What does the perimeter calculator do?

The perimeter calculator finds the total length around the outside of the selected 2D shape. It supports square, rectangle, triangle, circle, parallelogram, rhombus, quadrilateral side-sum mode, regular polygon, ellipse, circle sector and annulus.

The result follows the unit of the values you enter. If you enter centimetres, the perimeter is read as centimetres; if you enter metres, the result is read as metres.

What does perimeter mean?

Perimeter is the total distance around the boundary of a shape. For a square, it is the sum of four equal sides; for a rectangle, it is the sum of two lengths and two widths; for a circle, the perimeter is called circumference.

In practice, perimeter is useful when you think about edging, borders, frames, fencing length, or the total outside length of a shape.

Perimeter vs area

Perimeter measures the outside length of a shape, while area measures the surface covered inside the shape. This calculator calculates perimeter, not area.

• Perimeter is expressed in length units, such as cm, m or km.
• Area is expressed in square units, such as cm² or m².
• Use perimeter for borders and edges; use area for covered surface.

Supported shapes

The calculator covers 11 common geometry cases used in school math and practical measurement tasks.

• Square
• Rectangle
• Triangle
• Circle / circumference
• Parallelogram
• Rhombus
• Quadrilateral / four-side sum mode
• Regular polygon
• Ellipse
• Circle sector
• Annulus / ring

Perimeter formulas by shape

The perimeter formula depends on how the boundary of the shape is formed. Straight-sided shapes usually add side lengths; circular shapes use π.

• Square: P = 4a
• Rectangle: P = 2(a + b)
• Triangle: P = a + b + c
• Circle: C = 2πr or C = πd
• Parallelogram: P = 2(a + b)
• Rhombus: P = 4a
• Quadrilateral: P = a + b + c + d
• Regular polygon: P = n × s
• Circle sector: P = arc length + 2r
• Annulus: P = 2π(R + r)

Square, rectangle and triangle examples

A square perimeter is four times one side, a rectangle perimeter is twice the sum of length and width, and a triangle perimeter is the sum of its three sides.

• Square example: if a = 5, then P = 4 × 5 = 20.
• Rectangle example: if a = 20 and b = 15, then P = 2(20 + 15) = 70.
• Triangle example: sides 3, 4 and 5 give P = 3 + 4 + 5 = 12.

Circle circumference: radius or diameter

For a circle, use C = 2πr when you know the radius, or C = πd when you know the diameter. Both formulas describe the same boundary length because the diameter is twice the radius.

For example, if r = 10, then C = 2π × 10 ≈ 62.8318. If the same circle is entered as d = 20, then C = π × 20 ≈ 62.8318.

Regular polygon perimeter

A regular polygon has equal side lengths, so its perimeter is the number of sides multiplied by one side length.

For example, a regular hexagon with n = 6 and side length 4 has P = 6 × 4 = 24.

Why is ellipse perimeter approximate?

Ellipse perimeter is approximate because it is not calculated with a simple exact elementary formula like a square or circle. The calculator uses a Ramanujan approximation.

In ellipse mode, the inputs are interpreted as the semi-major axis and the semi-minor axis. When the two axes are close, the ellipse is closer to a circle; when they differ more, the approximation note becomes especially important.

Sector and annulus perimeter

A circle sector perimeter is the arc length plus the two radii. It is not just the curved arc.

An annulus perimeter is the total length of both circular boundaries: the outer circle plus the inner circle. The formula is P = 2π(R + r).

• Sector angle must be greater than 0 and less than 360 degrees.
• A 360° sector is a full circle and should be handled by circle mode.
• For an annulus, the outer radius must be greater than the inner radius.

How to use the calculator

Select the shape first, then enter the measurements required for that shape. The calculator displays the perimeter result, formula and a short substitution step.

1. Choose the shape.
2. Enter the side, radius, diameter, angle or axis values requested.
3. Use decimal values when needed.
4. Check the result, formula and calculation step.
5. Read any special validation or approximation notes for triangle, sector, annulus or ellipse modes.

Common mistakes

The most common perimeter mistakes are confusing perimeter with area, entering invalid shape dimensions, or assuming that a unit label converts units.

• Reading a perimeter value as if it were an area value.
• Entering triangle sides that cannot form a real triangle.
• Using diameter where the calculator expects radius, or radius where it expects diameter.
• Treating the ellipse approximation as exact.
• Entering an inner radius larger than the outer radius in annulus mode.
• Expecting the calculator to solve missing sides or irregular coordinate shapes.

Limitations

This calculator is designed for perimeter and circumference calculations of supported shapes. It is not a full geometry solver.

• It does not calculate area or volume.
• It does not solve for missing sides from a given perimeter.
• It does not calculate irregular polygon perimeter from coordinates.
• It does not convert units.
• Ellipse perimeter is approximate.
• The quadrilateral/trapezoid-style mode sums four sides; it does not verify all trapezoid geometry properties.