Perimeter Calculator
Enter dimensions to find the perimeter (total boundary length) of the most common shapes. The primary result is the rectangle perimeter 2(l+w). The circumference result uses length as the radius. The content below explains each shape's formula and real-world uses for perimeter calculations.
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Formula
Rectangle: P = 2(l+w) | Circle: C = 2πr | Square: P = 4s | Triangle: P = a+b+c
Perimeter is the total length of all sides of a polygon, or the circumference for a circle. Rectangle: add all four sides, which simplifies to 2(length + width) since opposite sides are equal. Square: four equal sides, so P = 4×side. Equilateral triangle: 3×side; for scalene triangle, sum all three sides. Circle: circumference = 2πr = πd, where r is radius and d is diameter.
How to use the Perimeter Calculator
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Enter your shape
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Enter your length / side / radius
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Enter your width (rectangle only)
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Read your results instantly
Results update in real time as you type.
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Perimeter of rectangles and squares
A rectangle has two pairs of equal sides. Rather than adding all four separately, the formula 2(l + w) shortens the calculation. For a 10 m × 5 m room: P = 2(10 + 5) = 30 m.
Square perimeter is even simpler: P = 4s. A square room with side 7 m has perimeter 28 m.
Perimeter is essential for fencing, baseboards, framing a picture, and installing trim. It's strictly a boundary measurement — increasing area doesn't always increase perimeter in proportion. A 10×10 square (area 100, perimeter 40) has less perimeter per unit area than a 1×100 rectangle (area 100, perimeter 202).
Circumference of circles
The circumference of a circle is C = 2πr = πd, where r is radius and d is diameter. For a circle with radius 10 m: C = 2π × 10 ≈ 62.83 m.
Circumference appears in wheel travel distance (one full rotation = circumference), track layouts, hula hoops, pizza crusts, and tree measurements (foresters measure trunk circumference and convert to diameter). The relationship between circumference and diameter is exactly π — the definition of π itself.
For a running track, the inner lane has a smaller circumference than the outer lane, which is why sprinters in outer lanes start ahead (staggered starts equalize the actual distance run).
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Perimeter in architecture and landscaping
In architecture, perimeter determines the exterior wall length — directly tied to material costs (siding, brickwork, windows). For a given floor area, compact rectangular buildings (close to square) minimize perimeter and therefore wall cost. Sprawling L-shaped or U-shaped buildings have more wall per unit of floor area.
In landscaping, perimeter tells you how much edging, fencing, or border material you need. A 20 m × 15 m garden requires 2(20+15) = 70 m of fence. If you add a 2 m gate, order 68 m of fencing.
Perimeter can also approximate the length of a walking path around a park or sports field. For standard tracks, the inner perimeter is 400 m — if the field inside is roughly elliptical with semi-axes 36.8 m and 84.39 m, the circumference formula for an ellipse approximates this.
Tips & Insights
Don't confuse radius and diameter
The circumference formula C = 2πr uses the radius. If you measure across the circle (diameter), use C = πd instead. For a wheel 60 cm in diameter: C = π × 60 ≈ 188.5 cm = 1.885 m per revolution. At 100 rpm, it travels 188.5 m/min.
Perimeter scales linearly with size
If you double all dimensions of a rectangle, the perimeter doubles. Area quadruples. This linear vs. square relationship is why large buildings are relatively cheaper per floor area to enclose than small buildings of the same shape.
Irregular polygon perimeter
For any polygon (triangle, hexagon, irregular shape), perimeter = sum of all side lengths. For a triangle with sides 5, 7, and 9: P = 21. No formula needed beyond addition. GPS-enabled mapping apps calculate garden perimeters this way — they sum the geodesic distances between your marked boundary points.
Worked Examples
Garden fencing
Perimeter = 2(12 + 8) = 40 m. You need 40 m of fencing. If posts go every 2 m, you need 20 posts. Add a 1.2 m gate: order 38.8 m of fence material and 20 posts.
Wheel circumference for travel calculation
Circumference = 2π × 0.35 ≈ 2.199 m. Each wheel rotation covers 2.199 m. At 500 RPM (a bicycle going roughly 18 km/h), the wheel rotates about 500 times per minute, covering 500 × 2.199 ≈ 1,100 m per minute.
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Frequently Asked Questions
What is the difference between perimeter and area?
Perimeter is the total length of the boundary (measured in units like m or ft). Area is the amount of space enclosed inside the boundary (measured in square units like m² or ft²). A shape with the same perimeter can have very different areas depending on its proportions.
What is the circumference of a circle?
Circumference is the perimeter of a circle: C = 2πr (using radius) or C = πd (using diameter). π ≈ 3.14159. It's the total length of the circle's boundary.
How do I find the perimeter of a triangle?
Add all three side lengths: P = a + b + c. For an equilateral triangle (all sides equal), P = 3s. For a right triangle with legs 3 and 4, the hypotenuse is √(9+16) = 5, so P = 3 + 4 + 5 = 12.
Does a square or circle have more perimeter for the same area?
For equal area, the circle has the smallest perimeter (circumference). The square has more perimeter than a circle of equal area. This is the isoperimetric theorem: among all shapes with equal perimeter, the circle has the greatest area.
How do I calculate perimeter for an irregular shape?
Measure and sum every side length. For curves, use a string to trace the boundary, then measure the string length. GIS software and digital design tools can calculate perimeters of any traced shape automatically.
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