Perimeter Calculator — 2D Shapes
Calculate the perimeter and circumference of common 2D shapes.
What Is the Perimeter Calculator — 2D Shapes?
The Perimeter Calculator computes the perimeter (total boundary length) of common 2D shapes. Select a shape, enter the required dimensions, and get the exact perimeter. For triangles, it also computes the area using Heron's formula. For circles, the perimeter is called the circumference.
Formula
How to Use
Select the shape from the dropdown. Enter the required dimensions for that shape. Click Calculate to see the perimeter (or circumference for circles). For triangles, the tool also checks the triangle inequality and shows the area.
Example Calculation
Rectangle: l=8, w=5 P = 2(8+5) = 2×13 = 26 units Triangle: a=3, b=4, c=5 P = 3+4+5 = 12 units s = 6, Area = √(6×3×2×1) = √36 = 6 sq units Circle: r=10 C = 2×π×10 = 62.832 units
Understanding Perimeter — 2D Shapes
Perimeter is one of the most practical geometric measurements. Fencing a yard, framing a picture, running track on a field, tiling a border — all require perimeter calculations. The word "perimeter" comes from the Greek words peri (around) and metron (measure).
For a given area, the shape with the minimum perimeter is a circle (isoperimetric inequality). This is why soap bubbles are spherical (minimizing surface area for a given volume), and why circular containers are efficient. Conversely, for a given perimeter, the circle encloses the maximum area.
The isoperimetric problem — finding the shape of maximum area for a given perimeter — was known to the ancient Greeks and has a rigorous modern proof using calculus of variations. The answer is always a circle.
Frequently Asked Questions
What is the difference between perimeter and area?
Perimeter is the total length of the boundary (measured in units: cm, m, etc.). Area is the surface enclosed inside the boundary (measured in square units: cm², m², etc.).
What is the circumference of a circle?
The circumference is the perimeter of a circle. C = 2πr = πd. It is the distance you would travel if you walked along the edge of the circle once.
What is a regular polygon?
A regular polygon has all sides equal and all angles equal. Examples: equilateral triangle (3 sides), square (4), pentagon (5), hexagon (6). Its perimeter is simply n × s where n is the number of sides and s is the side length.
What is Heron's formula?
Heron's formula computes the area of a triangle from its three side lengths, without needing the height. It uses the semi-perimeter s = (a+b+c)/2: Area = √(s(s−a)(s−b)(s−c)).
Can I use this for irregular shapes?
For irregular polygons, add up all side lengths. For irregular curves, the perimeter must be computed using arc length integrals, which is beyond the scope of this calculator.
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