Calculate the perimeter of rectangles, squares, triangles, circles and many other shapes instantly with formulas, step-by-step solutions and real-life examples.
Perimeter is the total distance around the outside of a flat shape โ add up every side. A rectangle is P = 2(l + w), a square is P = 4s, and any triangle is simply a + b + c. A circle's perimeter has its own name, circumference, found with C = 2ฯr. Pick a shape below, enter its dimensions, and the calculator returns the perimeter with every step shown, plus unit conversions.
Choose a shape:
Enter the dimensions โ results update as you type. Every measurement must use the same unit.
Keyboard: Enter calculates, Esc resets.
| Unit | Perimeter |
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Need the area instead? Use the area calculator.
| Property | Value |
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Common uses: tap one to jump straight to the matching shape.
Perimeter is the total distance around the outside edge of a flat (two-dimensional) shape. Walk around the boundary and add up every side, and the total is the perimeter โ always expressed in the same linear units as the sides themselves: millimetres, metres, feet, never squared.
For a circle the boundary has no straight sides to add, so the concept gets its own name: circumference. The maths is different (it involves ฯ rather than simple addition), but the idea is identical โ the total distance around the outside.
| Measurement | What it measures | Unit | Everyday example |
|---|---|---|---|
| Perimeter | Distance around the boundary | m, ft (linear) | Fencing around a yard |
| Area | Space covered inside the boundary | mยฒ, ftยฒ (squared) | Turf to cover the yard |
Shapes with the same perimeter can have very different areas, and vice versa. A 4ร4 square and a 1ร7 rectangle both have a perimeter of 16, but their areas are 16 and 7 โ nearly double. Of all rectangles with a fixed perimeter, the square always encloses the most area, which is why enclosures tend toward square proportions when material is limited. For area work, see the area calculator.
P = 2(l + w). Add the length and width, then double it โ equivalent to adding all four sides, since opposite sides match. A rectangle 8 ร 5 has a perimeter of 2(8 + 5) = 26 units.
P = 4s. All four sides are equal, so multiply one side by four. A square of side 6 has a perimeter of 24 units, and its diagonal โ a separate measurement, not part of the perimeter โ is sโ2 โ 8.485.
P = a + b + c. Simply add the three sides โ this works for every triangle, right-angled or not, equilateral, isosceles or scalene. For 3, 4 and 5 the perimeter is 12. Not every three numbers form a triangle: the two shorter sides must add to more than the longest, or the shape cannot close (the triangle inequality).
P = 2ฯr, or equivalently ฯd using the diameter. A circle of radius 7 has a circumference of 2ฯ ร 7 โ 43.98 units. Circumference is the one "perimeter" with its own name and its own irrational constant, because a circle has no straight sides to sum.
P = n ร s, where n is the number of sides and s the length of each. A regular hexagon (n = 6) with 4-unit sides has a perimeter of 24. This works for any regular polygon โ pentagon, octagon, decagon โ because every side is identical by definition.
For any polygon that doesn't fit a named shape, the rule never changes: measure every straight edge and add them together. Composite shapes โ an L-shaped block, a room with a bay window โ are handled the same way: trace the actual boundary, including every notch and projection, and sum those segments. It's a common mistake to use only the outer bounding rectangle's dimensions and skip the internal edges the shape actually has.
| Field | Use | Example |
|---|---|---|
| Construction | Skirting, cornice, edge trim, formwork | 13.8 m of skirting for a 4.2 ร 3.6 m room after doorways |
| Surveying | Boundary length for legal descriptions | A closed traverse's perimeter is the sum of its leg lengths |
| Landscaping | Fencing, edging, garden borders | 41 m of fencing for a 12 ร 9 m yard, less a gate |
| Home improvement | Wallpaper border, picture framing, hemming | A frame for an A3 print needs about 1.5 m of moulding |
| Sport | Running track and field markings | A standard track's inner perimeter is 400 m |
| Agriculture | Paddock fencing, irrigation channel length | Perimeter fencing scales with boundary, not area |
Measuring boundaries is older than measuring area. Egyptian land surveyors re-marked field boundaries with knotted ropes after the Nile's annual floods, effectively measuring perimeter directly since the rope itself traced the edge. The Greeks formalised the idea within Euclidean geometry, and the word "perimeter" comes from the Greek peri (around) and metron (measure) โ literally "measure around". Archimedes' work bounding the circumference of a circle between inscribed and circumscribed polygons, around 250 BCE, remains the conceptual basis for computing ฯ to this day.
