Perimeter Calculator

The perimeter is the total distance around the edge of a flat shape. For a rectangle, use P = 2 × (L + W): an 8 m by 5 m yard has a perimeter of 2 × (8 + 5) = 26 m (about 85.3 ft). This perimeter calculator does the same for six shapes (rectangle, square, triangle, circle, regular polygon and trapezoid) and shows the exact formula and every step of the arithmetic.

For the space inside a shape, use the Area Calculator; for every property of one shape, the Circle Calculator, Triangle Calculator and Trapezoid Calculator go deeper. When the perimeter is a shopping list, the Fence Calculator turns a boundary into posts and rails and the Linear Feet Calculator adds up running lengths of trim or lumber.

The perimeter formulas for every shape

Each shape has its own formula, but they all come down to "add up the boundary." Here are the ones this tool uses:

Here L and W are the rectangle's length and width, s is a side length, r is the circle's radius (or d its diameter, with C = πd), and n is the number of equal sides on a regular polygon. In the trapezoid, a and c are the parallel sides and b and d the legs. The circle result is properly called the circumference, but it measures the same thing as a perimeter: the distance around.

What perimeter actually means

Perimeter is a one-dimensional length. Unlike area, which fills the inside of a shape and is measured in square units, perimeter only follows the outline, so it is measured in plain linear units such as feet, meters and inches. The word comes from the Greek peri ("around") and metron ("measure"). If your answer ever ends up in square units, you have accidentally calculated area instead.

How to use this perimeter calculator

You can get an answer in seconds:

1. Pick a shape: tap rectangle, square, triangle, circle, regular polygon or trapezoid. The matching formula appears immediately, and each shape opens with sample values from the examples on this page that you can overwrite.
2. Enter the dimensions: type each measurement the shape needs. For a rectangle that is length and width; for a circle, the radius or (after tapping "I know the diameter") the diameter; for a regular polygon, the number of sides and one side length; for a trapezoid, the two parallel sides and the two legs.
3. Choose the unit you measured in: every dimension must use that unit. The result also shows the same perimeter in feet or meters (inches or centimeters for small units, miles or kilometers for large ones).
4. Read the result: the large number at the top is the perimeter (or circumference). The step-by-step card shows exactly how it was calculated, and the area appears wherever the inputs fix it.

The result updates instantly as you type, so you can experiment: double a side and watch the perimeter respond.

Worked example 1: a rectangle

Suppose a garden bed is 8 m by 5 m. Add the two different sides first: 8 + 5 = 13. Then double, because there are two of each: 2 × 13 = 26 m, or about 85.3 ft. If you were edging it with brick, you would buy 26 m of edging (plus a little extra for cuts). Notice the area of the same bed is 8 × 5 = 40 m², a square-unit measurement and a completely different quantity from the perimeter.

Perimeter of a rectangle chart (length × width)

Every value below is 2 × (L + W). Read down to your length and across to your width; the cell is the perimeter in the unit you measured in.

Worked example 2: a circle

A circular patio has a radius of 7 ft. The circumference is C = 2 × π × r = 2 × 3.14159 × 7 = about 43.98 ft. If you only knew the diameter (14 ft), you would get the same answer with C = π × d = 3.14159 × 14; in the calculator, tap "I know the diameter" and enter 14. That circumference tells you how much edging or coping you need to run around the patio's rim.

Circle circumference by radius and diameter

Circumference is a circle's perimeter, C = 2πr. The diameter column is just 2 × the radius, so you can look up either measurement.

Worked example 3: a regular hexagon

A regular hexagon has 6 equal sides. If each side is 4 in, the perimeter is simply n × s = 6 × 4 = 24 in. The same logic scales to any regular polygon: a regular pentagon (5 sides) with 10 cm sides has a perimeter of 5 × 10 = 50 cm. Because all sides are equal, you never have to measure more than one.

Quick reference table

These ready-made results assume the dimensions shown; swap in your own numbers above for an exact answer.

Who this calculator is for

Anyone who needs the distance around a shape, including:

• Students and teachers checking geometry homework or showing the working step by step.
• DIY and home projects: measuring fencing, baseboard, picture-frame trim, garden edging or ribbon.
• Crafters and sewers figuring out binding, piping or border length.
• Landscapers and contractors estimating curbing or perimeter materials before a job.
• Anyone who wants a quick, transparent answer with the formula spelled out.

Key terms explained

• Perimeter: the total length of the boundary of a flat shape.
• Circumference: the perimeter of a circle, found with 2πr.
• Radius (r): the distance from the center of a circle to its edge, half the diameter.
• Diameter (d): the distance straight across a circle through the center; d = 2r.
• Regular polygon: a many-sided shape whose sides (and angles) are all equal, so P = n × s.
• Side (s): one straight edge of a shape; for squares and regular polygons every side is the same.

Perimeter vs. area: don't mix them up

Perimeter and area answer different questions. Perimeter is how far it is around the edge (a length, in feet or meters). Area is how much surface fits inside (in square feet or square meters). You use perimeter for fencing, framing and edging; you use area for paint, flooring, sod and turf. Two shapes can share the same area but have wildly different perimeters: a long, thin rectangle has a much bigger perimeter than a square of the same area. When your project needs the inside surface rather than the boundary, switch over to the Area Calculator; it covers the same shapes in square units.

