Area Calculator
Calculate the area and perimeter of 8 common geometric shapes instantly. Select a shape, enter the dimensions, and see the formula applied.
Last updated: March 2026
How to Use the Area Calculator
- Select a shape from the dropdown menu (Rectangle, Square, Triangle, Circle, Trapezoid, Parallelogram, Ellipse, or Rhombus).
- Enter the required dimensions for your shape. The input fields change automatically based on your selection.
- Read the results instantly — area and perimeter update as you type, with the formula displayed below.
- Share or clear your inputs using the buttons below the form.
Area Formulas for All 8 Shapes
Each geometric shape has a unique formula derived from its properties. Understanding these formulas helps you apply them correctly in real-world situations like flooring, landscaping, and construction.
- Rectangle: A = length × width. The most fundamental area formula, used for rooms, screens, and plots of land.
- Square: A = side². A special case of a rectangle where all sides are equal.
- Triangle: A = ½ × base × height. The height must be perpendicular to the base.
- Circle: A = π × r². The circumference (perimeter) is 2πr ≈ 6.2832r.
- Trapezoid: A = ½ × (a + b) × h. Average the two parallel bases, then multiply by height.
- Parallelogram: A = base × height. Like a rectangle but with slanted sides; height is perpendicular, not the slant side.
- Ellipse: A = π × a × b. Uses the two semi-axes; a circle is a special ellipse where a = b.
- Rhombus: A = (d₁ × d₂) / 2. Uses the two diagonals; all sides are equal in a rhombus.
All perimeter formulas use the sum of outer edges (or the integral approximation for ellipses using Ramanujan's formula).
Real-World Applications of Area Calculations
Area calculations are used constantly in everyday life and professional contexts:
- Flooring and tiling: Calculate room area in square feet or square meters to determine how many tiles, planks, or rolls of carpet to purchase. Add 10% for waste.
- Painting walls: Estimate wall area (height × width) to determine how many gallons of paint to buy. One gallon typically covers 350–400 sq ft.
- Land and real estate: Land is measured in square meters (m²), acres (1 acre = 4,047 m²), or hectares (1 ha = 10,000 m²). A standard football field is about 0.5 hectares.
- Gardening: Know the area of garden beds to calculate fertilizer, mulch, or soil needed per square foot.
- Architecture: Building plans are designed using area to determine material quantities, cost estimates, and structural load calculations.
Unit Conversion Reference
- 1 m² = 10,000 cm² = 10.764 sq ft
- 1 sq ft = 144 sq in = 0.0929 m²
- 1 acre = 43,560 sq ft = 4,047 m²
- 1 hectare = 10,000 m² = 2.471 acres
- 1 sq km = 1,000,000 m² = 100 hectares
How to Calculate Area If...
How do I calculate the area of a 10×15 room?
The area of a 10×15 room is 150 square units. Select Rectangle, enter 10 for length and 15 for width. The formula is A = l × w = 10 × 15 = 150 sq ft (if measured in feet).
How do I calculate the area of a triangle with base 8 and height 5?
The area is 20 square units. Use A = ½ × 8 × 5 = 20. The height must be perpendicular to the base — not the length of a slanted side.
How do I find the area of a circle with diameter 14?
A circle with diameter 14 has area ≈ 153.94 square units. Radius = diameter / 2 = 7. A = π × 7² ≈ 3.1416 × 49 ≈ 153.94.
How do I calculate the area of a square with perimeter 20?
A square with perimeter 20 has area 25 square units. Perimeter = 4 × side → side = 20 / 4 = 5. Area = 5² = 25.
How do I find the area of a trapezoid with bases 6 and 10 and height 4?
The area is 32 square units. A = ½ × (6 + 10) × 4 = ½ × 16 × 4 = 32.
How do I calculate the area of an ellipse with axes 10 and 6?
The area is approximately 47.12 square units. Use semi-major axis a = 5 and semi-minor axis b = 3. A = π × 5 × 3 ≈ 47.12.
How many square feet is a room that is 12 by 14 feet?
A 12×14 foot room is 168 square feet. This is a standard bedroom size. To convert to square meters: 168 × 0.0929 ≈ 15.6 m².
How do I calculate the area of an L-shaped room?
Divide the L-shape into two rectangles, calculate each area separately, then add them together. For example, a 10×8 section plus a 4×5 section = 80 + 20 = 100 sq ft total.
How do I convert square feet to square meters?