| Mistake | Why it goes wrong | How to avoid it |
|---|---|---|
| Confusing perimeter with area | They answer different questions and use different units | Perimeter is linear (m); area is squared (mยฒ) |
| Using diameter instead of radius for circumference | C = ฯd already accounts for the full diameter; doubling again overstates it | Use C = 2ฯr or C = ฯd, not both together |
| Forgetting a side on an irregular shape | Every boundary edge must be counted, including notches | Trace the actual outline, not just a bounding box |
| Assuming all polygon sides are equal | Only regular polygons have equal sides โ irregular ones need every side added | Check whether "regular" applies before using P = ns |
| Mixing units | Metres with centimetres gives a meaningless total | Convert every measurement first |
| Ignoring openings when ordering trim | Doorways and gates reduce the actual material needed | Subtract opening widths from the calculated perimeter |
P = 2(l + w) | Square: P = 4sP = a + b + c | Circle: P = 2ฯr = ฯdP = ns | Parallelogram: P = 2(a + b)P = 4s | Kite: P = 2(a + b) | Trapezoid: P = a+b+c+da + b > c for all three pairings1) 2(9+4)=26 m 2) 4ร7=28 cm 3) 6+8+10=24 cm 4) 2ฯร5โ31.42 m 5) 5ร3=15 cm
1) 4ร4.5=18 cm 2) 10+6+8+6.5=30.5 units 3) 2(5+8)=26 4) 8ร3.2=25.6 m 5) No โ 4+5=9, which is less than 10, so it fails the triangle inequality 6) 2(15+10)โ1.2=48.8 m 7) 2.5 m โ 8.20 ft 8) r=C/(2ฯ)=62.8/6.2832โ9.99 โ 10
What is perimeter?
Perimeter is the total distance around the outside boundary of a flat shape โ add up every side. It's always measured in linear units such as metres or feet, never squared, because it's a length rather than an area.
How do you calculate perimeter?
Add together the lengths of every side of the shape. Named shapes have shortcuts โ a rectangle is 2(l + w), a square is 4s โ but the underlying rule is always the same: sum every boundary edge.
What is the perimeter formula?
Each shape has its own: rectangle P = 2(l + w), square P = 4s, triangle P = a + b + c, circle P = 2ฯr, regular polygon P = ns. For an irregular shape there's no shortcut โ measure and add every side.
How do you find the perimeter of a rectangle?
P = 2(l + w) โ add the length and width, then double the result. A rectangle 8 ร 5 has a perimeter of 2(8 + 5) = 26 units, the same as adding all four sides individually (8+5+8+5).
How do you find the perimeter of a square?
P = 4s โ multiply one side by four, since all four sides are equal. A square with 6 cm sides has a perimeter of 24 cm.
How do you calculate triangle perimeter?
Add the three sides: P = a + b + c. This works for every triangle regardless of type โ right-angled, equilateral, isosceles or scalene. Not every three lengths can form a triangle: the two shorter sides must add to more than the longest (the triangle inequality).
How do you calculate polygon perimeter?
For a regular polygon, multiply the side length by the number of sides: P = ns. A regular hexagon with 4-unit sides has a perimeter of 24. For an irregular polygon, there's no shortcut โ measure and add every individual side.
What is the difference between area and perimeter?
Perimeter measures the distance around a shape's boundary, in linear units. Area measures the space enclosed inside it, in square units. A 4ร4 square and a 1ร7 rectangle share a perimeter of 16, but their areas differ sharply โ 16 versus 7.
How do you calculate circumference?
C = 2ฯr, using the radius, or C = ฯd using the diameter โ never both together, which would double-count. A circle of radius 7 has a circumference of 2ฯ ร 7 โ 43.98 units.
What units are used for perimeter?
