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Area & Perimeter Calculator

Calculate the area and perimeter of circles, squares, rectangles, triangles, trapezoids, and ellipses. Formulas are shown alongside every result so you can check the math yourself.

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Area —
Perimeter / Circumference —
Shape —

Circle

Enter the radius to calculate area, circumference, and diameter.

Results

Area — A = πr²
Circumference — C = 2πr
Diameter — d = 2r

Shape Formulas & Concepts

Area in real life

Area tells you how much surface a shape covers. You use it when buying flooring (how many m² of tile?), painting a wall (how many liters of paint?), or planning a garden (how many m² need seeding?). Always match your units — if the width is in meters and height is in centimeters, convert first.

Area is always expressed in square units: cm², m², ft², acres, hectares.

Perimeter vs. area

Perimeter is the total length of the boundary around a shape — like how much fencing you need around a yard. Area is how much space is inside — like how much grass you would need to cover the yard.

Two shapes can have the same perimeter but very different areas. A square has the largest area for a given perimeter among all rectangles. A circle has the largest area for any given perimeter of any shape.

Common formulas cheat sheet

  • Circle: A = πr², C = 2πr
  • Square: A = s², P = 4s
  • Rectangle: A = wh, P = 2(w+h)
  • Triangle (sides a,b,c): A = √(s(s−a)(s−b)(s−c))
  • Trapezoid: A = (a+b)/2 × h
  • Ellipse: A = πab

Units of area

The unit of area is always the square of the length unit used as input. Common conversions:

  • 1 m² = 10,000 cm²
  • 1 hectare = 10,000 m²
  • 1 acre ≈ 4,047 m²
  • 1 ft² = 144 in²
  • 1 mile² = 640 acres

This calculator is unit-agnostic — enter values in any consistent unit and the result will be in that unit squared.

Unit Converter

Convert between length, area, volume, and mass units. Handy when your measurements are in mixed units before calculating area.

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Scientific Calculator

Full scientific calculator with trig, logarithms, powers, and constants — useful for custom geometry calculations.

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Statistics Calculator

Calculate mean, median, standard deviation, and more from a list of numbers — ideal for analyzing a dataset of measurements.

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FAQ

What is the difference between area and perimeter?

Area is the amount of two-dimensional space inside a shape, measured in square units (cm², m², ft²). Perimeter is the total length of the shape's outer boundary, measured in linear units (cm, m, ft). For circles the boundary is called the circumference instead of perimeter.

How do you find the area of a circle?

Use the formula A = πr², where r is the radius. Multiply π (approximately 3.14159) by the square of the radius. The circumference is C = 2πr. Enter the radius in the Circle tab above to get instant results.

What is Heron's formula and when do you use it?

Heron's formula finds the area of a triangle when you know all three side lengths but not the height. Compute the semi-perimeter s = (a+b+c)/2, then the area is A = √(s(s−a)(s−b)(s−c)). It is especially useful in surveying and construction where side lengths are easier to measure than height.

What are the area formulas for common shapes?

Circle: A = πr². Square: A = s². Rectangle: A = w × h. Triangle: A = √(s(s−a)(s−b)(s−c)) where s = (a+b+c)/2. Trapezoid: A = (a+b)/2 × h where a and b are parallel sides and h is height. Ellipse: A = π × a × b where a is the semi-major axis and b is the semi-minor axis.

What is a semi-major axis of an ellipse?

An ellipse looks like a stretched circle. The semi-major axis (a) is half the length of its longest diameter — the distance from the center to the farthest point on the edge. The semi-minor axis (b) is half the shortest diameter. When a = b the shape is a perfect circle. The area is A = πab and the perimeter is approximated using the Ramanujan formula.