Cylinder Volume & Surface Area Calculator

A right circular cylinder is a geometric solid with two parallel circular bases connected by a curved surface. This calculator computes both the volume and total surface area from the base radius and cylinder height.

Cylinder formulas

For a cylinder with radius r and height h:

• Volume: V = π × r² × h
• Total surface area: SA = 2 × π × r × (r + h)
• Lateral area: LA = 2 × π × r × h

The total surface area includes both circular bases (2 × π × r²) plus the lateral area (2 × π × r × h).

Example 1: cylinder with integer dimensions

Problem: A cylinder has radius r = 5 cm and height h = 12 cm.

1. Volume:
   • V = π × 5² × 12 = π × 25 × 12 ≈ 942.48 cm³.
2. Surface area:
   • SA = 2 × π × 5 × (5 + 12) = 2 × π × 5 × 17 ≈ 534.07 cm².

Answer: V ≈ 942.48 cm³, SA ≈ 534.07 cm².

Example 2: cylinder with decimal measurements

Problem: A cylindrical tank has radius r = 1.5 m and height h = 3.2 m.

1. Volume:
   • V = π × 1.5² × 3.2 = π × 2.25 × 3.2 ≈ 22.62 m³.
2. Surface area:
   • SA = 2 × π × 1.5 × (1.5 + 3.2) = 2 × π × 1.5 × 4.7 ≈ 44.30 m².

Answer: V ≈ 22.62 m³, SA ≈ 44.30 m².

Common uses of the cylinder calculator

• Calculating the capacity of water tanks, barrels and cylindrical containers.
• Estimating paint quantities needed to cover cylindrical surfaces.
• Determining the volume of pipes and cylindrical conduits.
• Solving solid geometry problems in mathematics and physics.
• Designing cylindrical packaging and containers in product engineering.
• Computing materials for columns, pillars and circular architectural elements.

Common mistakes when working with cylinders

• Using the diameter instead of the radius in formulas without dividing by 2.
• Confusing lateral area with total surface area.
• Forgetting to include both bases when calculating total surface area.
• Mixing units, such as radius in cm and height in meters.

Pro tip

When working with hollow cylinders (like pipes), compute the material volume by subtracting the inner volume from the outer: V_material = π × (R_outer² − R_inner²) × h. This is essential for estimating material weight and cost.