Any linear unit โ millimetres, centimetres, metres, kilometres, inches, feet or yards โ matching whatever unit the sides were measured in. Australia uses the metric system, so construction and landscaping figures are usually in millimetres or metres.
Can perimeter be negative?
No. A length can't be negative, and perimeter is a sum of lengths, so it's always positive. A negative result in a calculation always indicates an input error.
How do builders use perimeter?
For material quantities that run around a boundary: skirting board, cornice, edge trim and formwork are all ordered by the linear metre of perimeter, usually with door and window openings subtracted and a waste allowance added.
How do surveyors calculate perimeter?
By summing the length of every boundary leg in a land survey โ the perimeter of a parcel is the total of its individual segment lengths, each itself calculated with the distance formula between coordinate points.
What is the perimeter of irregular shapes?
The sum of every straight edge on the boundary โ there's no shortcut formula. For an L-shaped block or a room with a bay window, trace the actual outline including every notch and projection, and add each segment.
Can I calculate perimeter online?
Yes โ enter the dimensions for any of the nine shapes above and the calculator returns the perimeter instantly, with the formula, the working, and conversions to other units.
How accurate is the calculator?
It uses standard double-precision floating-point arithmetic, accurate to about 15 significant figures, far beyond any practical tape-measure precision. Results display to four decimal places.
Can children use this calculator?
Yes โ enter any two or three simple dimensions and the calculator shows the formula and the working step by step, which makes it useful for checking homework as well as for producing an answer.
What is the perimeter of a circle?
A circle's perimeter has its own name โ circumference โ found with C = 2ฯr or C = ฯd. It isn't called "perimeter" in most textbooks purely by convention, but conceptually it's the same measurement: the total distance around the boundary.
How is perimeter used in real life?
Fencing a yard, framing a picture, hemming fabric, bordering a garden bed, running skirting board around a room, marking out a running track, and describing a land parcel's boundary in a legal survey are all perimeter calculations.
What are common perimeter mistakes?
Confusing perimeter with area (linear versus square units); doubling the diameter and the radius together for a circle; missing a side on an irregular shape; assuming an irregular polygon has equal sides; mixing units; and forgetting to subtract door or gate openings when ordering material.
Why is perimeter important?
It's the number that turns a boundary into a material quantity or a cost โ fencing, trim, edging and framing are all priced by the linear metre or foot, so perimeter is usually the very first calculation in a materials list.
How is perimeter used in construction?
Skirting, cornice, edge trim and formwork quantities all come directly from a room or slab's perimeter, typically with door and window openings subtracted and 5โ10% added for waste and offcuts.
How is perimeter different from area?
Perimeter is a one-dimensional measurement โ a length around a boundary. Area is two-dimensional โ the space enclosed. They use different units (linear versus square) and don't move in lockstep: shapes can share a perimeter while having very different areas, or vice versa.
Can perimeter help estimate fencing?
Yes โ that's one of its most common uses. Calculate the perimeter of the area to be fenced, subtract the width of any gates, and the result is the length of fencing material required.
How do I measure perimeter?
Measure each straight side of the shape with a tape measure or from a plan, then add them together โ or use the shortcut formula if the shape is a rectangle, square, regular polygon or circle. For a circle, measure the diameter (easier than the radius) and use C = ฯd.
A one-page reference with every perimeter formula on this page plus the triangle inequality rule. Use the button to print it or save it as a PDF.
MegaCalcOnline.com · Perimeter formulas for common shapes
| Shape | Formula | Notes |
|---|---|---|
| Rectangle | P = 2(l + w) | l and w are the two side lengths |
| Square | P = 4s | All sides equal |
| Triangle | P = a + b + c | Works for any triangle |
| Circle | P = 2πr = πd | Called circumference |
| Regular polygon | P = ns | n sides, each of length s |
| Parallelogram | P = 2(a + b) | Opposite sides equal |
| Rhombus | P = 4s | All sides equal |
| Kite | P = 2(a + b) | Two pairs of adjacent equal sides |
| Trapezoid | P = a + b + c + d | No shortcut — add all four sides |
Triangle inequality: a + b > c for every pairing, or the sides cannot form a triangle. Units: always linear (mm, cm, m, ft), never squared.