The perimeter calculator above measures the distance all the way round the outside of a shape, for the six outlines that cover almost every practical case. It reports the enclosed area alongside, because in real work you nearly always need both — the perimeter tells you how much edging, fencing, skirting or framing to buy, and the area tells you how much covering material goes inside it.
Arb Digital publishes this as part of a free geometry set. The two figures in the results panel that you will not find on most perimeter pages are the shape efficiency and the equivalent circle radius, and both are explained below. They answer a question people often have but rarely phrase: is this shape a sensible one for the job, or is it wasting boundary?
What This Perimeter Calculator Does
Pick a shape, enter its dimensions, and the tool returns the perimeter in your chosen unit along with the enclosed area in that unit squared. A rectangle 8 cm by 5 cm has a perimeter of 26 cm and an area of 40 cm². Switch to a circle of radius 5 and the perimeter — properly called the circumference — is 31.42 cm around an area of 78.54 cm².
The allowance field adds a percentage for cuts, joins and overlaps, which is what turns a geometric number into a materials order. For a triangle the calculator also validates the three sides against the triangle inequality, and for an ellipse it uses Ramanujan's approximation, since an ellipse has no exact elementary perimeter formula.
How to Use It
- Choose the shape from the dropdown. The input fields change to match, so you are never entering a dimension the shape does not have.
- Enter the dimensions in one consistent unit. Mixing units between fields is the most common cause of a wrong answer.
- Select the unit so both the perimeter and the squared area label correctly.
- Add an allowance if you are buying material to run around the edge. Ten percent is a common starting point for mitred trim.
- Compare the shape efficiency against other options if the outline is still up for decision — it shows how much boundary the shape costs for the area it encloses.
The Formulas Behind Each Shape
Perimeter is simply the total length of the boundary, so for any straight-sided shape you add up the sides. A rectangle gives P = 2(l + w), so 2 × (8 + 5) = 26. A square is P = 4s. A triangle is P = a + b + c. A regular polygon with n equal sides is P = n × s.
Curved shapes need a constant. A circle's boundary is C = 2πr, which for r = 5 is 31.416. An ellipse has no exact elementary formula at all, so this tool uses Ramanujan's approximation — accurate to about one part in a million for near-circular shapes and never worse than roughly 0.04% even for extremely flattened ones. Our ellipse calculator sets that out in full, and MathWorld's perimeter entry gives the formal definitions.
Areas come from the matching formulas: lw for a rectangle, s² for a square, Heron's formula for a triangle from three sides, πr² for a circle, πab for an ellipse and ½ × perimeter × apothem for a regular polygon.
Perimeter Does Not Determine Area
This is the single most important thing to understand about perimeter, and it catches people out constantly. Two shapes with identical perimeters can enclose wildly different areas. A 10 by 10 square and a 1 by 19 rectangle both have a perimeter of 40, but the square encloses 100 square units and the strip encloses 19 — less than a fifth of it, for exactly the same amount of fencing.
The relationship runs one way only. A larger area needs at least a certain perimeter, but a larger perimeter guarantees nothing about area. This is why land is not priced by boundary length, why a long thin room costs disproportionately more to skirt than a square one of the same floor area, and why anyone quoting a job from a perimeter alone is guessing at the material inside it.
Shape Efficiency and the Isoperimetric Rule
The efficiency figure in the results is 4πA / P², sometimes called the isoperimetric quotient. It answers the question "how much area does this shape enclose compared with the best possible shape of the same perimeter?" A circle scores exactly 1, or 100%. Nothing can beat it: for any fixed perimeter, the circle encloses the maximum possible area, a result known as the isoperimetric inequality.
Everything else scores below 1. A regular hexagon scores about 0.907, a square 0.785, an equilateral triangle 0.605, and our 8 by 5 rectangle 0.743. As a rectangle grows more elongated the score collapses — a 1 by 19 strip scores 0.149, meaning it wastes about 85% of its enclosing potential.
This is not an abstraction. If you are enclosing a paddock, designing a room, planning a plot or sizing packaging, the efficiency score tells you directly how much boundary material the shape is costing you for the space it delivers. Squarer is cheaper. The equivalent circle radius alongside it gives the same information as a length: it is the radius of the circle that encloses the same area, so comparing your actual perimeter against 2π times that radius shows the shortfall in concrete terms.
