What is perimeter?
Perimeter is the distance around the outside edge of a flat shape. Walk the boundary of your backyard and count the steps — that is the perimeter. It is measured in ordinary length units: feet, meters, inches, yards. The Perimeter Calculator on this page takes the sides of a rectangle, square, triangle, circle, trapezoid, parallelogram, regular polygon or ellipse and gives you that distance in all eight units at once, as you type.
The reason perimeter matters is that a lot of things get sold by the running foot. Fencing. Baseboard. Crown moulding. Garden edging. Gutter. Picture framing. Weatherstripping. Ribbon. Christmas lights. In every one of those errands the question is the same: how long is the edge? A yard measuring 40 ft by 25 ft has a perimeter of 130 ft, so that is your fence order before gates. A room measuring 12 ft by 10 ft has a perimeter of 44 ft, so that is your baseboard before you cut out the doorways.
Perimeter is also the first place people slip, because the word sits so close to area. Perimeter is the edge. Area is the surface inside. Fence is perimeter; grass seed is area. Both questions come up on the same afternoon, and they have different answers in different units.
How to use the Perimeter Calculator
There is no Calculate button and nothing to sign up for. The answer appears while you are still typing.
- Pick your shape. Rectangle is selected when the page opens. The chips cover the eight shapes people actually measure, including the three that area calculators handle badly.
- Pick your unit. One dropdown covers every box — mm, cm, m, km, in, ft, yd or mi. Feet is the default. If you measured a room as 12 feet 6 inches, type
12.5with feet selected rather than mixing the two. - Type the sides. The letter on each input box matches the letter on the diagram beside it, so there is no guessing which number is b. Measure the real edges — the slanted ones too.
- Read the answer. You get the perimeter in your unit, the formula with your own numbers substituted in, and the same distance listed in all eight units. Copy the headline, or copy any single row.
This is the whole tool. Perimeter of an ellipse is not a locked feature, the unit table is not a trial, and there is no version of this page that counts how many shapes you measured this month. The pattern it is built against is the one where a number that costs nothing to compute gets stapled to a per-seat subscription: the basic answer sits behind a sign-up wall, the useful part sits behind a 14-day clock, and the unit conversion you needed lives in a different product on the same invoice. Here it is one page that does one thing.
The formula for every shape
Every perimeter formula is the same idea: add up the edges. The shortcuts only exist because some shapes repeat the same edge twice. Here is how to find the perimeter of each of the eight shapes the calculator covers.
Rectangle: 2 × (l + w) · Square: 4 × s · Triangle: a + b + c · Circle: 2 × π × r · Trapezoid: a + b + c + d · Parallelogram: 2 × (a + b) · Regular polygon: n × s
Start with the perimeter of a rectangle, because it is the one most people need. Take a room that measures 12 ft by 10 ft. Length is 12, width is 10, and the two of them each appear twice as you walk the walls. The Perimeter Calculator shows the line 2 × (12 + 10) = 44 ft — your numbers, not a generic template — and then the same 44 feet as 13.4112 m, 528 in, 14.6667 yd and 13,411.2 mm. If you are ordering baseboard in metric and measuring in feet, that table is the second tool you would otherwise have gone looking for.
A circle is the same exercise with π doing the walking. A circular patio with a 7 ft radius gives 2 × π × 7 = 43.9823 ft of edging. Note that a circle's perimeter has its own name — circumference — but it is the same measurement.
The ellipse is the odd one. There is no exact formula for the distance around an ellipse; it cannot be written as a finite combination of the usual functions. This page uses Ramanujan's second approximation, which lands within roughly one part in a billion for ordinary ellipses. Semi-axes of 3 m and 2 m give ≈ 15.8654 m, and the answer is printed with an approximately sign and a note saying why, rather than being rounded quietly and presented as fact.
Common perimeters at a glance
Every row below is the Perimeter Calculator's own output, so you can check the page against the table.
| Shape and sides | Formula with your numbers | Perimeter | In meters |
|---|---|---|---|
| Rectangle, 12 ft × 10 ft | 2 × (12 + 10) | 44 ft | 13.4112 m |
| Rectangle, 40 ft × 25 ft | 2 × (40 + 25) | 130 ft | 39.624 m |
| Square, 10 ft side | 4 × 10 | 40 ft | 12.192 m |
| Triangle, 3-4-5 cm | 3 + 4 + 5 | 12 cm | 0.12 m |
| Circle, 5 cm radius | 2 × π × 5 | 31.4159 cm | 0.3142 m |
| Trapezoid, 6 + 5 + 10 + 5 ft | 6 + 5 + 10 + 5 | 26 ft | 7.9248 m |
| Parallelogram, 12 ft and 8 ft | 2 × (12 + 8) | 40 ft | 12.192 m |
| Hexagon, 10 ft sides | 6 × 10 | 60 ft | 18.288 m |
| Octagon, 4 ft sides | 8 × 4 | 32 ft | 9.7536 m |
| Ellipse, 3 m and 2 m semi-axes | Ramanujan II | ≈ 15.8654 m | ≈ 15.8654 m |
Two things worth noticing. The square with a 10 ft side and the parallelogram with 12 ft and 8 ft sides both come to 40 ft, but they enclose wildly different amounts of ground — equal perimeter does not mean equal area, which is why a long skinny yard costs far more to fence per square foot than a square one. And the hexagon at 60 ft beats the 12 × 10 room at 44 ft even though a hexagon with 10 ft sides feels like a similar-sized thing. Counting edges is the only reliable method; intuition is not.
