The Shape Perimeter Calculator calculates the distance around a shape — the length of fencing, edging, trim or border you need.
It adds the side lengths for straight-sided shapes (P = 2(l + w) for a rectangle), uses 2πr for circles and includes the straight edges of semicircles and sectors. For irregular shapes, enter the corners as coordinates and the calculator adds the distance between each pair of corners.
Shape Perimeter Calculator
Perimeter of a rectangle, square, triangle, circle, semicircle, sector, L-shape, regular polygon or any irregular shape from coordinates.
Formula
| Shape | Perimeter |
|---|---|
| Rectangle | P = 2(l + w) |
| Square | P = 4a |
| Triangle | P = a + b + c |
| Circle | C = 2πr |
| Semicircle | P = πr + 2r |
| Sector | P = rθ + 2r (θ in radians) |
| L-shape | P = 2(W + H) |
| Regular polygon | P = n × s |
| Irregular (coordinates) | P = Σ √((xᵢ₊₁ − xᵢ)² + (yᵢ₊₁ − yᵢ)²) |
Where: l = length, w = width, a = side, r = radius, θ = sector angle, W and H = overall width and height of the L-shape, n = number of sides, s = side length.
How the Calculation Works
Step 1: Identify every edge of the shape, straight or curved.
Step 2: Find each edge’s length. Curved edges use arc length (2πr for a full circle, rθ for an arc).
Step 3: Add the edges. For coordinates, each edge length comes from the distance formula between neighboring corners.
Variables Explained
| Variable | Meaning | Unit |
|---|---|---|
| P | Perimeter | cm, m, in, ft |
| r | Radius | cm, m, in, ft |
| θ | Sector angle | degrees |
| x, y | Corner coordinates | cm, m, ft… |
Example Calculation
Semicircle
Given: radius = 5 cm
Result: P = 3.14159 × 5 + 10 ≈ 25.71 cm
L-shaped patio
Given: overall 10 m wide and 8 m high, with a rectangular notch cut from one corner
Result: P = 2 × (10 + 8) = 36 m
Irregular shape
Given: corners (0, 0), (12, 0), (14, 7), (6, 11), (−1, 6) cm
Result: P ≈ 42.91 cm (area 121.5 cm²)
Common Length Conversion Table
| Unit | Equivalent |
|---|---|
| 1 m | 100 cm = 3.2808 ft |
| 1 ft | 12 in = 0.3048 m |
| 1 yd | 3 ft = 0.9144 m |
| 1 in | 2.54 cm |
Shape Properties
Why an L-shape has the same perimeter as its rectangle
Cutting a rectangular notch from a corner removes two edge pieces but adds two inner edges of exactly the same lengths. So the perimeter of any L-shape equals 2 × (overall width + overall height), even though its area is smaller.
Dimensions Explained
Perimeter vs area
Perimeter is a length (m, ft) — for fencing, edging and trim. Area is in square units (m², ft²) — for flooring, paint or turf.
Openings and gates
The perimeter is the full distance around. If a fence has a gate or a wall already forms one side, subtract that length when ordering materials.
Frequently Asked Questions
How do you find the perimeter of a shape?
Add the lengths of all its sides. For circles, use 2πr.
How do you find the perimeter of an irregular shape?
Measure every side and add them, or enter the corner coordinates and let the calculator add the distances.
How do you find the perimeter of an L-shape?
Add all six sides, which always equals 2 × (overall width + overall height).
What is the perimeter of a semicircle?
The curved half plus the diameter: πr + 2r.
How do you find the perimeter of a regular polygon?
Multiply the number of sides by the side length.