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    Perimeter Calculator

    Calculate the perimeter of various geometric shapes

    How It Works

    Overview

    The perimeter calculator measures the total distance around the boundary of a two-dimensional shape. Pick a shape, enter its dimensions, and the calculator returns the boundary length in linear units. For a circle, this length is called circumference rather than perimeter — the distinction is purely terminology.

    Perimeter is one of the most practical geometry calculations: it's the number you need when buying fencing, decorative trim, picture-frame moulding, garden edging, or weather stripping. Polygons (rectangles, triangles, trapezoids) just sum their side lengths, while circles use the constant π to relate radius to circumference.

    The Formula

    Rectangle: P = 2(l + w) | Square: P = 4s | Circle: C = 2πr

    The formula depends on the shape:

    • Rectangle: P = 2 × (length + width)
    • Square / Rhombus: P = 4 × side
    • Circle (circumference): C = 2 × π × radius = π × diameter
    • Triangle: P = a + b + c (sum of all three sides)
    • Parallelogram: P = 2 × (a + b), where a and b are adjacent sides
    • Trapezoid: P = a + b + 2c when the two non-parallel sides are equal
    • Regular polygon: P = n × side, where n is the number of sides

    Worked Example

    Suppose you want to put decorative trim around a rectangular bedroom that's 14 ft × 11 ft, plus a circular mirror with a diameter of 3 ft.

    • Room perimeter: 2 × (14 + 11) = 50 ft of trim
    • Subtract a 3 ft door opening: 50 − 3 = 47 ft of trim needed
    • Mirror circumference: π × 3 ≈ 9.42 ft of frame
    • Total trim order: 47 + 9.42 ≈ 56.4 ft, plus 10% waste ≈ 62 ft

    For comparison, a square room with the same 50 ft perimeter would be 12.5 ft per side — same boundary length, but different shape and area.

    When to Use This

    • Fencing — determine how much fence material is needed to enclose a yard or paddock.
    • Trim and moulding — calculate baseboard, crown moulding, or picture-frame length.
    • Garden edging — measure flexible edging around irregular flowerbeds.
    • Sports tracks and routes — find the lap distance around an oval or rectangular path.
    • Weather stripping and seals — order the right length to seal a door, window, or hatch.

    Common Mistakes to Avoid

    • Confusing diameter with radius. Circumference uses radius in the 2πr form, or diameter in the πd form — don't mix them.
    • Forgetting to subtract openings. When ordering fence or trim, deduct gates, doors, and windows from the total perimeter.
    • Mismatched units. Convert all sides to a single unit before adding them together.
    • Using the wrong formula for non-equilateral shapes. A scalene triangle's perimeter requires all three side lengths, not 3 × one side.
    • Skipping the waste factor. Real-world projects need 5–15% extra for cuts, joins, and miscalculations.

    Frequently Asked Questions

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