Area & Perimeter Calculator

Q: What is the area of a circle with radius 5?

Area = π × r² = π × 5² = 25π ≈ 78.54 square units. The circumference is 2π × 5 = 10π ≈ 31.42 units.

Q: What is the perimeter formula for a rectangle?

Perimeter = 2 × (length + width). For example, a 6 by 4 rectangle has perimeter = 2 × (6 + 4) = 20 units.

Q: How do you find the area of a triangle?

Area = (base × height) / 2. The height must be perpendicular to the base. Example: a triangle with base 8 and height 5 has area = (8 × 5) / 2 = 20 square units.

Calculate area and perimeter for 7 common shapes. Select a shape, enter the measurements, and get instant results with formulas.

Select a Shape

Radius (r)

Area = πr² · Circumference = 2πr · Diameter = 2r

Length (l)

Width (w)

Area = l × w · Perimeter = 2(l + w)

Side (a)

Area = a² · Perimeter = 4a · Diagonal = a√2

Base (b)

Height (h)

Side a

Side c

Area = ½ × b × h · Perimeter = a + b + c

Base 1 (a)

Base 2 (b)

Height (h)

Side c

Area = ½(a+b) × h · Perimeter = a+b+c+d

Base (b)

Height (h)

Side (a)

Area = b × h · Perimeter = 2(a + b)

Semi-major axis (a)

Semi-minor axis (b)

Area = πab · Perimeter ≈ π(3(a+b) − √((3a+b)(a+3b)))

Formula applied

Area vs Perimeter

Area is the space inside a 2D shape, measured in square units (cm², m², ft²). Perimeter is the total length around the outside of a shape, measured in linear units. For circles, the perimeter is called the circumference.

Common Shape Formulas

Circle: Area = πr², Circumference = 2πr · Rectangle: Area = l × w, Perimeter = 2(l+w) · Triangle: Area = ½bh · Square: Area = a², Perimeter = 4a

Frequently Asked Questions

What is the area of a circle with radius 5?

Area = π × 5² = 25π ≈ 78.54 square units. The circumference = 2π × 5 ≈ 31.42 units.

What is the perimeter formula for a rectangle?

Perimeter = 2 × (length + width). A 6 × 4 rectangle has perimeter = 2 × (6 + 4) = 20 units.

How do you find the area of a triangle?

Area = (base × height) ÷ 2. The height must be perpendicular to the base. Example: base 8, height 5 → Area = 20 square units.