Perimeter is the total distance around the outer edge of a shape. This calculator works it out for squares, rectangles, triangles, circles, polygons, and irregular shapes in a few seconds. Choose your shape, enter the measurements you already have, pick a unit, and the result shows up right away along with the formula behind it.
What Is the Perimeter of a Shape and How Is It Different From Area?
Perimeter is the length of the line that runs around the outside of a shape. It is measured in units of length, such as centimeters, meters, inches, or feet, the same units you would use to measure a single side.
Area is a different measurement altogether. It tells you how much surface sits inside that boundary, and it is measured in square units instead of linear ones. A simple way to keep the two apart: if you are buying fencing, you need the perimeter, and if you are buying flooring or paint, you need the area. Mixing the two up is one of the most common mistakes people make when working with shapes, even though the numbers can look similar at first glance.
What Is the Perimeter Formula for Each Common Shape?
Every shape has its own way of arriving at the perimeter, though most of them come down to adding up the sides. Here is a quick reference for the shapes this calculator supports.
Shape | Formula | What the letters mean |
Square | P = 4a | a = length of one side |
Rectangle | P = 2(a + b) | a = length, b = width |
Triangle | P = a + b + c | a, b, c = the three sides |
Circle | P = 2πr or P = πd | r = radius, d = diameter |
Semicircle | P = πr + 2r | r = radius (includes the straight edge) |
Sector | P = r(θ + 2), θ in radians | r = radius, θ = central angle |
Trapezoid | P = a + b + c + d | a, b, c, d = the four sides |
Parallelogram | P = 2(a + b) | a, b = two adjacent sides |
Rhombus | P = 4a | a = length of one side |
Kite | P = 2(a + b) | a, b = two unequal adjacent sides |
Annulus (ring) | P = 2π(R + r) | R = outer radius; r = inner radius |
Regular polygon | P = n × a"Circumference" | n = number of sides, a = side length |
An ellipse does not fit neatly into this list. There is no exact formula for its perimeter, so it is worked out using an approximation, most commonly one of Ramanujan's formulas, which gets extremely close to the real value.
How Do You Calculate the Perimeter of an Irregular Shape?
Irregular shapes do not follow a single formula because their sides are not equal or symmetrical. The most reliable method is to measure each side individually and add them together in order, all the way around the shape. If part of the boundary is curved, use a flexible tape or break that section into small straight segments you can measure separately.
For shapes drawn or surveyed with coordinates rather than a tape measure, there is another option. Enter the x and y position of each corner in order, and the calculator adds up the straight-line distance between each pair of points. This is closer to how surveyors and mapping tools calculate a boundary, and it is useful when you already have a sketch or a set of coordinates instead of physical measurements.
What Units Should You Use When Measuring Perimeter?
Perimeter is always given in linear units, things like millimeters, centimeters, meters, inches, feet, or yards, never in squared units. Before adding anything up, make sure every side is recorded in the same unit. Mixing centimeters with inches, for example, will throw the whole result off even if each individual measurement is correct. This calculator lets you pick a unit once and converts everything automatically, so that particular mistake is one less thing to worry about.
How Do You Find a Side Length or Radius From a Known Perimeter? (Reverse Formulas)
Sometimes the perimeter is the number you already have, and what you actually need is a side length or radius. This comes up in design work where a fixed length of material sets the boundary first, and the shape has to be built around it.
What you know | What you want | Formula |
Circumference | Radius | r = P / (2π) |
Circumference | Diameter | d = P / π |
Perimeter of a regular polygon | Side length | a = P / n |
These are simply the forward formulas rearranged, so the same logic applies, just worked out backward.
How Is Perimeter Used in Everyday and Professional Projects?
Outside the classroom, "perimeter" shows up any time a project is priced or measured by length rather than by area. Fencing a yard, adding trim around a room, framing a picture, and marking out the edge of a piece of land all come down to the same basic calculation, just applied in a different setting.
How Much Fencing Do You Need for a Yard or Plot?
Fencing is usually priced by the linear foot, so the accuracy of your perimeter measurement has a direct effect on the budget. When measuring, leave out any stretch where a house wall already forms part of the boundary, and account for gates separately since they are priced and installed differently from a solid fence line. As a reference point, a square one-acre lot needs roughly 835 feet of fencing, while a rectangular acre with a 2 to 1 ratio needs closer to 885 feet.
If you want the exact length and an estimated cost for your own lot, the fence calculator handles both in one step.
How Do You Measure a Room's Perimeter for Trim or Molding?
Baseboards, crown molding, and chair rails are all priced by the room's perimeter, though not in exactly the same way. Baseboards stop at doorways, so subtract the width of each door opening from the total. Crown molding usually runs the full perimeter without a break, since it sits along the ceiling line rather than the floor. For a room that is not a simple rectangle, split it into smaller rectangles, work out each one separately, and add the results together.
Our room and trim calculator does this automatically once you enter the room's shape and dimensions.
Can You Find the Area of a Shape From Its Perimeter?
Not usually. Two shapes can share the same perimeter and still enclose very different amounts of space; a rectangle is the clearest example of this. There is one exception: for regular shapes such as squares, regular polygons, and circles, you can work backward from the perimeter to find the side length or radius and then use that to calculate the area.
If that is what you need, the area calculator takes the perimeter or the side measurements and returns the area directly.
How Is the Perimeter of a Circle (Circumference) Calculated?
A circle's boundary length has its own name, circumference, and it is calculated as 2πr or πd depending on whether you know the radius or the diameter. On this calculator, circle-based shapes such as circle, semicircle, sector, and annulus are all shown under the general perimeter result for consistency, but the underlying math is identical to circumference.
If you are working with circles specifically, the circumference calculator is built around that one shape and its variations.
How Do You Calculate the Perimeter of a Plot of Land?
For a rectangular plot, the calculation is the same as any rectangle, double the sum of the length and width. Irregular parcels are more involved. Professionals typically record the coordinates of each corner and use them to work out both the area and the perimeter at once. Treat any result from this method as a planning estimate rather than a legal figure, and bring in a licensed surveyor for anything tied to a property transaction or boundary dispute.
For coordinate-based input on your own plot, the land and plot calculator is set up specifically for that.
Frequently Asked Questions
How do you calculate the perimeter of a shape?
Identify the shape, measure every side (or the radius for a circle), make sure the units match, then either add the sides together or apply the shape's formula.
What is the difference between perimeter and area?
Perimeter is the length of a shape's boundary, measured in linear units. Area is the space inside that boundary, measured in square units.
How do you find the perimeter of an irregular shape?
Measure each side and add them together. For curved sections, use a flexible tape or break the curve into small straight segments first.
Why is a circle's perimeter called circumference?
Circumference specifically refers to the boundary of a circle. It is calculated as 2πr or πd, where r is the radius and d is the diameter.
Does a semicircle's perimeter include the straight edge?
Yes. A semicircle's perimeter is the curved half of the circle plus the diameter, since that straight edge is part of the shape's boundary.