Area & Perimeter Calculator
Calculate area and perimeter for various geometric shapes
Shape Visualization
Common Shapes Reference
Square
s = side length
Rectangle
l = length, w = width
Triangle
b = base, h = height
Circle
r = radius, π ≈ 3.14159
Area is measured in square units. Perimeter is measured in linear units.
Area & Perimeter Calculator —
Instant Results for Every Shape
The most accurate area and perimeter calculator online. Calculate area, perimeter, circumference and surface measurements for rectangles, squares, circles, triangles, and more — instantly, free, with formulas and step-by-step solutions.
Geometry Basics
What is Area and Perimeter? A Clear Explanation
Understanding the difference between area and perimeter is fundamental to geometry, construction, land measurement, and everyday problem-solving. These two concepts describe very different properties of a two-dimensional shape.
What is Area?
Area refers to the total amount of two-dimensional space enclosed within the boundary of a shape. It measures the interior surface of a figure. Area is always expressed in square units — such as square feet (ft²), square meters (m²), square centimeters (cm²), square yards, or hectares. When you calculate the area of a room, a plot of land, or a field, you're measuring how much flat space it covers.
What is Perimeter?
Perimeter is the total length of the boundary or outline of a two-dimensional shape. It is the sum of all the side lengths of a figure. Unlike area, perimeter is a linear measurement expressed in units such as feet, meters, centimeters, or inches — not square units. Perimeter answers the question: "How far is it around this shape?"
Area vs Perimeter — Key Differences
| Property | Area | Perimeter |
|---|---|---|
| Definition | Space enclosed within a shape | Total length of the outer boundary |
| Units | Square units (ft², m², cm²) | Linear units (ft, m, cm) |
| Measures | Interior surface / coverage | Outer boundary / outline length |
| Use Cases | Flooring, painting, land measurement, tiling | Fencing, framing, border installation |
| Example | How many tiles to cover a room? | How much fencing for a plot? |
| Formula Type | Multiplication of dimensions | Addition of all sides |
Geometry Formulas List
Area and Perimeter Formulas for All Shapes
Our geometry formula calculator supports all major 2D shapes. Below are the standard math formulas used to calculate area and perimeter for each shape. Every calculation on this tool uses these exact formulas to give you accurate, reliable results.
A = l × wPerimeter:
P = 2(l + w)l = length, w = width
A = s²Perimeter:
P = 4ss = side length
A = πr²Circumference:
C = 2πrr = radius
A = ½ × b × hPerimeter:
P = a + b + cb = base, h = height
A = ½(a+b)×hPerimeter:
P = a+b+c+da,b = parallel sides
A = b × hPerimeter:
P = 2(a + b)b = base, h = height
Complete Math Formulas Reference Table
Use this geometry formulas list as a quick reference for all area and perimeter calculations:
| Shape | Area Formula | Perimeter / Circumference Formula | Units |
|---|---|---|---|
| Rectangle | A = l × w | P = 2(l + w) | m², ft², cm² |
| Square | A = s² | P = 4s | m², ft² |
| Circle | A = πr² | C = 2πr | m², cm² |
| Triangle | A = ½bh | P = a + b + c | m², ft² |
| Trapezium | A = ½(a+b)h | P = a+b+c+d | m², cm² |
| Parallelogram | A = b × h | P = 2(a+b) | m², ft² |
| Rhombus | A = ½(d₁×d₂) | P = 4a | m², cm² |
| Pentagon (Regular) | A = ¼√(5(5+2√5))s² | P = 5s | m², ft² |
Tool Guide
How to Calculate Area and Perimeter Online — Step by Step
Our online area calculator is designed for speed and accuracy. Whether you need to find the area of a rectangle for a flooring project or calculate the perimeter of a circular garden, follow these simple steps:
- 1 Select your shape — Choose from rectangle, square, circle, triangle, trapezium, parallelogram, or other supported shapes from the shape selector dropdown.
- 2 Enter your dimensions — Input the required measurements (length, width, radius, height, etc.) in the fields provided. All fields are clearly labeled.
- 3 Choose your unit — Select from meters, feet, centimeters, inches, yards, or other available units for accurate results in your preferred measurement system.
- 4 Click Calculate — Hit the calculate button to instantly get both area and perimeter results, displayed with the correct square units and linear units.
- 5 Review the formula & steps — The calculator shows you the formula used and the step-by-step working so you can understand and verify every result.
