# Circular Cylinder Calculator

## Circular Cylinder Shape

r = radius

h = height

V = volume

L = lateral surface area

T = top surface area

B = base surface area

A = total surface area

π = pi = 3.1415926535898

√ = square root

## Calculator Use

This online calculator will calculate the various properties of a cylinder given 2 known values. It will also calculate those properties in terms of PI π. This is a right circular cylinder where the top and bottom surfaces are parallel but it is commonly referred to as a "cylinder."

**Units:** Note that units are shown for convenience but do not affect the calculations. The units are in place to give an indication of the order of the results such as ft, ft^{2} or ft^{3}. For example, if you are starting with mm and you know r and h in mm, your calculations will result with V in mm^{3}, L in mm^{2}, T in mm^{2}, B in mm^{2} and A in mm^{2}.

Below are the standard formulas for a cylinder. Calculations are based on algebraic manipulation of these standard formulas.

## Cylinder Formulas in terms of r and h:

- Calculate volume of a cylinder:
- V = πr
^{2}h

- V = πr
- Calculate the lateral surface area of a cylinder (just the curved outside)**:
- L = 2πrh

- Calculate the top and bottom surface area of a cylinder (2
circles):
- T = B = πr
^{2}

- T = B = πr
- Total surface area of a closed cylinder is:
- A = L + T + B = 2πrh + 2(πr
^{2}) = 2πr(h+r)

- A = L + T + B = 2πrh + 2(πr

** The area calculated is only the lateral surface of the outer cylinder wall. To calculate the total surface area you will need to also calculate the area of the top and bottom. You can do this using the circle calculator.

### Cylinder Calculations:

Use the following additional formulas along with the formulas above.

- Given radius and height calculate the volume, lateral surface area and total surface area.

Calculate V, L, A | Given r, h- use the formulas above

- Given radius and volume calculate the height, lateral surface area and total surface area.

Calculate h, L, A | Given r, V- h = V / πr
^{2}

- h = V / πr
- Given radius and lateral surface area calculate the height, volume and total surface area.

Calculate h, V, A | Given r, L- h = L/2πr

- Given height and lateral surface area calculate the radius, volume and total surface area.

Calculate r, V, A | Given h, L- r = L/2πh

- Given height and volume calculate the radius, lateral surface area and total surface area.

Calculate r, L, A | Given h, V- $r = √( V / πh )