Find perimeter and circumference of various geometric shapes including rectangles, squares, triangles, circles, and sectors. Get step-by-step solutions for all your perimeter calculations.
You have a rectangular garden that is 12 meters long and 8 meters wide. How much fencing do you need to enclose it?
Formula: P = 2(l + w) = 2(12 + 8)
Solution: P = 2 × 20 = 40 meters of fencing
Don't forget to account for a gate if needed — subtract the gate width from the total.
A square field has sides of 75 meters. An athlete runs 3 laps around the field.
Perimeter of field: P = 4s = 4 × 75 = 300 meters
Total distance for 3 laps: 3 × 300 = 900 meters
This is equivalent to 0.9 km — a great warm-up distance!
A triangular park has sides measuring 30 m, 40 m, and 50 m. What distance does a jogger cover in one lap around the park?
Formula: P = a + b + c = 30 + 40 + 50
Solution: P = 120 meters
This is a 3-4-5 triangle scaled by 10 — a right triangle! The jogger covers 120 m per lap.
A bicycle wheel has a radius of 35 cm. How far does the bike travel in one full rotation of the wheel?
Formula: C = 2πr = 2 × π × 35
Solution: C = 219.91 cm ≈ 2.2 m
In 100 rotations, the bike travels about 220 meters. Wheel circumference is critical for speedometer calibration!
A 12-inch pizza (radius 6 inches) is cut into 8 equal slices. What is the crust length (arc) of one slice?
Formula: Arc = (θ/360) × 2πr = (45/360) × 2π × 6
Solution: Arc = 4.71 inches of crust per slice
The total perimeter of the slice includes 2 radii (12 inches) plus the arc, totaling 16.71 inches of edge.
The perimeter is the total distance around the outside of a two-dimensional shape. For circles, the perimeter is called the circumference. Below are the formulas for the most common shapes.
Always ensure all measurements are in the same unit before calculating. Convert if necessary — our calculator handles this automatically.
For circle calculations, π is approximately 3.14159. Our calculator uses high precision for accurate results.
Perimeter measures the distance around a shape, while area measures the space inside. Don't confuse the two!
For rectangles and squares, you can verify by adding all sides individually. For circles, check with C = πd as an alternative formula.
The perimeter is the total distance around the boundary of a two-dimensional shape. It is a linear measurement — meaning it measures length, not area. For polygons (shapes with straight sides), the perimeter is found by adding up the lengths of all sides. For circles, the perimeter is called the circumference, calculated using π (pi).
Perimeter is one of the most fundamental concepts in geometry and has countless practical applications. Whether you're installing a fence around your yard, framing a picture, or calculating how much trim you need for a room, you're working with perimeter.
Unlike area (which measures the space inside a shape) or volume (which measures the space inside a 3D object), perimeter simply measures the boundary length. This makes it an essential first step in many construction, design, and measurement tasks.
Calculating perimeter depends on the shape you're working with. Here's a breakdown of the most common formulas and when to use each one:
Rectangle: P = 2(l + w). A rectangle has two pairs of equal sides. Add the length and width, then multiply by 2. For a rectangle with length 10 m and width 6 m: P = 2(10 + 6) = 2 × 16 = 32 m.
Square: P = 4s. All four sides of a square are equal. Simply multiply the side length by 4. For a square with side 7 cm: P = 4 × 7 = 28 cm.
Triangle: P = a + b + c. Add all three side lengths together. For a triangle with sides 5, 6, and 7 cm: P = 5 + 6 + 7 = 18 cm. If two sides are equal, it's an isosceles triangle. If all three are equal, it's equilateral.
Circle (Circumference): C = 2πr. Use π ≈ 3.14159. For a circle with radius 5 cm: C = 2 × 3.14159 × 5 = 31.42 cm. Alternatively, use the diameter: C = πd.
Circle Sector: P = 2r + (θ/360) × 2πr. First find the arc length (the curved part of the sector), then add two radii. For a sector with radius 10 cm and angle 60°: Arc = (60/360) × 2π × 10 = 10.47 cm, then P = 2 × 10 + 10.47 = 30.47 cm.
All three sides are equal. Perimeter = 3 × side. Example: side = 6 cm → P = 18 cm.
Two sides are equal. Perimeter = 2a + b where a = equal sides, b = base.
All three sides are different. Perimeter = a + b + c (sum of all sides).
Has one 90° angle. The longest side (hypotenuse) can be found using the Pythagorean theorem if needed.
Understanding perimeter is essential in many everyday situations. Here are some practical applications:
Calculate how much baseboard, crown molding, or wallpaper border you need for a room. Measure the perimeter of the room and subtract door openings.
Determine how much fencing, edging, or decorative trim is needed for gardens, patios, and lawns. Perimeter calculations help estimate material costs.
Track running distances around tracks, fields, and courts. A standard 400-meter track has an oval shape with specific dimensions.
Calculate the total length of frame material needed for pictures, mirrors, and artwork. The frame length equals the perimeter of the artwork.
⚠️ Important Note: This Perimeter Calculator is for educational and informational purposes only. While every effort has been made to ensure accuracy, results should be verified independently for critical applications such as construction, engineering, manufacturing, or any project where precise measurements are required. Always double-check your measurements and calculations for high-stakes applications.