Cylinder Calculator

Volume = π × r² × h, where r is the radius and h is the height. For example, a cylinder with radius 5 cm and height 10 cm has volume = π × 5² × 10 = π × 250 ≈ 785.4 cm³. If you know the diameter, divide by 2 to get the radius first. For tanks and containers, this tells you how much liquid they can hold.

Lateral surface area is just the curved side: 2πrh (imagine a label wrapped around a can). Total surface area includes both circular ends: 2πrh + 2πr². For a can with r=3 cm and h=10 cm: Lateral = 2π × 3 × 10 ≈ 188.5 cm². Total = 188.5 + 2π × 9 ≈ 245.0 cm². Use lateral area for wrapping material, total area for painting or coating.

Rearrange the volume formula: r = √(V ÷ (π × h)). For example, if a tank holds 1000 liters (1,000,000 cm³) and is 100 cm tall: r = √(1,000,000 ÷ (π × 100)) = √(3183.1) ≈ 56.4 cm diameter. This is useful when designing tanks or containers for specific capacities.

Calculate the total surface area (2πrh + 2πr²), then divide by paint coverage. For a tank with r=1m and h=2m: Area = 2π(1)(2) + 2π(1)² = 4π + 2π = 6π ≈ 18.85 m². If paint covers 10 m²/liter, you need ~1.9 liters. Add 10-15% for waste and overlap. For inside coating, use just the lateral area plus one base.

The H/D ratio affects surface area efficiency. For a fixed volume, a ratio of 1:1 (height equals diameter) minimizes total surface area—optimal for material costs. Tall, narrow cylinders (H/D > 2) are good for vertical storage but use more material. Short, wide cylinders (H/D < 0.5) are stable but take more floor space. Industrial tanks typically use H/D between 0.5 and 2.