Height of a Cylinder Calculator
Enter any two known measurements of a right circular cylinder and this calculator will find its height instantly. Choose from five solve modes: volume + radius, lateral surface area + radius, total surface area + radius, diagonal + radius, or volume + base area. Results update as you type, with a full worked solution, a labeled shape diagram, and unit switching between metric and imperial.
What is the height of a cylinder?
A right circular cylinder is a 3D solid with two parallel, congruent circular bases connected by a curved lateral surface. The height (h) is the perpendicular distance between the two bases, measured along the axis. It is the same as the length of the cylinder when the bases are horizontal. The height, together with the radius of the base, fully determines every other measurement: volume, surface areas, and the space diagonal.
How to calculate the height of a cylinder
The approach depends on which measurements you have. If you know the volume (V) and radius (r), rearrange the volume formula V = πr²h to get h = V / (πr²). If you know the lateral surface area (Aₗ = 2πrh) and radius, use h = Aₗ / (2πr). If you have the total surface area (A = 2πr² + 2πrh) and radius, solve for h as (A - 2πr²) / (2πr). If you know the space diagonal (d) and radius, the formula is h = √(d² - 4r²). Finally, if you know the volume and the base area (Aᵇ = πr²) but not the radius, use h = V / Aᵇ. This calculator handles all five cases automatically.
Worked example: finding height from volume and radius
Suppose a cylindrical water tank has a radius of 5 cm and holds 785.4 cm³. Step 1: apply h = V / (πr²). Step 2: square the radius: 5² = 25 cm². Step 3: multiply by π: π x 25 = 78.54 cm². Step 4: divide the volume: 785.4 / 78.54 = 10.00 cm. The tank is 10 cm tall. The lateral surface area would be 2π x 5 x 10 = 314.16 cm², and the total surface area would be 314.16 + 2 x 78.54 = 471.24 cm².
Practical uses of cylinder height calculations
Cylinder height calculations appear across engineering, manufacturing, and everyday tasks. Plumbers need the height of a pipe segment from a known volume of liquid it must carry. Sheet-metal workers compute height from a target lateral area to minimize material waste. Tank designers solve for height given a required capacity and a fixed footprint radius. In packaging, a can's height is chosen alongside radius to meet a volume target while keeping the total surface area (and therefore material cost) low. The diagonal formula is useful in structural analysis to find the axial length of a cylindrical strut from the overall end-to-end measurement.
Cylinder height formulas - quick reference
| Known inputs | Formula for h | Notes |
|---|---|---|
| Volume + Radius | h = V / (πr²) | Most common case |
| Lateral Area + Radius | h = Aₗ / (2πr) | Useful for sheet-metal problems |
| Total Area + Radius | h = (A - 2πr²) / (2πr) | Requires A > 2πr² |
| Diagonal + Radius | h = √(d² - 4r²) | Requires d > 2r |
| Volume + Base Area | h = V / Aᵇ | When radius is unknown |
Each row shows which two known values are needed and the formula for finding height (h). r = radius, V = volume, Aₗ = lateral area, A = total area, Aᵇ = base area, d = space diagonal.
Frequently asked questions
What is the formula for the height of a cylinder?
The most common formula is h = V / (πr²), where V is the volume and r is the base radius. Other formulas depend on what you know: h = Aₗ / (2πr) from lateral area and radius; h = (A - 2πr²) / (2πr) from total surface area and radius; h = √(d² - 4r²) from the space diagonal and radius; and h = V / Aᵇ from volume and base area. All five are available in this calculator.
How do I find the height of a cylinder if I only know the volume?
Volume alone is not enough - you also need the radius (or base area). With both, use h = V / (πr²) or equivalently h = V / Aᵇ. If you have the lateral surface area instead of the radius, you can combine it with volume using h = Aₗ² / (4πV), though this calculator covers the more intuitive paired-input approach.
What is the space diagonal of a cylinder?
The space diagonal (d) is the longest straight line that fits inside a cylinder - it runs from one point on the rim of the base to the diametrically opposite point on the rim of the top. Its length is d = √(h² + 4r²). To find height from the diagonal and radius, rearrange to h = √(d² - 4r²). Note that the diagonal must be longer than the diameter (2r), otherwise h would be imaginary.
Does the height of a cylinder affect its volume proportionally?
Yes - volume is directly proportional to height. If you double the height while keeping the radius fixed, the volume doubles. This is visible in the chart above, which shows volume growing linearly with height. By contrast, doubling the radius quadruples the volume (because the base area scales with r²).
Can I use this calculator for oblique cylinders?
The formulas used here are for right circular cylinders only - where the axis is perpendicular to the bases. For an oblique cylinder, the volume formula is the same (V = πr²h, where h is still the perpendicular height between the two parallel bases), but the lateral surface area formula is different and depends on the slant. If you need the slant height rather than the perpendicular height, use the Pythagorean theorem with the slant and the offset distance.
What units does this calculator support?
You can switch between metric (centimetres, square centimetres, cubic centimetres) and imperial (inches, square inches, cubic inches) using the Units selector. All inputs and outputs update together. For other unit systems, convert your inputs to cm or inches first, then convert the height result back.