# Cylinder Calculator 3D

Cylinder graphic:

Results:

Insert two values for the cylinder:

Use keys `↑` and `↓` for value changes

_{B}= π·r

^{2}A

_{L}= 2·π·r·h A

_{S}= 2·π·r·(r+h) V = π·r

^{2}·h

Precision with 3 decimal places

## Interactive 3D-Cylinder

### All formulas for the Cylinder at a glance

Here you see the necessary formulas for the calculation of a right circular cylinder:

Link to graphic: https://www.matheretter.de/img/wiki/cylinder-formulas.png

Explanations:

Diameter = 2·radius → d = 2·r

Perimeter = 2·Pi·radius → p = 2·π·r

Base Area = Pi·radius² → A_{B} = π·r²

Lateral Surface = perimeter · height → A_{L} = 2·π·r·h

Surface Area = 2·base area + lateral surface → A_{S} = 2·π·r² + 2·π·r·h = 2·π·r·(r+h)

Volume = base area · height → V = π·r²·h

### What is a cylinder?

For the circular cylinder there are the following formulas: The perimeter p is 2·Pi·r (this is the formula for the perimeter of the circle), the base area A

_{B}is Pi·r² (this is the formula for the area of a circle), the lateral surface is perimeter times height, A

_{L}= p·h and therefore A

_{L}= 2·Pi·r·h, the surface area consists of the circular areas on top and on bottom (2 times the base area) and the lateral surface, so surface is A

_{S}= 2·A

_{B}+ A

_{L}and thus A

_{S}= 2·(π·r²) + (2·π·r·h), while the 2·π·r is often factored out and we get: A

_{S}= 2·π·r·(r+h). The volume of the cylinder is base area times height, thus V = A

_{B}·h = π·r²·h. cylinder with radius, base area and diameter of the base area. Characteristics of a cylinder.

**Example from daily life (form of a cylinder):**

Drinking glass, pipe, building stone, engine cylinder, chair leg, pen, form of a pill etc.

#### Flächenberechnung beim Zylinder (Grafik):

Frequently asked Questions about cylinders:

- Calculate the cylinder radius at a given height and surface
- Calculate surface of a cylinder? Exercise
- Cylinder with an attached cone. Calculate the height of the cylinder.
- Calculate volume of a cylinder from only diameter and height
- Complete the following table for cylinders.
- more questions on cylinders...

Value 1 | Value 2 | Radius computable |
Height computable |
Solution formula for radius Radius is always computable |
Solution formula for height Radius is partially assumed |
---|---|---|---|---|---|

Radius | Height | yes | yes | Radius provided | Height provided |

Radius | Perimeter | yes | no | Radius provided | Height not computable - Details |

Radius | Base area | yes | no | Radius provided | Height not computable - Details |

Radius | Surface area | yes | yes | Radius provided | h = ^{AS} / _{2·π·r} – rSee equivalent transformation |

Radius | Lateral surface | yes | yes | Radius provided | h = ^{AL}/_{2·π·r} See equivalent transformation |

Radius | Volume | yes | yes | Radius provided | h = ^{V}/_{r2·h} See equivalent transformation |

Height | Perimeter | yes | yes | r = ^{p} / _{2·π} See equivalent transformation |
Height provided |

Height | Base area | yes | yes | r = ^{AB}/_{π} See equivalent transformation |
Height provided |

Height | Surface area | yes | yes | r_{1,2} = – ^{h}/_{2} ± √( ^{h2}/_{4} + ^{AS}/_{2·π} )See equivalent transformation |
Height provided |

Height | Lateral surface | yes | yes | r = ^{AL}/_{2·π·h} See equivalent transformation |
Height provided |

Height | Volume | yes | yes | r = ± √( ^{V}/_{h·π} ) See equivalent transformation |
Height provided |

Perimeter | Base area | yes | no | r = ^{p} / _{2·π} See equivalent transformation |
Height not computable - Details |

Perimeter | Surface area | yes | yes | r = ^{p} / _{2·π} See equivalent transformation |
h = ^{AS} / _{p} – rSee equivalent transformation |

Perimeter | Lateral surface | yes | yes | r = ^{p} / _{2·π} See equivalent transformation |
h = ^{AL} / _{p}See equivalent transformation |

Perimeter | Volume | yes | yes | r = ^{p} / _{2·π} See equivalent transformation |
h = 2·^{V} / _{u·r} See equivalent transformation |

Base area | Surface area | yes | yes | r = ^{AB}/_{π} See equivalent transformation |
h = r · ^{AS} / _{2·AB} – r See equivalent transformation |

Base area | Lateral surface | yes | yes | r = ^{AB}/_{π} See equivalent transformation |
h = r · ^{AL} / _{2·AB} See equivalent transformation |

Base area | Volume | yes | yes | r = ^{AB}/_{π} See equivalent transformation |
h = ^{AL} / _{AB} See equivalent transformation |

Surface area | Lateral surface | yes | yes | If we have the height, we can calculate the radius from the formule of the lateral surface: r = ^{AL} / _{2·π·h}See equivalent transformation |
h = ± √( ^{AL2} / _{2·π·AS – 2·π·M} )See equivalent transformation |

Surface area | Volume | yes | yes | 0 = r^{3} + ^{AS} / _{-2·π} · r + ^{V} / _{π}3 Solutions for the cubic equation See equivalent transformation |
If we have the height, we can calculate the radius from the formule of the lateral surface: h = ^{AS} / _{2·π·r} – rSee equivalent transformation |

Lateral surface | Volume | yes | yes | r = 2·^{V}/_{AL} See equivalent transformation |
If we have the height, we can calculate the radius from the formule of the lateral surface: h = ^{AL}/_{2·π·r} See equivalent transformation |