Perimeter Calculator

Units

Length (L)

Width (W)

Perimeter = 2(L + W) • Area = L × W

Results

Perimeter—

Area (if applicable)—

Converted perimeter—

Converted area—

Perimeter Calculator (With Area Formulas for All Shapes)

The perimeter is the distance around a shape. It is measured by adding all side lengths, or for curved shapes, using specific formulas such as the circumference of a circle.

Perimeter Calculator – How It Works

Select a shape (rectangle, square, triangle, circle, sector, polygon).
Enter the side lengths, radius, diameter, or angles as needed.
The calculator shows both perimeter and area (if applicable) in metres or feet, with conversions.
Results include step-by-step formulas for learning and quick verification.

Perimeter & Area Formulas

Rectangle

Perimeter: \( P = 2(L + W) \)

Area: \( A = L \times W \)

Square

Perimeter: \( P = 4a \)

Area: \( A = a^2 \)

Triangle (General)

Perimeter: \( P = a + b + c \)

Area (Heron’s): \( A = \sqrt{s(s-a)(s-b)(s-c)} \), where \( s = \frac{a+b+c}{2} \)

Right Triangle

Perimeter: \( P = a + b + \sqrt{a^2 + b^2} \)

Area: \( A = \frac{ab}{2} \)

Isosceles Triangle

Perimeter: \( P = 2a + b \)

Area: \( A = \tfrac{1}{2}\, b \sqrt{\,a^2 - \left(\tfrac{b}{2}\right)^2} \)

Circle

Perimeter / Circumference: \( C = 2\pi r = \pi d \)

Area: \( A = \pi r^2 \)

Sector of a Circle

Perimeter: \( P = \text{arc} + 2r \)

Arc length: \( r\theta \) (radians) or \( \frac{\pi r \theta}{180} \) (degrees)

Area: \( A = \tfrac{1}{2} r^2 \theta \) (radians) or \( \frac{\pi r^2 \theta}{360} \) (degrees)

Parallelogram

Perimeter: \( P = 2(a + b) \)

Area depends on height or angle (\(A = ab \sin\alpha\)), not shown here.

Rhombus

Perimeter: \( P = 4a \)

Area often by diagonals: \( A = \tfrac{1}{2} d_1 d_2 \) (optional).

Regular Polygon (n-gon)

Perimeter: \( P = ns \)

Area: \( A = \dfrac{n\,s^2}{4\,\tan\!\left(\dfrac{\pi}{n}\right)} \)

Custom Shape

Perimeter: \( P = \displaystyle\sum_{i=1}^{k} s_i \)

Area requires additional information (angles, coordinates, or height).

Why Use a Perimeter Calculator?

✅ Save time compared to manual calculation.

✅ Avoid mistakes with triangle inequalities, sector conversions, etc.

✅ Get both perimeter and area instantly.

✅ Convert between metres and feet.

✅ Great for students, teachers, architects, engineers, and DIY projects.

Frequently Asked Questions

What is the equation for perimeter?

The perimeter of a shape is the total distance around it. For polygons, add all the side lengths. For curved shapes like circles, use specific formulas (e.g. circumference of a circle: \(C = 2\pi r\)).

What is the formula for perimeter of a rectangle?

The formula is \(P = 2(L + W)\), where \(L\) is length and \(W\) is width.

What is the formula for perimeter of a square?

The formula is \(P = 4a\), where \(a\) is the length of one side.

What is the formula for perimeter of a triangle?

For a general triangle: \(P = a + b + c\). For a right triangle: \(P = a + b + \sqrt{a^2+b^2}\). For an isosceles triangle: \(P = 2a + b\).

What is the circle perimeter formula?

The perimeter of a circle is called the circumference: \(C = 2\pi r = \pi d\).

What is the perimeter of a sector formula?

The perimeter is the arc length plus twice the radius. Arc length is \(r\theta\) (radians) or \(\pi r \theta/180\) (degrees).

Can the calculator also find area?

Yes. For most shapes (rectangle, square, triangle, circle, sector, regular polygon), the calculator shows both perimeter and area together.