [(12+8) × 5] ÷ 2 = (20 × 5) ÷ 2 = 50 square feet. Height must be perpendicular distance between parallel sides.
Key Takeaways
Calculating square footage requires understanding geometric formulas specific to each shape. Accurate area measurements ensure proper material ordering, cost estimation, and spatial planning for construction, renovation, and design projects.
Essential principles to remember:
- Rectangle: Area = Length × Width
- Circle: Area = πr² (radius squared times pi)
- Triangle (base): Area = ½ × base × height
- Triangle (sides): Use Heron's formula with semi-perimeter
- Trapezoid: Area = [(base1 + base2) × height] ÷ 2
- Parallelogram: Area = base × perpendicular height
- Sector: Area = (angle/360) × πr²
- Ring: Area = π(R² - r²) = outer circle minus inner circle
- Always use perpendicular height, not slanted sides
- Add 10% waste factor when ordering materials
Getting Started: Use the interactive square footage calculator at the top of this page to calculate area for any shape. Select your shape type from the tabs (rectangle, circle, triangle, trapezoid, parallelogram, ring, border, or sector), enter the required dimensions, and receive instant area calculations in square feet. Choose the appropriate calculator for your specific measurement needs.