# Height of a Cylinder Calculator

Created by Dominik Czernia, PhD
Reviewed by Bogna Szyk and Adena Benn
Last updated: Nov 17, 2022

This height of a cylinder calculator quickly finds the height of a right circular cylinder in ten different ways. Do you wonder how to find the height of a cylinder? Just choose which two of the parameters you know, enter specified values, and compute the height.

Keep reading if you want to learn what are the possible height of a cylinder formula. In most cases, you can estimate it knowing only two of the below quantities:

• Volume;
• Longest diagonal;
• Base surface area;
• Lateral surface area; or
• Total surface area.

Our height of a cylinder calculator is a handy tool dedicated to the right circular cylinder. This type of cylinder consists of two congruent circles (called bases). They lie precisely one above the other, and that's why we call it a right cylinder. On the other hand, if one of the bases is shifted, then a cylinder is oblique. The term circular is more obvious - bases have the form of circles. You should remember that the word cylinder may correspond to different shapes (generalized cylinder), but we usually have the right circular cylinder in mind.

This calculator answers the question how to find the height of a cylinder. If you want to estimate other parameters, check out our right cylinder calc!

## What's the height of a cylinder formula?

There are five basic equations that completely describe the cylinder with a given radius $r$ and height $h$:

1. Volume of a cylinder:
$\quad V = \pi r^2 h$
1. Base surface area of a cylinder:
$\quad A_\mathrm{b} = 2 \pi r^2$
1. Lateral surface area of a cylinder:
$\quad A_\mathrm{l} = 2 \pi r h$
1. Total surface area of a cylinder:
$\quad A = A_\mathrm{b} + A_\mathrm{l}$
1. Longest diagonal of a cylinder:
$\quad d^2 = 4 r^2 + h^2$

Sometimes, however, we have a different set of parameters. With this height of a cylinder calculator, you can now quickly use ten various height of a cylinder formulas, which can be derived directly from the above equations:

$\quad h = \frac{V}{\pi r^2}$
1. Given radius and lateral area:
$\quad h = \frac{A_\mathrm{l}}{2 \pi r}$
1. Given radius and total area:
$\quad h = \frac{A - 2 \pi r^2}{2 \pi r^2}$
1. Given radius and longest diagonal:
$\quad h = \sqrt{d^2 - 4r^2}$
1. Given volume and base area:
$\quad h = \frac{2 V}{A_\mathrm{b}}$
1. Given volume and lateral area:
$\quad h = \frac{A^2_\mathrm{l}}{4 \pi V}$
1. Given base area and lateral area:
$\quad h = \sqrt{\frac{A^2_\mathrm{l}}{2 \pi A_\mathrm{b}}}$
1. Given base area and total area:
$\quad h = \frac{A - A_\mathrm{b}}{\sqrt{2 \pi A_\mathrm{b}}}$
1. Given base area and diagonal:
$\quad h = \sqrt{d^2 - \frac{2 }{\pi}A_\mathrm{b}}$
1. Given lateral area and total area:
$\quad h = \frac{A_\mathrm{l}}{\sqrt{2 \pi (A - A_\mathrm{l})}}$

Are you interested in right circular cylinder calculations? You certainly need to check out the cylinder volume calculator and surface area of a cylinder calculator!

## How to find the height of a cylinder

The height of a cylinder calculator is very easy to use for a wide range of different problems. Sometimes you will know the volume and the base area of a cylinder, and you won't know its height. Another time you will have only surface areas specified. If you ever face that kind of problem, use this calculator to estimate height in three simple steps:

1. Determine which parameters of a cylinder you know. You need to have at least two of them.
2. Enter values of the selected variables.
3. Read out the result of the calculations.

Remember that with the height of a cylinder calculator, you can choose units of every parameter you want. Be sure to check out the length converter and volume conversion tools as well. They can be very helpful in many computations.

## FAQ

### How do I find the height of a cylinder from its surface area?

To find the height of a cylinder from its total surface area and radius, proceed as follows:

1. Multiply the square of the radius with and subtract the value from the total surface area.

2. Divide the result of step 1 by the value 2π × radius.

3. Congrats! You have calculated the height of the cylinder.

### How do I calculate the height of a cylinder from volume and radius?

To calculate the height of a cylinder from its volume and radius, follow the given instructions:

1. Take the square of the radius and multiply it by π.

2. Divide the volume of the cylinder by the result from step 1.

3. You will get the height of the cylinder.

### What is the height of a cylinder with a radius of 5 cm and a volume of 900 cm³?

11.46 cm. The formula for calculating the height of the cylinder given its volume and radius is height = volume / (π × radius²).

Substituing the values in the formula we get, height = 900 cm³ / (π × 5 cm × 5 cm) = 11.46 cm

### What is the height of a cylinder that has a radius of 8 cm and a lateral surface area of 1005.5 cm²?

20 cm. To find the height of the cylinder, we will use the formula height = lateral surface area / (2π × radius).

Hence, the height of the cylinder will be height = 1005.5 cm² / (2π × 8 cm) = 20 cm.

Dominik Czernia, PhD
in
Volume
cu in
Diagonal (d)
in
Surface areas
Base surface area
in²
Lateral surface area
in²
Total surface area
in²
Height
Height (h)
in
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