Height of a Cylinder Calculator

Find a cylinder's height from its volume, lateral surface area, or total surface area — plus the resulting volume and surface areas.

Quick Facts

Volume formula
V = πr²h
Solve for height: h = V / (πr²).
Lateral surface area
L = 2πrh
Just the curved side wall; h = L / (2πr).
Total surface area
A = 2πr² + 2πrh
Adds the two circular bases; h = (A − 2πr²) / (2πr).

Your Results

Calculated
Height
-
h, solved from your known value
Volume
-
V = πr²h
Lateral Surface Area
-
L = 2πrh
Total Surface Area
-
A = 2πr² + 2πrh

Ready

Choose a method, enter the radius and known value, then press Calculate.

Formula and Method for the Height of a Cylinder

A right circular cylinder has a radius r and a height h. Its volume is V = πr²h, its lateral (curved-side) surface area is L = 2πrh, and its total surface area — lateral plus the two circular bases — is A = 2πr² + 2πrh. This calculator solves each of those equations for height, so you can work backward from whichever quantity you already know: volume, lateral surface area, or total surface area.

How the calculation works

Choose which known quantity you have, enter the radius and that value in matching units, and the calculator isolates h algebraically. From volume: h = V / (πr²). From lateral surface area: h = L / (2πr). From total surface area: h = (A − 2πr²) / (2πr), since the two circular bases (2πr²) must be subtracted before dividing by the circumference term. Once height is known, the tool also reports the volume, lateral surface area, and total surface area for the full cylinder.

Common mistakes

  • Radius vs. diameter: all three formulas use radius, not diameter. If you only have the diameter, divide it by 2 before entering it as the radius.
  • Lateral vs. total surface area: lateral surface area excludes the top and bottom circles; total surface area includes them. Using the wrong one shifts the result by 2πr².
  • Mismatched units: the known value's unit must match the radius unit family — volume in cubic units (ft³, m³) and surface area in square units (ft², m²) that correspond to the same length unit as the radius.
  • Impossible inputs: when solving from total surface area, the value must exceed 2πr² (the area of the two bases alone), otherwise there is no positive height that satisfies the equation.

Real-world applications

  • Tank, pipe, and silo design often starts from a required volume and a fixed radius to determine the height needed.
  • Sheet-metal and can manufacturing use lateral surface area to calculate how much material wraps around the side.
  • Packaging and coating jobs use total surface area (including the ends) to estimate paint, labels, or insulation needed.
  • Reverse-engineering a container's dimensions from its stated capacity and a measured or assumed radius.

Frequently Asked Questions

What is the formula for the height of a cylinder given its volume?
Rearrange the volume formula V = πr²h to solve for height: h = V / (πr²). For example, a cylinder with a 4 ft radius and a volume of 200 ft³ has a height of 200 / (π × 4²) ≈ 3.98 ft.
How do I find the height from the lateral (side) surface area?
Lateral surface area is L = 2πrh, so height is h = L / (2πr). This uses only the curved side of the cylinder, not the top and bottom circles.
How do I find the height from the total surface area?
Total surface area is A = 2πr² + 2πrh (the two circular bases plus the curved side), so height is h = (A − 2πr²) / (2πr). The total surface area must be greater than 2πr² for a positive height to exist.
What is the difference between lateral and total surface area of a cylinder?
Lateral surface area covers only the curved side wall (2πrh). Total surface area adds the two flat circular ends (2πr²) to that, giving A = 2πr² + 2πrh.

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