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Cylinder Calculator

Calculate cylinder volume and surface area

Volume

785.40

Surface Area

471.24

Base Area

78.54

Units

Volume

785.40

cubic units

Surface Area

471.24

square units

Lateral Surface Area

314.16

square units

Base Area

78.54

square units

Cylinder Preview

h = 10
r = 5

Formulas Used

Cylinder Volume

Volume = π × r² × h

The volume of a cylinder is the base area (π × r²) multiplied by the height.

Where:

r= Radius of the circular base
h= Height of the cylinder
π= Pi, approximately 3.14159

Cylinder Surface Area

Surface Area = 2πr² + 2πrh

Total surface area includes two circular bases (2πr²) and the lateral curved surface (2πrh).

Where:

r= Radius of the circular base
h= Height of the cylinder
2πr²= Area of two circular bases
2πrh= Lateral (curved) surface area

Example Calculations

1Cylinder: Radius 5, Height 10

Inputs

Radius5
Height10

Result

Volume785.40
Surface Area471.24
Lateral Surface Area314.16
Base Area78.54

Base Area = π × 5² = 78.54. Volume = 78.54 × 10 = 785.40. Lateral SA = 2π × 5 × 10 = 314.16. Total SA = 314.16 + 2 × 78.54 = 471.24.

2Cylinder: Radius 3, Height 7

Inputs

Radius3
Height7

Result

Volume197.92
Surface Area188.50
Lateral Surface Area131.95
Base Area28.27

Base Area = π × 3² = 28.27. Volume = 28.27 × 7 = 197.92. Lateral SA = 2π × 3 × 7 = 131.95. Total SA = 131.95 + 2 × 28.27 = 188.50.

Frequently Asked Questions

Q

How do you calculate the volume of a cylinder?

Volume of a cylinder = π × r² × h, where r is the radius and h is the height. For example, a cylinder with radius 5 and height 10 has volume = π × 5² × 10 = 785.40 cubic units.

  • A 5-gallon bucket (r=5.5", h=14.5") holds about 1,437 in³ or 5.98 gallons
  • To find radius from diameter, divide diameter by 2 before plugging into the formula
  • Volume in liters: multiply cubic centimeters by 0.001 (1 L = 1,000 cm³)
  • For a half-filled cylinder, simply halve the height in the formula
Q

How do you calculate the surface area of a cylinder?

Surface area = 2πr² + 2πrh = 2πr(r + h). This includes both circular bases and the curved lateral surface. For radius 5 and height 10: SA = 2π(5)² + 2π(5)(10) = 471.24 square units.

  • Use total surface area when calculating paint or coating for a closed tank
  • For an open-top container (like a bucket), subtract one base: SA = πr² + 2πrh
  • A standard 55-gallon drum (r=11.25", h=33.5") has ~3,162 in² total surface area
  • Surface area determines material cost – sheet metal for a cylinder with r=3 ft, h=6 ft needs ~170 ft²
Q

What is the lateral surface area of a cylinder?

Lateral surface area = 2πrh, which is the curved surface area (excluding the two circular bases). For radius 5 and height 10: LSA = 2π(5)(10) = 314.16 square units.

  • The lateral surface "unrolls" into a rectangle of width 2πr and height h
  • Use lateral area to calculate label size for cans or wrapping around columns
  • A soda can (r=1.3", h=4.8") has a lateral area of ~39.2 in²
  • Doubling the radius quadruples the base area but only doubles the lateral area
Q

What is the base area of a cylinder?

Base area = πr², which is the area of one circular base. A cylinder has two bases, so total base area = 2πr². For radius 5: base area = π(5)² = 78.54 square units per base.

  • Doubling the radius increases base area by 4× (π(2r)² = 4πr²)
  • A 12" pizza pan (r=6") has a base area of ~113.1 in²
  • For pipes, the annular area = π(R² – r²) where R is outer and r is inner radius
  • Base area is used to calculate pressure at the bottom: Pressure = Force / Base Area

Understanding Cylinder Calculations

A cylinder has two circular bases and a curved lateral surface. Volume is calculated as base area times height.

The surface area includes both circular bases and the lateral (curved) surface. The lateral surface area is the curved part only.

All cylinder calculations depend on the radius of the base and the height of the cylinder.

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Last Updated: Mar 26, 2026

This calculator is provided for informational and educational purposes only. Results are estimates and should not be considered professional financial, medical, legal, or other advice. Always consult a qualified professional before making important decisions. UseCalcPro is not responsible for any actions taken based on calculator results.

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