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Area Calculator - Rectangle, Circle, Triangle & More | Calcoul

Free online area calculator. Calculate the area of rectangles, squares, circles, triangles, trapezoids, ellipses, and parallelograms. Includes perimeter calculations.

9 min read

iAbout This Calculator

The area calculator is your comprehensive tool for calculating the surface area of various two-dimensional geometric shapes. Whether you're a student working on geometry homework, a professional calculating material requirements, or a homeowner planning a renovation project, knowing how to calculate area is essential. This calculator supports seven common shapes: rectangles, squares, circles, triangles, trapezoids, ellipses, and parallelograms. Each shape has its own formula, and our calculator handles the math instantly, providing both area and perimeter (or circumference) where applicable. Understanding area calculations is fundamental in mathematics, construction, interior design, landscaping, and countless other fields. From calculating flooring needs to determining the size of a garden plot, area calculations appear in everyday life more often than you might think. Our calculator eliminates the need to remember complex formulas or perform tedious calculations by hand.

?How to Use

  1. 1

    Select the shape you want to calculate from the dropdown menu: rectangle, square, circle, triangle, trapezoid, ellipse, or parallelogram.

  2. 2

    Enter the required measurements for your selected shape. Different shapes require different inputs (length/width for rectangle, radius for circle, etc.).

  3. 3

    All measurements should be in the same unit (meters, feet, inches, etc.). The result will be in square units of your chosen measurement.

  4. 4

    Click Calculate to see the area result. For most shapes, the perimeter or circumference will also be displayed.

  5. 5

    To calculate a different shape, simply select a new shape from the dropdown and enter new measurements.

  6. 6

    For triangles, you can use base and height (most common) or three sides if you know them (uses Heron's formula).

fFormula

A_{rect} = l \times w \quad A_{circle} = \pi r^2 \quad A_{triangle} = \frac{1}{2}bh

Rectangle: Area = length × width. Square: Area = side². Circle: Area = π × radius². Triangle: Area = ½ × base × height (or use Heron's formula with three sides). Trapezoid: Area = ½ × (base₁ + base₂) × height. Ellipse: Area = π × a × b (where a and b are semi-axes). Parallelogram: Area = base × height.

l
Length (rectangle)
w
Width (rectangle)
r
Radius (circle)
b
Base (triangle, parallelogram)
h
Height (triangle, trapezoid, parallelogram)
a, b
Semi-major and semi-minor axes (ellipse)

Examples

Rectangular Room Floor Area

Inputs: shape: rectangle, length: 5, width: 4
Area: 20 sq units

A room measuring 5 meters by 4 meters has a floor area of 20 square meters (5 × 4 = 20). The perimeter is 18 meters (2 × (5 + 4) = 18). If buying flooring at $50/sq meter, you'd need $1,000 worth of flooring plus extra for waste.

Circular Garden Bed

Inputs: shape: circle, radius: 3
Area: 28.27 sq units

A circular garden with a radius of 3 meters has an area of approximately 28.27 square meters (π × 3² ≈ 28.27). The circumference is about 18.85 meters. This helps determine how much mulch or soil is needed.

Triangular Sail

Inputs: shape: triangle, base: 8, height: 6
Area: 24 sq units

A triangular sail with a base of 8 feet and height of 6 feet has an area of 24 square feet (½ × 8 × 6 = 24). This calculation is essential for determining sail material requirements.

Trapezoidal Pool Cover

Inputs: shape: trapezoid, base1: 10, base2: 6, height: 4
Area: 32 sq units

A trapezoidal pool cover with parallel sides of 10 and 6 feet and a height of 4 feet has an area of 32 square feet (½ × (10 + 6) × 4 = 32).

Use Cases

Home Renovation & Flooring

Calculate the floor area of rooms to estimate flooring materials, carpet, or tiles needed. Knowing exact area helps avoid over-ordering or running short on materials.

Landscaping & Gardening

Determine the area of garden beds, lawns, or patios. Calculate how much soil, mulch, grass seed, or paving stones you'll need for your outdoor projects.

Painting & Wall Coverage

Calculate wall areas to estimate paint quantities. Most paint cans cover a specific square footage, so knowing your area helps buy the right amount.

Education & Homework

Students can verify their geometry homework or understand how area formulas work in practice. Teachers can demonstrate area concepts with real-time calculations.

Construction & Architecture

Professionals calculate material requirements for roofing, siding, or sheet materials. Accurate area calculations prevent costly material waste or shortages.

Frequently Asked Questions

What's the difference between area and perimeter?
Area measures the surface inside a shape (in square units like sq meters), while perimeter measures the distance around the outside edge (in linear units like meters). Think of area as the amount of paint needed to cover a surface, and perimeter as the length of fence needed to surround it.
How do I calculate the area of an irregular shape?
Break the irregular shape into simpler geometric shapes (rectangles, triangles, circles). Calculate each area separately, then add them together. For very complex shapes, you might need to subtract areas (calculate a larger shape minus a smaller one cut out of it).
Why is the area of a circle calculated using π (pi)?
Pi (approximately 3.14159) represents the ratio of a circle's circumference to its diameter. This constant naturally appears in all circle calculations because circles have a fundamentally different geometry than straight-sided shapes. The formula A = πr² can be derived through calculus or by dividing a circle into many thin triangles.
What is Heron's formula for triangles?
Heron's formula calculates triangle area using only the three side lengths: Area = √[s(s-a)(s-b)(s-c)], where s is the semi-perimeter (a+b+c)/2. This is useful when you know the sides but not the height. Our calculator uses base×height by default but supports Heron's formula too.
How accurate are these calculations?
The calculations are mathematically exact to 4 decimal places. Any small differences from hand calculations are due to rounding of π or intermediate values. For practical purposes like buying materials, results are more than precise enough.
Can I use this for calculating land area?
Yes, but for simple shapes only. Real land parcels often have irregular boundaries. For simple rectangular or triangular lots, this calculator works well. Enter measurements in meters or feet, and the result will be in square meters or square feet. Note: 1 acre ≈ 43,560 sq ft ≈ 4,047 sq meters.
What's the difference between a trapezoid and a parallelogram?
A trapezoid has exactly one pair of parallel sides (the bases), while a parallelogram has two pairs of parallel sides. A parallelogram's opposite sides are equal in length, but a trapezoid's non-parallel sides can be any length. Both have different area formulas reflecting these geometric differences.
How do I calculate the area of an ellipse?
An ellipse area is calculated as π × a × b, where 'a' is the semi-major axis (half the longest diameter) and 'b' is the semi-minor axis (half the shortest diameter). If the ellipse were a circle, both would be equal (the radius). An ellipse is essentially a stretched circle.

Conclusion

The area calculator is an essential tool for anyone working with measurements and space. From simple tasks like calculating how much carpet to buy, to more complex applications in construction and design, understanding area is fundamental. Our calculator supports the most common geometric shapes and provides instant, accurate results. Remember to keep your units consistent, add extra for waste when buying materials, and break complex shapes into simpler components when needed. Whether you're a student, professional, or DIY enthusiast, this calculator makes geometry accessible and practical.

Last updated: January 5, 2026

Author: Calcoul Team

Reviewed by: Mathematics Expert

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