Cylinder Calculator Online
Calculate cylinder volume, lateral area, total surface area, and fluid capacity with step-by-step formulas.
Input Parameters
Live Result
Details
Steps
Compute Circular Base Area: A_base = π · r²
Calculate Cylinder Volume: V = A_base · h
Compute Base Perimeter / Circumference: C = 2 · π · r
Calculate Lateral Surface Area: A_lateral = 2 · π · r · h
Calculate Total Surface Area: A_total = A_lateral + 2 · A_base
Quick Answer & Understanding Your Result
A right circular cylinder is a 3D solid bounded by two parallel congruent circular bases and a curved lateral surface, with volume V = π · r² · h and total surface area A = 2πr(r + h).
Fundamental Cylinder Formulas
- Volume: Internal capacity: V = π · r² · h (Circular base area multiplied by vertical height).
- Lateral Surface Area: Unrolled rectangular side jacket: A_l = 2 · π · r · h.
- Total Surface Area: Lateral area plus top and bottom bases: A_t = 2πr · h + 2πr² = 2πr(r + h).
- Base Area (Single): Flat circular bottom: A_b = π · r².
- Base Perimeter (Circumference): Boundary curve: C = 2 · π · r.
Industrial & Architectural Applications
- Storage Silos & Pipe Design: Sizing grain silos, fuel tanks, and industrial piping fluid flow capacities.
- Can & Container Packaging: Engineering beverage cans, aerosol containers, and cylindrical packaging.
- Hydraulic & Pneumatic Cylinders: Computing piston stroke volume and fluid displacement in heavy machinery.
Input the base radius and height in the calculator above to get instant volume, surface area, and liquid capacity figures.
Formula & Calculation Logic
Mathematical Formular is the radius of the circular base and h is the vertical height of the cylinder. The unrolled lateral surface forms a rectangle with width 2πr and height h.
Step-by-Step Guide
Enter Base Radius
Input the radius of the cylinder's circular base.
Enter Height
Input the perpendicular vertical height between the two circular bases.
Select Unit
Choose your linear unit (meters, centimeters, millimeters, inches, or feet).
Examine Computed Metrics
Review volume, lateral area, total surface area, and fluid capacity in liters and gallons.
Worked Examples Table
| Example | Input Values | Calculated Result | Explanation |
|---|---|---|---|
| Cylinder: Radius 4m, Height 10m | V = π · 16 · 10 = 160π ≈ 502.6548 m³, Lateral = 2π·4·10 = 80π ≈ 251.3274 m². | ||
| Beverage Can: Radius 3cm, Height 12cm | V = π · 9 · 12 = 108π ≈ 339.292 cm³ (equals ~339.3 mL). |
Frequently Asked Questions
Evidence-Based Methodology & Authoritative References
Wolfram MathWorld - Cylinder
ISO 80000-2: Quantities and Units - Mathematics
Standard: Volume, Lateral & Total Surface Area
Formula: Volume: V = π · r² · h
Last Reviewed: August 21, 2026
Primary Source: Wolfram MathWorld - Cylinder
Reference Document: ISO 80000-2: Quantities and Units - Mathematics
Computation Privacy: 100% client-side 0ms computation, zero data retention
Calculated results are modeled based on standard scientific and mathematical formulas. Please verify with domain-specific technical documentation for specialized applications.
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Calculated results are modeled based on standard scientific and mathematical formulas. Please verify with domain-specific technical documentation for specialized applications.