Free Height of a Cylinder Calculator

The Height of a Cylinder Calculator is an online resource that lets you quickly determine the height of a right circular cylinder from any two known parameters. Whether you need to find cylinder height for a geometry problem or an engineering task, this tool handles ten different input combinations—such as radius and volume, lateral surface area and total area, or base area and diagonal. Simply enter the two values you have, and the calculator applies the appropriate cylinder height formula to return the answer immediately.

A right circular cylinder consists of two parallel, congruent circular bases stacked directly above each other. This alignment makes it a "right" cylinder, whereas oblique cylinders result when the bases are shifted. This calculator is dedicated to the standard right circular cylinder, which is the most common form encountered in practice.

Basic Geometry and Formulas

For a right circular cylinder with radius $r$ and height $h$, five fundamental equations describe its properties:

• Volume: $V = \pi r^{2} h$
• Base surface area: $B = \pi r^{2}$
• Lateral surface area: $L = 2 \pi r h$
• Total surface area: $A = 2 \pi r^{2} + 2 \pi r h$
• Longest diagonal (from one base edge to the opposite base edge): $d^{2} = 4 r^{2} + h^{2}$

By rearranging these equations, we can calculate cylinder height for any pair of known quantities. The calculator uses ten derived height formulas covering all practical cases.

Derived Height Formulas (Selected Examples)

Known Parameters	Height Formula
Radius $r$ and Volume $V$	$h = \dfrac{V}{\pi r^{2}}$
Radius $r$ and Lateral Area $L$	$h = \dfrac{L}{2 \pi r}$
Radius $r$ and Total Area $A$	$h = \dfrac{A - 2 \pi r^{2}}{2 \pi r}$
Radius $r$ and Diagonal $d$	$h = \sqrt{d^{2} - 4 r^{2}}$
Volume $V$ and Base Area $B$	$h = \dfrac{V}{B}$
Volume $V$ and Lateral Area $L$	$h = \dfrac{L^{2}}{4 \pi V}$
Base Area $B$ and Lateral Area $L$	$h = \dfrac{L}{2 \sqrt{\pi B}}$
Lateral Area $L$ and Total Area $A$	$h = \dfrac{L}{\sqrt{2 \pi (A - L)}}$

Each formula is derived by substituting known expressions into the fundamental equations and solving for $h$. For instance, from $L = 2 \pi r h$ we obtain $h = L/(2 \pi r)$; from $A = 2 \pi r^{2} + L$ we get $r^{2} = (A-L)/(2\pi)$ and then combine with the lateral area equation to yield the last row.

How to Use the Calculator

1. Select the two parameters you already know (radius, volume, diagonal, base area, lateral area, or total surface area).
2. Enter the values in the chosen units (the tool supports metric, imperial, and other common units).
3. Read the computed height instantly—no manual algebra or unit conversions needed.

The calculator automatically identifies which of the ten formulas to apply, ensuring accuracy every time.

Example

Suppose you have a cylindrical tank with a radius of 5 cm and a volume of 900 cm³. The height is obtained using $h = \dfrac{V}{\pi r^{2}}$:

$$h = \frac{900}{\pi \times 5^{2}} \approx 11.46\ \text{cm}.$$

This matches the result you would get from the calculator.

Whether you are a student learning geometry or a professional dealing with cylindrical parts, this tool provides a fast, reliable way to find cylinder height online and verify your manual calculations. It is designed specifically for right circular cylinder height determination, so you can trust its outputs for the most common cylinder shape.