From a rectangle's perimeter to its missing side and area

A classic homework question gives the perimeter and one side and asks for the other side or the area. The trick: half the perimeter equals length + width, so subtract the side you know to find the side you don't, then multiply for the area. Every row below is worked with P ÷ 2 − known side.

Worked in full for the first row: a rectangular garden with a 50 m perimeter and a 15 m length has a width of 25 − 15 = 10 m, so its area is 15 × 10 = 150 m².

Tips for accurate results

• Use one unit: convert all measurements to the same unit (all feet, or all inches) before entering them.
• Radius vs. diameter: if you measured straight across the circle, tap "I know the diameter" instead of halving the number yourself.
• Measure the outside edge only: for composite shapes, ignore interior lines and trace just the outer boundary.
• Add a waste allowance: for real-world materials, buy a little more than the exact perimeter to cover cuts and overlaps.
• Regular vs. irregular: n × s only works when every side is equal; otherwise add each side by hand.

Related concepts and calculators

Perimeter sits alongside a family of geometry and math tools. To find the surface inside a shape instead of around it, use the Area Calculator. For a circle on its own (circumference, area, radius and diameter all in one place) the Circle Calculator is the dedicated tool, and for triangle-specific work such as angles the Triangle Calculator goes further than the perimeter sum here. For a curved edge that is only part of a circle, the Arc Length Calculator gives the length of the arc. Working backward from a circle's area to its radius takes a square root, r = √(A ÷ π), which the Square Root Calculator handles, and when you scale a plan up or down the Scale Calculator converts the drawing's lengths. For polygons with unequal sides, simply sum the sides yourself: the same add-everything principle this calculator uses for triangles and trapezoids.

Real-world projects that need a perimeter

Perimeter is one of those numbers that shows up the moment you start buying materials by the running foot or meter. A few common jobs and how the figure is used:

• Fencing a yard: the perimeter is the starting point for the length of fence you need. Measure the boundary, subtract the gate openings, and allow a little extra for cuts; the Fence Calculator then turns that length into posts, rails and panels. A square-ish lot fences cheaper than a long, narrow one of the same area.
• Baseboard, crown molding and trim: the perimeter of a room (minus doorways) tells you how many feet of molding to buy. Trim is sold in fixed lengths, so round up to whole boards and allow extra for mitered corners.
• Picture frames and matting: the perimeter of the artwork sets the length of frame stock; each of the four corners is cut at 45 degrees, so a little overage prevents a short final piece.
• Garden edging and curbing: brick, steel or plastic edging is priced per foot, so the bed's perimeter is your shopping list. Curved beds are easier to estimate as a circle or part-circle circumference.
• Sewing, quilting and upholstery: binding, piping and border trim all run around the edge, so the perimeter of the panel plus a seam allowance is the length to cut.
• Pools and patios: coping, tile bands and safety fencing all follow the perimeter, while the water surface or paving needs area instead.

In every case the boundary length is the cost driver, which is why a quick, transparent perimeter is worth more than it looks: a 5% miscalculation on a long fence line can be a costly extra trip to the supplier.

Composite and irregular shapes

Most real rooms, yards and parcels are not perfect rectangles; they are composite shapes made of several rectangles, or irregular outlines with sides of different lengths. The good news is that the rule never changes: the perimeter is still just the total of the outside edges. To handle an L-shaped room, for example, walk the outline and write down every wall length in order, then add them all. Do not add the interior step where the two rectangles meet on the inside; only the outer boundary counts. A reliable method is to label the corners, list each side once as you travel around, and check that you finish back where you started. For a shape that mixes straight and curved edges, measure the straight parts directly and treat each curved part as a fraction of a circle's circumference (a quarter-round corner is one-quarter of 2πr). Because there is no single formula for an irregular outline, careful measurement beats any shortcut, and a sketch with every side labeled is the best defense against double-counting or skipping an edge.

Limitations and assumptions

• The polygon formula assumes a regular polygon (all sides equal). For irregular polygons, add each side individually.
• The trapezoid option takes all four side lengths, with a and c as the parallel sides; it does not derive a missing slanted side from the parallel sides and height. Its area comes from the four sides, which is not possible when a and c are equal (a parallelogram).
• It works in two dimensions only; it does not compute the surface perimeter of 3D objects.
• All inputs must be in the same unit. The result is converted to feet or meters for you, but feet mixed with inches inside one shape is not.

Sources

• Common Core State Standards for Mathematics: Grade 3 Measurement and Data, 3.MD.D.8 (perimeters of polygons, including an unknown side) and Grade 7 Geometry, 7.G.B.4 (the circumference of a circle).
• NIST Digital Library of Mathematical Functions, §3.12 Mathematical Constants: π as the ratio of a circle's circumference to its diameter, 3.14159 26535 89793…
• Euclid's Elements, Book I, Proposition 20: in any triangle the sum of any two sides is greater than the remaining one (the triangle inequality the calculator checks).
• NIST Special Publication 811, Appendix B.8 conversion factors: 1 ft = 0.3048 m, 1 in = 0.0254 m, 1 yd = 0.9144 m and 1 mi = 1,609.344 m, all exact.