Shape Guides
Rectangle & Square Area and Perimeter Calculator
Rectangle Area Calculator
The rectangle area calculator is one of the most frequently used geometry tools. To find the area of a rectangle, multiply its length by its width: A = l × w. For example, a room measuring 8 meters long and 5 meters wide has an area of 40 m². This is essential for flooring, carpeting, painting walls, and land surveys.
The rectangle perimeter formula is: P = 2(l + w). The same 8 × 5 room has a perimeter of 26 meters — useful for calculating baseboard lengths, fencing, or border tiles.
Square Area Calculator
A square is a special rectangle where all sides are equal. The square area calculator uses the formula A = s² where s is the side length. A square plot with 10 m sides has an area of 100 m². The square perimeter calculator formula is P = 4s — so that same plot has a perimeter of 40 meters.
Circle Area Calculator & Circumference Calculator
The circle area calculator uses the formula A = πr², where r is the radius (half the diameter) and π (pi) ≈ 3.14159. If you have a circular garden with a radius of 7 meters, its area is approximately 153.94 m². Our radius to area calculator handles this instantly.
The circumference calculator uses: C = 2πr. For the same garden, the circumference (perimeter equivalent for circles) is approximately 43.98 meters. Enter the radius and our tool calculates both area and circumference simultaneously.
r = d ÷ 2. Our circle area and circumference calculator accepts both radius and diameter inputs for your convenience.
Triangle Area and Perimeter Calculator
The triangle area calculator uses the standard formula A = ½ × base × height. For a triangle with a base of 12 cm and height of 8 cm, the area is 48 cm². Our tool supports all triangle types:
- Right triangle area calculator — uses legs as base and height
- Scalene triangle area calculator — uses Heron's formula with all 3 sides
- Equilateral triangle — all sides equal, area = (√3/4)s²
- Isosceles triangle — two equal sides, standard formula applies
The triangle perimeter calculator simply adds all three sides: P = a + b + c. Enter side lengths and our geometry solver online calculates both area and perimeter with full formula display.
Real-World Applications
Who Uses an Area & Perimeter Calculator?
This geometry calculator online serves a wide range of users — from students solving math word problems to construction professionals calculating material requirements and property owners measuring land.
Measurement Units
Supported Area Units — Square Feet, Meters & More
Our surface measurement calculator supports a comprehensive range of units, making it the ideal calculate dimensions online tool for international users. Switch between units instantly:
- Square feet area calculator — ft² for US & UK
- Square meter calculator — m² for international use
- Feet to meter area calculator — auto unit conversion
- Area in yards calculator — yd² for fabric & sports fields
- cm to meter area calculator — for precision work
- Hectare to square meter calculator — for agricultural land
- Acre calculator — used across South Asia & North America
- Marla / Kanal — Pakistan & India local units
Frequently Asked Questions
Area and Perimeter Calculator — FAQs
Answers to the most commonly asked questions about calculating area, perimeter, and using our geometry solver online.
P = 2(l + w). For a square with side s: P = 4s. For a triangle with sides a, b, c: P = a + b + c. For a circle (circumference): C = 2πr. Our free perimeter calculator handles all these automatically — just enter your dimensions and select your shape.
A = length × width. For example, a rectangle that is 10 meters long and 6 meters wide has an area of 60 m². This formula is used in our rectangle area calculator to deliver instant, accurate results. The area is always expressed in square units (m², ft², cm²).
A = π × r² where r is the radius. If you only know the diameter, divide it by 2 first to get the radius. For example, a circle with radius 5 m has an area of π × 25 ≈ 78.54 m². Our circle area calculator accepts both radius and diameter, and also shows the circumference: C = 2πr.
1 Marla = 272.25 sq ft, 1 Kanal = 20 Marla = 5,445 sq ft, and 1 Acre = 8 Kanals. To use our plot area calculator Pakistan, enter your plot's dimensions in feet or meters, select the output unit as Marla or Kanal, and the tool converts instantly. This makes it ideal for property measurement in Pakistan, land registration, and real estate valuation.
A = ½ × base × height. For a triangle with base = 10 cm and height = 6 cm: A = ½ × 10 × 6 = 30 cm². If you only know all three side lengths (scalene triangle), use Heron's Formula: first calculate the semi-perimeter s = (a+b+c)/2, then A = √(s(s-a)(s-b)(s-c)). Our triangle area and perimeter calculator supports both methods automatically.
1 m² = 10.764 ft². Conversely, to convert square feet to square meters, divide by 10.764 or multiply by 0.0929. Our feet to meter area calculator and square feet calculator Pakistan handles all these conversions automatically when you select input and output units. No manual conversion needed.
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