NUM8ERS Geometry Tools 📐 All Shapes Step-by-Step Solutions

Perimeter Calculator

Calculate the perimeter of any shape instantly. Select a shape, enter dimensions, and get step-by-step solutions with formulas and definitions.

🧮 Perimeter Calculator

Select any shape below, enter your measurements, and calculate the perimeter instantly.

Square Perimeter Calculator

Formula
P = 4s
📖 Definition

A square is a regular quadrilateral with four equal sides and four right angles (90°). The perimeter is the total distance around the square.

Perimeter
0
P = 4 × 5 = 20

📚 All Perimeter Formulas

Quick reference for all shape perimeter formulas with variable definitions.

⬜ Square

P = 4s

s = side length. All 4 sides equal.

▬ Rectangle

P = 2(l + w)

l = length, w = width.

△ Triangle

P = a + b + c

Sum of all 3 sides.

⭕ Circle

C = 2πr = πd

r = radius, d = diameter.

▱ Parallelogram

P = 2(a + b)

a, b = adjacent sides.

◇ Rhombus

P = 4s

s = side. All 4 sides equal.

⏢ Trapezoid

P = a+b+c+d

Sum of all 4 sides.

⬠ Pentagon

P = 5s

s = side. 5 equal sides.

⬡ Hexagon

P = 6s

s = side. 6 equal sides.

🛑 Octagon

P = 8s

s = side. 8 equal sides.

⬭ Ellipse

P ≈ π[3(a+b)-√...]

Ramanujan's formula. a, b = axes.

🔷 n-gon

P = n × s

n = sides, s = side length.

📖 How to Calculate Perimeter

Step-by-Step Instructions

1. Identify the Shape: Determine what type of shape you're measuring (square, rectangle, triangle, circle, etc.).

2. Measure All Sides: For polygons, measure each side. For circles, measure the radius or diameter. Ensure all measurements use the same unit.

3. Apply the Formula: Use the appropriate formula for your shape. For irregular shapes, simply add all side lengths together.

4. Calculate: Perform the mathematical operations. The result will be in the same unit as your measurements.

💡 Pro Tip: For real-world applications like fencing or trim, always add 5-10% extra material to account for cuts and waste.

❓ Frequently Asked Questions

Common questions about perimeter calculations answered.

What is perimeter?+

Perimeter is the total distance around the outside of a two-dimensional shape. It is calculated by adding up the lengths of all the sides. For circular shapes, the perimeter is called circumference.

What is the difference between perimeter and area?+

Perimeter measures the length around a shape (in linear units like cm, m, ft), while area measures the space inside a shape (in square units like cm², m², ft²). Perimeter is 1-dimensional; area is 2-dimensional.

How do I find the perimeter of an irregular shape?+

For irregular shapes, measure each side individually and add all the measurements together. If the shape has curved sections, use a flexible measuring tape or break it into measurable segments.

Why is a circle's perimeter called circumference?+

The term "circumference" comes from Latin "circumferre" meaning "to carry around." It specifically refers to the perimeter of circular shapes. Mathematically, C = 2πr or C = πd.

What units should I use for perimeter?+

Perimeter uses the same units as the side lengths (cm, m, in, ft, km, etc.). Make sure all measurements are in the same unit before calculating. The result will be in that same linear unit.

How is perimeter used in real life?+

Perimeter is used for calculating fencing for yards, framing for pictures, border materials for gardens, trim for rooms, running track distances, and many construction and crafting projects.

What is a regular polygon?+

A regular polygon has all sides equal in length and all interior angles equal. Examples include equilateral triangles, squares, regular pentagons, and regular hexagons. Perimeter = n × s.

How accurate is the ellipse perimeter formula?+

There is no simple exact formula for an ellipse's perimeter. We use Ramanujan's approximation: P ≈ π[3(a+b) - √((3a+b)(a+3b))], which is highly accurate (within 0.001% error).