Right Cylinder Calculator: find A, V, A_l, A_b

The base surface area of a right circular cylinder A_b is simply the sum of the areas of two bases. Its value is expressed in squared units of length, e.g., square meters m² or square feet ft². Check out area conversion calculator to learn how to convert between different area units! Because both bases of a right circular cylinder are the same circles with the radius r, the base surface area of a cylinder is two times the area of a circle:

a_b = 2 × π × r²

But what if you don't know the radius of the base? There are several different ways to estimate the base surface area of a cylinder:

1. With given total area and lateral area:

   A_b = A − A_l

2. With given volume and height:

   A_b = 2 × V / h

3. With given lateral area and height:

   A_b = A_l²/(2 × π × h²)

4. With given longest diagonal and height:

   A_b = π/2 × (d² − h²)

To find the lateral surface area of a right circular cylinder A_l, we open the cylinder like a carton box and flatten it out to find out which geometric figures it contains – this is the so-called net of a solid. As you can see below, a right circular cylinder consists of two circles (bases) and one rectangle (lateral surface).

The first side of that rectangle is the height h of the cylinder, and the second side equals the circumference of the base – 2 × π × r (circle with radius r), as shown in the circumference calculator. Therefore, the lateral surface area of a right circular cylinder A_l can be found just like the area of a rectangle:

A_l = 2 × π × r × h

There are also other equations that lead to the lateral surface area of a cylinder:

1. With given total area and base area:

   A_l = A − A_b

2. With given volume and height:

   A_l = √(4 × π × h × V)

3. With given base area and height:

   A_l = √(2 × π × h² × A_b)

4. With given longest diagonal and height:

   A_l = √(d²h²π² − h⁴π²)

If you need to make several calculations with rectangles, then our area of a rectangle calculator might be the right tool to check!

The total surface area of a right circular cylinder A is the sum of all the areas of the faces that a cylinder has, i.e., a top base, a bottom base, and a side. Therefore, the total surface area of a right circular cylinder is the sum of its base surface area A_b and its lateral surface area A_l:

A = A_b + A_l = 2 × π × r² + 2 × π × r × h

and after some trivial simplification

A = 2 × π × r × (r + h)

The volume of a right circular cylinder V is the space enclosed by a cylinder. Its value is expressed in cubic units of length, e.g., cubic meters m³ or cubic feet cu ft. Try our volume conversion to learn how to convert between different volume units! The volume of a right circular cylinder is a product of the height h and the area of one base A_b/2 = π × r². Thus, it can be found with the following equation:

V = A_b/2 × h = π × h × r²

It is worth remembering that this formula holds whether or not the cylinder is a right cylinder – it is also true for oblique cylinders. In the case of a right circular cylinder, you can also use other formulas to estimate the volume of a cylinder:

1. With given lateral area and height:

   V = A_l² / (4 × π × h)

2. With given lateral area and radius:

   V = A_l × r / 2

3. With given base area and lateral area:

   V = √(A_l² × A_b / (8 × π))

4. With given longest diagonal and height:

   V = (π × h × d² − π × h³)/4