Perimeter, Circumference and the Words People Use
Perimeter is the general word for the distance round any closed plane figure. Circumference is the same quantity when the figure is a circle or another curved shape, and it is the conventional term there. Both are lengths measured in metres, feet or inches — never in squared units, which is the difference from area. In the SI system documented by NIST, length is a base quantity and area is derived from it, which is exactly why one carries an exponent and the other does not.
A related term you may meet is girth, used in shipping to mean the perimeter of a package's cross-section, and in forestry for the circumference of a trunk. Postal size limits often combine length and girth into a single allowance, and the girth in that calculation is the perimeter of the end face, not half of it.
Where a boundary is not smooth, perimeter becomes genuinely slippery. The measured length of a rugged coastline increases the finer the ruler you use, because smaller ruler lengths follow more of the detail. This is the coastline paradox, and it is why quoted coastline figures for the same country can differ by large factors between sources. For anything with fractal-like roughness there is no single true perimeter, only a perimeter at a stated measurement scale.
From Perimeter to a Materials Order
A perimeter figure buys the things that run around an edge: skirting board, coving, fencing, edge trim, kerbing, guttering, picture framing, seam tape. In each case you order the perimeter plus an allowance, because every corner costs a cut and every mitre wastes stock. The allowance field handles that; 10% is a reasonable default for a simple rectangular room, more if the shape has many corners.
Two practical adjustments the raw number does not include. First, deduct openings where the trim genuinely stops — a doorway breaks a run of skirting, so subtract its width. Second, buy in the stock lengths your supplier actually sells; needing 26 m of 3 m board means nine boards and 27 m purchased, not 26.
The area figure alongside is what feeds the covering calculation, and each material has its own rules. Take it to the flooring calculator or carpet calculator for floors, the tile calculator for tiling, the paint calculator for coverage per coat, the wall area calculator for walls with openings deducted, and the concrete calculator when the area has a depth. This page gives you the clean geometry; those apply the trade rules on top.
Awkward Outlines and Composite Shapes
Real rooms and plots are rarely one clean shape. For an L-shaped outline the perimeter is simply the total of all the outside edges walked once — and note that unlike area, you do not add the perimeters of the two rectangles you split it into, because the shared internal edge is not part of the boundary at all. That double-counting is the classic mistake with composite perimeters.
For a shape mixing straight and curved edges, such as a rectangle with a semicircular end, add the straight sections to the curved arc length. For an outline defined by corner coordinates, our polygon calculator sums the edges for you, and for a partial circle the arc length calculator gives the curved portion directly.
Arb Digital builds calculators that answer one question properly, rank for the searches behind it, and put your business in front of people already looking for it. Browse the set we publish, or talk to us about your own.
Browse All Free Tools Talk to Arb DigitalCommon Mistakes to Avoid
- Adding the perimeters of sub-shapes — splitting an L-shaped room into two rectangles works for area but double-counts the shared internal edge for perimeter.
- Labelling a perimeter in squared units — perimeter is a length. Only the area carries the exponent.
- Assuming equal perimeters mean equal areas — a 10 by 10 square and a 1 by 19 strip share a perimeter of 40 but differ fivefold in area.
- Using the diameter in place of the radius — circumference is 2πr or πd, and mixing the two doubles the answer.
- Ordering the exact perimeter — corners waste material, doorways interrupt runs, and stock comes in fixed lengths.
Related Free Tools From Arb Digital
Get the area side in detail with the rectangle area calculator, work out full circle properties with the circle calculator, and convert dimensions with the length converter or a finished area with the area converter. Everything sits in our free online tools hub.
Frequently Asked Questions
Perimeter equals twice the sum of the length and the width: P = 2(l + w). A rectangle 8 cm by 5 cm has a perimeter of 2 × 13 = 26 cm.
They measure the same thing — the distance round the outside of a shape. Circumference is the conventional word for circles and other curved figures; perimeter is the general term used for straight-sided shapes.
Yes, and the difference can be enormous. A 10 by 10 square and a 1 by 19 rectangle both have a perimeter of 40 units, but they enclose 100 and 19 square units respectively. Perimeter alone never determines area.
The circle, always. This is the isoperimetric inequality. The shape efficiency figure in the results compares your shape against that ideal, with a circle scoring 100%.
Walk the outside edge once and add every external side. Do not split it into rectangles and add their perimeters — that counts the shared internal edge, which is not part of the boundary.
No. Perimeter is a length, so it is measured in metres, feet or inches. Only area uses squared units such as square metres or square feet.
Use the allowance field to add a percentage for cuts and mitres, then round up to whole stock lengths, since suppliers sell fixed sizes. Also deduct doorways and other openings where the run genuinely stops.