Multiply square feet by 0.0929 to get square meters. For example, 200 sq ft × 0.0929 = 18.58 m². To convert m² to sq ft, multiply by 10.764.
How do I calculate the area of a rhombus with diagonals 10 and 6?
The area is 30 square units. A = (d₁ × d₂) / 2 = (10 × 6) / 2 = 30.
People Also Search For
How to calculate square footage of a room
To calculate square footage, measure the room's length and width in feet, then multiply them. A 12-foot by 10-foot room has 120 square feet. For irregularly shaped rooms, divide into rectangles, calculate each, and add the totals. Always measure at the longest and widest points.
Area calculator for land in acres and hectares
Measure your land dimensions in feet or meters, calculate the area, then convert using 1 acre = 43,560 sq ft or 1 hectare = 10,000 m². For rectangular plots, multiply length by width. For irregular plots, divide into rectangles or triangles. Professional surveyors use GPS or total station instruments for precise land measurement.
How to find area of irregular shapes
For irregular shapes, divide the shape into simpler geometric forms (rectangles, triangles, circles), calculate each area separately, then add or subtract them. This decomposition method works for any polygon. For truly irregular shapes, numerical integration or software like AutoCAD is used.
Area formula for all shapes cheat sheet
The key area formulas are: Rectangle = l×w, Square = s², Triangle = ½bh, Circle = πr², Trapezoid = ½(a+b)h, Parallelogram = bh, Ellipse = πab, Rhombus = d₁d₂/2. Memorizing these 8 formulas covers the vast majority of geometry problems in school and real-world use.
How much paint do I need to cover a wall (area calculation)
Calculate wall area (height × width), subtract door/window area, then divide by paint coverage (typically 350–400 sq ft per gallon). A 10×8 foot wall = 80 sq ft. Subtract a 21 sq ft door = 59 sq ft to paint. At 400 sq ft/gallon, less than 1 quart is needed per coat.
Difference between area and volume
Area is a 2D measurement in square units (m², ft²); volume is a 3D measurement in cubic units (m³, ft³). The area of a rectangle is length × width. The volume of a box (rectangular prism) is length × width × height. You cannot directly compare area and volume as they measure different quantities.
Frequently Asked Questions
What is the area of a 10×15 rectangle?
The area of a 10×15 rectangle is 150 square units. Multiply length × width: 10 × 15 = 150. If measured in feet, that's 150 sq ft; in meters, 150 m².
What is the area of a triangle with base 8 and height 5?
The area is 20 square units. Formula: A = ½ × base × height = ½ × 8 × 5 = 20. The height must be perpendicular to the base.
What is the difference between area and perimeter?
Area is the 2D space enclosed by a shape, measured in square units (m², ft²). Perimeter is the total length of the shape's boundary, measured in linear units (m, ft). A 4×4 square has area 16 m² but perimeter 16 m.
What is the difference between surface area and area?
Area applies to flat 2D shapes. Surface area applies to the outer face of 3D objects (like cubes or spheres). This calculator handles 2D plane shapes only.
How many hectares is 10,000 square meters?
Exactly 1 hectare. One hectare = 10,000 m². It's the standard unit for measuring land in most countries, equal to about 2.471 acres.
How do I convert square feet to square meters?
Multiply by 0.0929. For example, 500 sq ft × 0.0929 ≈ 46.5 m². To go the other way, multiply m² by 10.764 to get sq ft.
What is the formula for the area of a trapezoid?
A = ½ × (a + b) × h, where a and b are the lengths of the two parallel sides and h is the perpendicular height between them.
Is my data private?
Yes — all calculations are performed locally in your browser. No values you enter are sent to any server or stored anywhere.
Which shapes does this calculator support?
This calculator supports 8 shapes: Rectangle, Square, Triangle, Circle, Trapezoid, Parallelogram, Ellipse, and Rhombus. Each shape shows the relevant input fields automatically.
Can I use this to calculate flooring needed for a room?
Yes. Select Rectangle and enter your room's length and width in feet or meters. For L-shaped rooms, split into two rectangles, calculate each, and add the results. Add 10% to your order for cuts and waste.
How is the perimeter of an ellipse calculated?
There is no exact simple formula for an ellipse perimeter. This calculator uses Ramanujan's approximation: P ≈ π × [3(a+b) − √((3a+b)(a+3b))], which is accurate to within 0.02% for typical ellipses.