★ MATH · SHAPES · PERIMETER
A rectangle 8 by 5 has a perimeter of 26 — walk all four sides and you have covered 26 units. Pick a shape and the calculator works out the perimeter: rectangles, squares, triangles, circles and regular polygons, with the formula, the side-by-side breakdown and the answer to six places where π is involved. This one is the PERIMETER tool — the distance around a shape — the area-calculator page is the AREA tool — the space inside a shape — not the distance around it; the trapezoid-area-calculator page is the TRAPEZOID AREA tool — the area of a trapezoid — not a perimeter; and the fraction-calculator page is the FRACTION tool — adding and multiplying fractions — not lengths around a shape. No perimeter calculator exists on this site — this one is the first.
The perimeter is the distance around a shape: add up the lengths of every side and you have it. On the defaults it is exact: a rectangle 8 by 5 has a perimeter of 26, because 8 + 5 + 8 + 5 is 26. Circles are the exception — the circumference is 2π times the radius, and π never terminates, so a circle of radius 5 is 31.415927 to six places. Pick a shape, put the lengths in, and check the breakdown before you use the answer.
It means that walking around a rectangle 8 long and 5 wide covers 26 units — 8 along the top, 5 down the side, 8 back along the bottom, and 5 up the other side. The perimeter is the distance around a shape, nothing more: add up the lengths of every side and you have it. For a rectangle the opposite sides match, so the short way is twice the length plus the width — 2 × (8 + 5) is 26 — and the long way, 8 + 5 + 8 + 5, gives the same 26. If you were fencing this rectangle, 26 units of fence is what you would buy, before any allowance for a gate.
The circle is the only shape with a rounded answer. A circle has no straight sides, so its perimeter — the circumference — is 2π times the radius, and π never terminates. A circle of radius 5 has a circumference of 31.415927 to six places, and that is the value stopped at six places, not the whole value. Every other shape on this page is exact: a rectangle 12.5 by 7.25 has a perimeter of exactly 39.5, and a square of side 6 has a perimeter of exactly 24.
A triangle has to close. Three lengths only make a triangle if the two shorter ones add up to more than the longest — 3, 4 and 5 close, because 3 + 4 is 7, more than 5; 1, 2 and 10 do not, because 1 + 2 is 3, far short of 10, and the sides would never meet. The calculator refuses lengths that cannot close rather than adding them anyway.
A regular polygon has equal sides by definition. Regular means every side the same length and every angle the same, so the perimeter is just the number of sides times one side — a hexagon of side 4 is 6 × 4, which is 24, and a pentagon of side 3 is 5 × 3, which is 15. If the sides are not all equal, it is not regular, and you have to add the sides one by one instead — that is the triangle’s job, or the rectangle’s.
On the defaults: a rectangle 8 long and 5 wide.
And the other way: a square with a perimeter of 40 has sides of 10, because 40 ÷ 4 is 10 — the reverse box finds the side from the perimeter.
The defaults are a rectangle 8 by 5, chosen so the answer is a whole number you can check by hand. They are a starting point, not a lesson: your shape may be any of the five, and the calculator shows the formula it used, the side-by-side breakdown, and the verdict. Lengths must be more than 0 — a side of 0 is not a shape — and a triangle must close, a polygon needs 3 sides or more, and the number of sides must be a whole number. Put your numbers in, read the answer, and check the working before you use it.
These notes repeat in every explainer section because this page is built to be read start to finish: the circle is the only shape with a rounded answer; a triangle has to close; and a regular polygon has equal sides by definition.
