Perimeter Calculator

What is Perimeter?

The perimeter of any two-dimensional geometric shape is the total continuous distance around its boundary or outer edge. In practical terms, it represents the length of a boundary line or fence needed to enclose a given region.

While perimeter measures a one-dimensional path (with units such as centimeters, meters, inches, or feet), the area represents the two-dimensional region enclosed inside that boundary (measured in square units such as \(\text{cm}^2\) or \(\text{m}^2\)).

Perimeter Formulas for Common 2D Shapes

Depending on the geometry of the polygon or curved figure, the perimeter is calculated using distinct geometric formulas:

Shape	Perimeter Formula	Key Variables
Rectangle	\(P = 2(l + w)\)	\(l\) = length, \(w\) = width
Square	\(P = 4s\)	\(s\) = side length
Circle (Circumference)	\(C = 2\pi r = \pi d\)	\(r\) = radius, \(d\) = diameter
Triangle	\(P = a + b + c\)	\(a, b, c\) = side lengths
Regular Polygon	\(P = n \times s\)	\(n\) = number of sides, \(s\) = side length
Parallelogram	\(P = 2(a + b)\)	\(a, b\) = adjacent side lengths
Trapezoid	\(P = a + b + c + d\)	\(a, b\) = parallel bases, \(c, d\) = legs
Ellipse	\(P \approx \pi [3(a+b) - \sqrt{(3a+b)(a+3b)}]\)	\(a, b\) = semi-major and semi-minor axes
Circle Sector	\(P = 2r + \frac{\theta}{360^\circ}(2\pi r)\)	\(r\) = radius, \(\theta\) = central angle in degrees
Rhombus	\(P = 4s\)	\(s\) = side length

Practical Applications of Perimeter Calculations

Perimeter calculations are essential across many real-world disciplines:

Construction and Fencing: Determining the length of fencing, border edging, or foundation footings needed around a plot of land with our Fence Perimeter Calculator.
Interior Design: Measuring baseboard moldings, crown moldings, wallpapers, and picture framing materials.
Textiles and Crafts: Estimating ribbons, lace borders, sewing hems, and binding tapes around fabrics and quilts.
Engineering & Mechanics: Sizing belts, pulleys, gaskets, and perimeter seals for machinery.

Frequently Asked Questions

What is the difference between perimeter and area?

Perimeter measures the one-dimensional length of a shape's outer boundary, whereas area measures the two-dimensional surface space enclosed inside the boundary.

Can two shapes have the same perimeter but different areas?

Yes. For instance, a rectangle with sides 2 and 8 has a perimeter of 20 and an area of 16, while a rectangle with sides 5 and 5 (a square) has the same perimeter of 20 but a larger area of 25. For any given perimeter, a circle maximizes the enclosed area.

Why is the perimeter of an ellipse an approximation?

Unlike circles or polygons, the exact circumference of an ellipse cannot be written in terms of elementary arithmetic functions and requires complete elliptic integrals of the second kind. Ramanujan's formula provides an extremely accurate closed-form approximation.

How do you find the perimeter of an irregular polygon?

Measure each straight boundary segment individually and sum all their side lengths together: \(P = s_1 + s_2 + \dots + s_n\).

What unit is used for perimeter?

Perimeter uses linear distance units such as meters (m), centimeters (cm), millimeters (mm), feet (ft), inches (in), yards (yd), or miles (mi).

Report

What is Perimeter?

Perimeter Formulas for Common 2D Shapes

Practical Applications of Perimeter Calculations

Frequently Asked Questions

Related Tools

Recent Visits