Surface Area Calculator

Surface area of an object is defined as the total area region that the surface of the object covers. It is the sum of the areas of all surfaces of an 3D shaped object. Generally, surface area is defined for only three dimensional shapes/ objects. The SI unit of surface area is square metre (m²).

Formulas to Calculate Surface Area

The simple and universal formulas to find the surface area of a 3D shape are mentioned below. Get the useful formulae and use them to find the surface area.

Surface Area of Cube formula is A = 6a²

Surface Area of a Sphere formula is A = 4πr²

Surface Area of a Cone formula is A = πr² + πr√(r² + h²)

Surface Area of Cylinder formula is A = 2πr² + 2πrh

Surface Area of a Rectangular Prism (Box) formula is A = 2(ab + bc + ac)

Surface Area of a Pyramid formula is A = l * √(l² + 4 * h²) + l²

Surface Area of Triangular Prism formula is A = 0.5 * √((a + b + c) * (-a + b + c) * (a - b + c) * (a + b - c)) + h * (a + b + c)

Surface Area of Capsule formula is A = 2πr(2r + a)

Surface Area of a Canonical Frustum formula is A = π[ r₁² + r₂² + (r₁ * r₂) * √((r₁ - r₂)²+ h²) ]

Surface Area of Hemisphere formula is A = 3πr²

Cube Surface Area Formula

Cube is a three dimensional figure which is having 6 faces. Each face is a square having equal side length. The formula to calculate the surface area of a cube is mentioned here:

• Surface area of a Cube:
  • A = 6a²
• Volume of a Cube:
  • V = a3

Where,

a is the length of side of a cube

Sphere Surface Area Formula

To find the surface area of a sphere, all you need is wither radius or diameter of the sphere. The distance from centre and the point on the surface of a sphere is called radius. Its formulas are here.

• Surface Area of a Sphere:
  • A = 4 * π * r²
  • A = π * d²
• Volume of a Sphere:
  • V = (4/3)πr3

Where,

r is the radius

d is the diameter of a sphere

Cone Surface Area Formula

The formula to calculate the total surface area, lateral surface area, and base surface area of a cone are given here:

• Total Surface Area of Cone:
  • A = L + B = πrs + πr² = πr(s + r) = πr(r + √(r² + h²))
• Lateral Surface Area of Cone:
  • L = πrs = πr√(r² + h²)
• Base Surface Area of Cone:
  • B = πr²
• Volume of Cone:
  • V = (1/3)πr²h

Where,

r is the radius of the circular cone

s is the sector area of cone

h is the slant height

L is the lateral surface area

B is the base surface area

V is volume

S is the total surface area

Circular Cylinder Surface Area Formula

Circular cylinder is having two circles of equal radii one on the bottom one is at the top. Two straight and parallel lines joins those circles. Its formula to find the surface area is mentioned here.

• Total Surface Area of Cylinder:
  • A = L + T + B = 2πrh + 2(πr²) = 2πr(h+r)
• Bottom Surface Area Formula:
  • B = πr²
• Lateral Surface Area of Cylinder:
  • L = 2πrh
• Calculate the top surface area of a cylinder:
  • T = πr²
• Volume of cylinder is:
  • V = πr²h

Where,

r is the circle radius

L is the lateral surface area of cylinder

h is the height of cylinder

T is the top surface area of cylinder

B is bottom surface area of cylinder

A is the total surface area of cylinder

V is cylinder volume

Rectangular Prism Surface Area Formula

Get the formula to calculate the surface area and volume of a rectangular prism here:

• Surface Area of Rectangular Prism Formula:
  • A = 2(lw + lh + wh)
• Volume of Rectangular Prism:
  • V = lwh

Where,

l is the length of the rectangular prism

w is the width of the rectangular prism

h is the height of the rectangular prism

Pyramid Surface Area Formula

Pyramid is a shape having base and straight lines that joins all vertices of a base at a point called apex. Check out the formulas to compute the lateral, base and total surface area of a pyramid

• Total Surface Area of a Pyramid Formula:
  • A = L + B = a(a + √(a² + 4h²)) + a²
• Base Surface Area of Pyramid Formula:
  • B = a²
• Lateral Surface Area of Pyramid Formula:
  • L = a√(a² + 4h²)
• Volume of Pyramid Formula:
  • V = (1/3)a²h

Where,

a is the length of a base

h is the height of the pyramid

L is the later' surface area

B is the base surface area

A is the total surface area

Triangular Prism Surface Area Formula

• Top Surface Area of a Triangular Prism Formula:
  • Atop = 1/4(√[(a + b + c)(b + c - a)(c + a - b)(a + b - c)]
• Bottom Surface Area of a Triangular Prism Formula:
  • Abot = 1/4(√[(a + b + c)(b + c - a)(c + a - b)(a + b - c)]
• Lateral Surface Area of a Triangular Prism Formula:
  • Alat = h(a + b + c)
• Total Surface Area of a Triangular Prism Formula:
  • Atot = Atop + Abot + Alat
  • = [1/4(√[(a + b + c)(b + c - a)(c + a - b)(a + b - c)]] + [1/4(√[(a + b + c)(b + c - a)(c + a - b)(a + b - c)]] + h(a + b + c)
  • Atot = /2[√[(a + b + c)(b + c - a)(c + a - b)(a + b - c)]] + h(a + b + c)

Where,

a, b, c are the sides of a triangular prism

h is the height of the triangular prism

Capsule Surface Area Formula

• Surface Area of Capsule Formula:
  • A = 2πr(2r + a)
• Volume of Capsule Formula:
  • V = πr²((4/3)r + a)

Where:

r is the radius of capsule

a is the height of the capsule

Canonical Frustum Surface Area Formula

Below given are the formulas to find the base, lateral and total surface area of a Canonical Frustum:

• Lateral Surface Area of Canonical Frustum Formula:
  • L = π(r₁ + r₂)s = π(r₁ + r₂)√((r₁ - r₂)² + h²)
• Top Surface Area of Canonical Frustum Formula:
  • T = πr₁²
• Base Surface Area of Canonical Frustum Formula:
  • B = πr₂²
• Total Surface Area of Canonical Frustum Formula:
  • A = π(r₁² + r₂² + (r₁ * r₂) * s)
  • A = π[ r₁² + r₂² + (r₁ * r₂) * √((r₁ - r₂)² + h²)]
• Volume of Canonical Frustum Formula:
  • V = (1/3)πh (r₁² + r₂² + (r₁ * r₂))

Where,

r₁, r₂ is the radius

h is the height

Hemisphere Surface Area Formula

• Curved Surface Area of Hemisphere Formula:
  • C = 2πr²
• Base Surface Area of Hemisphere Formula:
  • B = = πr²
• Total Surface Area of Hemisphere Formula:
  • A = B + C = (2πr²) + (πr²) = 3πr²
• Volume of Hemisphere Formula:
  • V = (2/3)πr3

Where,

r is the radius of Hemisphere

Check out the simple and easy steps to calculate the surface area of any three dimensional geometric figure easily. Have a look at the following segments and find the answer quickly.

• Collect the useful parameters of the shape to find surface area from the given question.
• Place those values in the provided lateral, base and total surface area formulas.
• Do the further required math operations to get the result i.e total surface area of a shape or object.