Right Cylinder Calculator - Complete Solver

Comprehensive online calculator to calculate the the volume, areas, radius and height of a right cylinder given any two parameters.

Right circular cylinder diagram showing radius r and height h

Right circular cylinder with radius r and height h

Enter any TWO parameters below. The calculator will determine all remaining values (radius r, height h, lateral area AL, total area AT, and volume V). Note that in some cases there are conditions to satisfy in order to have a solution to the problem. In mode 9, where the total area and the volume are entered, there may be no solution, one solution or two solutions

📐 Cylinder Formulas

Basic Formulas

\(A_L = 2\pi r h\)

Lateral Surface Area (curved surface)

\(A_T = 2\pi r h + 2\pi r^2\)

Total Surface Area (including both bases)

\(V = \pi r^2 h\)

Volume

Derived Formulas

\(h = \dfrac{V}{\pi r^2}\)

Height from radius and volume

\(h = \dfrac{A_L}{2\pi r}\)

Height from radius and lateral area

\(r = \dfrac{A_L}{2\pi h}\)

Radius from height and lateral area

Solving for Radius

\(r = \sqrt{\dfrac{V}{\pi h}}\)

Radius from volume and height

\(r = \sqrt{\dfrac{A_T - A_L}{2\pi}}\)

Radius from total and lateral areas

\(r = \dfrac{2V}{A_L}\)

Radius from volume and lateral area

Quadratic/Cubic Solutions

\(2\pi r^2 + 2\pi h r - A_T = 0\)

Solve for r given AT and h

\(2\pi r^3 - A_T r + 2V = 0\)

Solve for r given AT and V (may have 2 solutions)

Where: r = radius, h = height, AL = lateral area, AT = total area, V = volume

Right Cylinder Complete Solver

Select which two parameters you know, enter their values, and click Calculate.

V = πr²h
AL = 2πrh
AT = 2πrh + 2πr²
Mode 1: Given radius (r) and height (h) → Calculate volume (V), lateral area (AL), and total area (AT)

Results

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-- unit²
-- unit²
-- unit³

More References and Links

Online Geometry Calculators and Solvers