Where perimeter goes wrong
The most expensive mistake is borrowing a perimeter formula from an area page. Area formulas ask for a perpendicular height — the straight-up distance between two sides — and that height is usually not one of the shape's actual edges. To walk around a triangle you need all three real sides, slants included. To walk around a trapezoid you need all four. That is why the Perimeter Calculator asks for more numbers than an area calculator does, and why reusing an area page for perimeter can be off by a lot.
The second one is a triangle that cannot exist. Type sides of 1, 2 and 10 and you get a message instead of a number: those three sides can't meet. The two shorter sides have to add up to more than the longest, or the sticks are too short to reach across and close the shape. Sides of 1, 2 and 3 fail too, by a hair — they lie flat in a line and enclose nothing. Plenty of calculators will happily hand back 13 for the first case. If you see that message, re-measure and check you did not record one side in inches and the rest in feet.
Third: negative numbers get a plain answer — sizes can't be negative, drop the minus sign — rather than a silent absolute value. And if your yard is not one of the eight shapes, split it into pieces you can measure, add the outside edges, and skip the internal lines where the pieces meet. Those lines are not boundary.
One practical note for anyone ordering material: buy more than the perimeter. Posts, corners and cuts eat fencing, and most installers add 5 to 10 percent. Subtract gates and doorways, then add the waste back.
Related calculations
Perimeter answers half the question. If you need the surface inside rather than the distance around — grass seed, paint, turf, tile — the area calculator handles the same eight shapes, and the square footage calculator is the one to reach for when you are pricing flooring by the room. For a plain rectangle in both directions at once, the rectangle area calculator is the shortest path.
For circles specifically, the circumference of a circle page works from a diameter as readily as a radius, which is handy when you measured across rather than from the center. If you know two sides of a right triangle but not the third, find it with the Pythagorean theorem calculator first, then bring all three back here. And if you need to move a measurement between systems before you type it, the length converter does it in one step.
Every one of those is a separate page that does a single job, with no account between you and the answer. 10% of every dollar Microapp earns goes to charity, off the top, audited quarterly — that is how the bill gets paid instead of by metering your calculations.
Frequently asked questions
How do I find the perimeter of an irregular shape?
Measure every straight edge of the boundary and add them up — no perimeter formula is doing anything cleverer than that. If the outline is complicated, break it into rectangles and triangles you can measure, then add only the outside edges and ignore the seams where your imaginary pieces touch. The seams are not part of the boundary, and including them is the usual reason a hand-worked irregular perimeter comes out too big.
What is the perimeter of a 12 by 10 room?
44 feet. The formula is 2 × (12 + 10), because you walk the 12 ft wall twice and the 10 ft wall twice. That is also 13.4112 m or 528 inches if you are buying trim in another system. For baseboard, subtract each doorway width from the 44 before ordering.
Is circumference the same thing as perimeter?
Yes. Circumference is the specific word for a circle's perimeter, the same way diameter is the specific word for the line through its middle. It is 2 × π × r, or π × d if you measured across. Pick the Circle chip and type the radius; if you only have the diameter, halve it first.
Why does the perimeter of an ellipse show an approximately sign?
Because no exact formula exists. An ellipse's perimeter cannot be written with a finite combination of the usual functions — it needs an infinite series or an elliptic integral. The Perimeter Calculator uses Ramanujan's second approximation, accurate to about one part in a billion, which is far finer than any tape measure. The sign is there because the honest answer is "very close," not "exact."
How much fencing do I need for my yard?
Measure each side, pick the matching shape, and type the sides — the perimeter is your fence length. Then do two things: subtract any gate or opening, since you are not fencing that span, and add 5 to 10 percent for posts, corners and cuts. A 40 ft by 25 ft yard reads 130 ft, so a 4 ft gate leaves 126 ft of fence and an order of roughly 135 ft of material.
Can two shapes have the same perimeter but different areas?
Constantly, and it is worth money. A 10 ft square and a 19 ft by 1 ft strip both have a 40 ft perimeter, but the square holds 100 square feet and the strip holds 19. Among all shapes with a fixed perimeter, the circle encloses the most area — which is why a round pen fences the most animals per foot of wire. Run the numbers on both with the area calculator before you commit to a layout.
Do all the sides have to be in the same unit?
Yes. One unit dropdown covers every box, so convert before you type rather than mixing feet and inches in different fields. Once you have an answer, switching the unit keeps your typed numbers and reinterprets them, and the table below the result shows the same distance from millimeters through miles — so you only ever have to measure once.