What is the formula for the volume of a cylinder?

The volume is found by multiplying the area of the circular base by the vertical height: Volume = π × r² × h. Think of it as stacking flat circular discs of area πr² up to a height of h.

How is the total surface area of a cylinder structured?

The total surface area includes two distinct parts: the curved rectangular wrapper (Lateral Area = 2πrh) and the two circular flat ends (Base Area = πr²). Summing them gives: Total Area = 2πrh + 2(πr²).

What is a right cylinder vs. an oblique cylinder?

In a right cylinder, the bases are perfectly aligned vertically, meaning the side lines are perpendicular to the base. In an oblique cylinder, the bases are skewed sideways, but the volume formula (Base Area × vertical height) remains identical.

Geometry Tool

Cylinder Calculator

Calculate the volume, lateral surface area, total surface area, and base area of a right circular cylinder. Simply enter the radius and height.

Interactive Cylinder Calculator Workspace

Live Solver

Base Radius (r)

Cylinder Height (h)

Outputs

Volume226.1947

Total Area207.3451

Lateral Area150.7964

Base Area28.2743

How We Solved It

1. Base Area: πr² = 3.14159 × 3² = 28.2743

2. Volume: Base Area × h = 28.2743 × 8 = 226.1947

3. Lateral Area (Wrapper): 2πrh = 2 × 3.14159 × 3 × 8 = 150.7964

4. Total Surface Area: Lateral Area + 2×(Base Area) = 150.7964 + 2×(28.2743) = 207.3451

Mathematical Formula & Variables

Equation ModelVolume = π × r² × h, Total Surface Area = 2 × π × r × (r + h)

Calculates the volume, base circular area, and external outer shell surface areas of a solid right circular cylinder.

Variable Definitions

Symbol	Description
r (Radius)	The radius of the parallel circular bases.
h (Height)	The vertical altitude distance separating the two parallel circular bases.
V (Volume)	The capacity or total three-dimensional space held inside the cylinder.
LA (Lateral Area)	The surface area of the curved sides (excluding the two circular ends).

How to Use the Cylinder Calculator

Enter the Radius of the circular cylinder base.
Enter the perpendicular vertical Height of the cylinder.
Examine the calculated Volume, Lateral Area, Base Area, and Total Area in the outputs section.
Follow the worked mathematical equations to understand how base area combines with lateral area.

Practical Example Calculation

Scenario Context: An engineer is calculating the fluid capacity of a cylindrical water tank with a radius of 3 meters and height of 8 meters.

Step 1: Identify inputs: Radius (r) = 3 m, Height (h) = 8 m.

Step 2: Calculate Base Area (BA): BA = π × r² = π × 3² = 9 × π ≈ 28.27 square meters.

Step 3: Calculate Volume (V): V = Base Area × Height = 28.274 × 8 ≈ 226.19 cubic meters.

Step 4: Calculate Lateral Area (LA): LA = 2 × π × r × h = 2 × π × 3 × 8 = 48 × π ≈ 150.80 square meters.

Step 5: Calculate Total Surface Area (TA): TA = LA + (2 × BA) = 150.796 + (2 × 28.274) = 150.796 + 56.548 ≈ 207.35 square meters.

The water tank holds 226.19 m³ of water, with a total surface area of 207.35 m².

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