There are five basic equations which completely describe the cylinder with given radius r and height h:
Volume of a cylinder: V = π * r² * h,
Base surface area of a cylinder: A_b = 2 * π * r²,
Lateral surface area of a cylinder: A_l = 2 * π * r * h,
Total surface area of a cylinder: A = A_b + A_l,
Longestdiagonalofacylinder: d² = 4 * r² + h².
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:
Given radius and volume: h = V / (π * r²),
Given radius and lateralarea: h = A_l / (2 * π * r),
Given radius and totalarea: h = (A - 2 * π * r²) / (2 * π * r),
Given radius and longest diagonal: h = √(d² - 4 * r²),
Given volume and basearea: h = 2 * V / A_b,
Given volume and lateralarea: h = A_l² / (4 * π * V),
Given basearea and lateralarea: h = √(A_l² / (2 * π * A_b)),
Given basearea and totalarea: h = (A - A_b) / √(2 * A_b * π),
Given basearea and diagonal: h = √(d² - 2 * A_b / π),
Given lateralarea and totalarea: h = A_l / √(2 * π * (A - A_l)).