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🔲 Perimeter Calculator

Find perimeter of rectangles, triangles, circles, and polygons from side lengths and radius.

Boundary Length — Fence, Frame, and Trim

BrainyCalculators editorial insight — unique to this tool

Rectangle perimeter 2(l + w) — a 12×15 ft room needs 54 ft of baseboard before waste factor. Circular perimeter is circumference 2πr. Land survey perimeter differs from area when pricing fencing vs sod.

When to use this calculator

Use when you need outer boundary length of 2D shapes. For enclosed space measure, use Area or Area Converter.

Finding interior area or 3D volume?

This page sums boundary length. For surface area inside a shape, use the Area Calculator →

Diameter = 2r will also be shown.

What is Perimeter?

Perimeter is the total distance around a 2D shape boundary. This calculator sums sides for polygons and uses 2πr for circles.

Use this page for fencing, framing, and homework boundary length. Area measures interior surface; volume measures 3D space.

Triangle calculator can solve sides and angles when not all edges are known upfront.

Perimeter Formulas

Circle: C = 2πr = πd
Rectangle: P = 2(l + w)
Square: P = 4s
Triangle: P = a + b + c
Regular Polygon: P = n × s
Parallelogram: P = 2(a + b)
Rhombus: P = 4s
Trapezoid: P = a + b + c + d

Example — Rectangle 10 × 6

Perimeter = 2 × (l + w) = 2 × (10 + 6) = 32 units
Area = l × w = 10 × 6 = 60 units²

How the Perimeter Calculator Works

Formula, assumptions, and calculation steps for this math tool.

Methodology

Math calculators apply the relevant arithmetic, algebraic, geometric, or numeric rule to the values entered and simplify the result where possible.

Calculation Steps

  1. Read the values and operation selected.
  2. Normalize signs, decimals, fractions, or units if needed.
  3. Apply the mathematical rule or formula.
  4. Format the answer and any intermediate values for checking.

Assumptions and Limits

  • Inputs must be within the supported domain of the operation.
  • Decimal answers may be rounded for readability.
  • Symbolic simplification is limited to the calculator scope.

Frequently Asked Questions

Perimeter is the total length of the boundary around a 2D shape. It is measured in linear units (m, cm, ft, etc.). Think of it as the distance you would walk if you traced the outline of the shape.

Perimeter measures the boundary length of a shape (linear units), while area measures the surface it encloses (square units). A shape with a large perimeter does not necessarily have a large area.

The circumference is the perimeter of a circle. It equals 2πr (using the radius) or πd (using the diameter). For a circle with radius 7: C = 2 × π × 7 ≈ 43.98 units.

Pi (π ≈ 3.14159) is the constant ratio of any circle's circumference to its diameter. This is true for every circle regardless of size. It appears in all circle formulas because of this fundamental relationship.

For an irregular polygon, add the lengths of all sides. If you have coordinates of vertices, you can calculate the distance between consecutive points using the distance formula: d = √((x₂−x₁)² + (y₂−y₁)²), then sum all distances.

Real-World Applications

🏡
Garden Fencing
Calculate the total length of fencing needed to enclose a rectangular garden — perimeter gives the linear metres of fence panels, posts, and gates required, with the calculation adjusted for any gate openings.
🖼️
Picture Frame Moulding
Estimate the total length of picture frame moulding for a set of artworks — each frame's perimeter (plus mitre cut waste allowance) determines the total linear footage to purchase from a framing supplier.
🏈
Sports Field Marking
Calculate the total line length for field sport markings — a standard NFL football field perimeter is approximately 346 yards, determining the quantity of marking paint required per season for maintenance.
🏗️
Skirting Board & Coving Installation
Measure the perimeter of a room to estimate skirting board or coving length — subtracting doorway widths from the total perimeter gives the linear metres of trim to order, with a 10% waste allowance for cuts.
🌊
Pool Coping and Tile Border
Calculate the perimeter of a swimming pool to estimate coping stone length and border tile quantities — a precise measurement prevents ordering excess material or running short on the final stretch.
🔒
Security Perimeter Planning
Security planners calculate site perimeters to size fence installations, determine sensor placement intervals, and estimate the number of CCTV cameras needed for full perimeter coverage.

Common Mistakes

1
Confusing perimeter with area
Perimeter measures the boundary length (linear measurement — metres, feet); area measures the enclosed surface (square measurement — m², ft²). Buying fencing requires perimeter; buying lawn seed requires area. Using area where perimeter is needed (or vice versa) produces wildly incorrect material estimates.
2
Using the wrong formula for circles
The perimeter of a circle is the circumference: C = 2πr = πd. A common mistake is confusing this with the area formula (A = πr²) or applying a rectangular perimeter formula to a circular area. The two formulas use r in different ways and produce results with different units.
3
Not measuring the actual path for irregular shapes
For irregular polygons, there is no formula — the perimeter must be calculated by measuring and summing each side individually. Estimating irregular perimeters by assuming a rectangular or circular approximation can introduce significant errors, especially for complex garden or site boundaries.
4
Forgetting to deduct openings (doors, gates, gaps)
When calculating material quantities for fence panels, skirting boards, or wall tiles, the total perimeter must be reduced by the width of any openings — doorways, gates, or intentional gaps. Buying material for the full perimeter without deductions wastes money on unused pieces.
5
Not adding a waste allowance for cuts and joints
Even when the perimeter is calculated correctly, linear materials (moulding, fencing, piping) require a 5–10% waste allowance for cut ends, mitre joints, and damaged pieces. Ordering exactly the calculated linear length typically results in a shortage.

Perimeter Formulas Quick Reference

Shape Formula Variables
Rectangle P = 2(l + w) l = length, w = width
Square P = 4s s = side length
Triangle P = a + b + c a, b, c = side lengths
Circle (circumference) C = 2πr = πd r = radius, d = diameter
Regular polygon P = n × s n = sides, s = side length
Ellipse (approx.) P ≈ π[3(a+b) − √((3a+b)(a+3b))] a, b = semi-major/minor axes

References

  1. Weisstein, Eric W. "Perimeter." MathWorld — A Wolfram Web Resource. mathworld.wolfram.com, 2024.
  2. Ramanujan, S. "Modular Equations and Approximations to π." Quarterly Journal of Mathematics, 1914.
  3. Coxeter, H.S.M. Introduction to Geometry. Wiley, 1969.
  4. NCTM. Principles and Standards for School Mathematics. National Council of Teachers of Mathematics, 2000.
  5. Stewart, J. Calculus: Early Transcendentals. Cengage, 2015.

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