| Output | Formula | What it means |
|---|---|---|
| Shape | input | Rectangle 8 × 5. |
| Perimeter | P = 2 × (length + width) | 26. |
| Perimeter (6dp unrounded) | decimal, 6 places | 26.000000. |
| Formula | by shape | P = 2 × (length + width). |
| Breakdown | side by side | 8 + 5 + 8 + 5 = 26. |
| Verdict | in words | A rectangle 8 by 5 has a perimeter of 26. |
| Reverse: Smallest whole side for a square perimeter of 40 or more | step | 10: Square, side 10: perimeter 40. |
| Reverse: Smallest whole radius for a circumference of 62.831853 or more | step | 10: Circle, radius 10: perimeter 62.831853. |
| Reverse: Smallest whole width for a 10-long rectangle perimeter of 30 or more | step | 5: Rectangle 10 × 5: perimeter 30. |
| Reverse: Smallest whole side for a regular octagon perimeter of 64 or more | step | 8: Regular octagon, side 8: perimeter 64. |
| Reverse: Smallest whole side for an equilateral triangle perimeter of 21 or more | step | 7: Triangle 7, 7, 7: perimeter 21. |
| Reverse: Largest whole radius for a circumference of 31.415927 or less | step | 5: Circle, radius 5: perimeter 31.415927. |
| Rectangle 8 × 5 | same model | Rectangle 8 × 5: perimeter 26. |
| Square, side 6 | same model | Square, side 6: perimeter 24. |
| Triangle 3, 4, 5 | same model | Triangle 3, 4, 5: perimeter 12. |
| Circle, radius 5 | same model | Circle, radius 5: perimeter 31.415927. |
| Regular hexagon, side 4 | same model | Regular hexagon, side 4: perimeter 24. |
| Rectangle 12.5 × 7.25 | same model | Rectangle 12.5 × 7.25: perimeter 39.5. |
| Circle, radius 10 | same model | Circle, radius 10: perimeter 62.831853. |
| Triangle 7, 7, 7 | same model | Triangle 7, 7, 7: perimeter 21. |
| Regular pentagon, side 3 | same model | Regular pentagon, side 3: perimeter 15. |
| Square, side 12.5 | same model | Square, side 12.5: perimeter 50. |
| Rectangle 0 × 5 (zero length) | same model | Lengths must be more than 0.. |
| Square, side −3 (negative) | same model | Lengths must be more than 0.. |
| Non-numeric input | same model | Enter a number for the length and the width.. |
| Triangle 1, 2, 10 (violates the triangle inequality) | same model | Those three sides cannot make a triangle — the two shorter sides must add up to more than the longest side.. |
| Polygon with 2 sides | same model | A regular polygon needs 3 sides or more.. |
| Polygon with 4.5 sides (non-integer) | same model | The number of sides must be a whole number.. |
| Circle, radius 0 | same model | Lengths must be more than 0.. |
| Rectangle 0.5 × 0.25 | same model | Rectangle 0.5 × 0.25: perimeter 1.5. |
| Circle, radius 1 | same model | Circle, radius 1: perimeter 6.283185. |
| Triangle 5, 5, 8 | same model | Triangle 5, 5, 8: perimeter 18. |
| Regular dodecagon, side 2.5 | same model | Regular dodecagon, side 2.5: perimeter 30. |
The arithmetic is exact on the numbers you type: a rectangle 8 by 5 has a perimeter of exactly 26, and a hexagon of side 4 has a perimeter of exactly 24. Circle results use π and are rounded to 6 decimal places; all other shapes are exact. A circle of radius 5 has a circumference of 31.415927 to six places — the true value continues past the sixth decimal, so carry the 6-place value into further working only if that precision is enough. The calculator refuses lengths that cannot make a shape: zero or negative sides, a triangle that cannot close, a polygon with fewer than 3 sides or a non-whole number of sides. Treat the breakdown as the check — if a side is wrong, the breakdown shows it.
A rectangle 8 by 5 has a perimeter of 26 — walk all four sides and you have covered 26 units. Square, side 6: perimeter 24. Triangle 3, 4, 5: perimeter 12. Circle, radius 5: perimeter 31.415927. Regular hexagon, side 4: perimeter 24. Smallest whole side for a square perimeter of 40 or more: 10. Smallest whole radius for a circumference of 62.831853 or more: 10. Smallest whole width for a 10-long rectangle perimeter of 30 or more: 5. Smallest whole side for a regular octagon perimeter of 64 or more: 8. Smallest whole side for an equilateral triangle perimeter of 21 or more: 7. Largest whole radius for a circumference of 31.415927 or less: 5. Source: Bright Side Kit, brightoolbox.com.
The perimeter is 26, because 8 + 5 + 8 + 5 is 26. The short way is 2 × (8 + 5), which is 2 × 13, which is 26 — in whatever units the sides were measured in.
Multiply one side by 4 — a square of side 6 has a perimeter of 24. All four sides are equal, so 4 × 6 is 24. A square of side 12.5 has a perimeter of 50.
Add the three sides — a triangle of 3, 4 and 5 has a perimeter of 12. The three sides must close: the two shorter ones have to add up to more than the longest, or the triangle cannot exist.
Multiply 2π by the radius — a circle of radius 5 has a circumference of 31.415927. The value is rounded to 6 decimal places because π never terminates; a circle of radius 10 is 62.831853.
Multiply one side by 6 — a hexagon of side 4 has a perimeter of 24. A regular polygon has equal sides, so the perimeter is the number of sides times one side: a pentagon of side 3 is 15.
Perimeter is the distance around a shape; area is the space inside it. A rectangle 8 by 5 has a perimeter of 26 and an area of 40 — fencing measures the perimeter, carpet measures the area. See the area-calculator for the inside.
No — those three lengths cannot make a triangle. The two shorter sides, 1 + 2, add up to 3, far short of 10, so the sides would never meet. The calculator refuses them rather than adding them anyway.
Divide by the number of sides — a square with a perimeter of 40 has sides of 10, because 40 ÷ 4 is 10. A regular octagon with a perimeter of 64 has sides of 8, and a circle with a circumference of 62.831853 has a radius of 10.