How do you calculate the volume and capacity of a cylinder?

The volume of a cylinder is calculated using the formula V = π × r² × h, where r is the base radius and h is the height. To convert volume to liquid capacity: 1 cubic meter (m³) equals 1,000 Litres or approximately 264.172 US liquid gallons. Total surface area is given by A = 2πr(r + h).

What is a frustum and how is its volume computed?

A frustum is a truncated cone (or pyramid) formed by cutting off the apex with a plane parallel to the base. The volume of a conical frustum with top radius r, bottom radius R, and vertical height h is V = (1/3) × π × h × (R² + r² + R×r). Its slant height is s = √((R - r)² + h²).

How is the liquid volume calculated in a partially filled horizontal cylindrical tank?

For a horizontal cylinder of radius R and length L filled to depth h (h ≤ 2R), the cross-sectional liquid area is a circular segment: A_seg = R² × arccos((R - h)/R) - (R - h) × √(2Rh - h²). The total liquid volume is V_liquid = A_seg × L. This calculator computes exact dipstick liquid holding volumes and ullage (empty headspace).

What is Cavalieri’s Principle in 3D geometry?

Cavalieri’s Principle states that if two three-dimensional solids have the same height and equal cross-sectional areas at every level parallel to their bases, their total volumes are equal. This fundamental theorem proves why right prisms/cylinders and oblique prisms/cylinders of identical base and height share the exact same volume formula.

How do you calculate the mass/weight of a 3D solid from its volume?

The mass is calculated using the physical density relationship: Mass (kg) = Volume (m³) × Density (kg/m³). For example, a 2 m³ solid block made of reinforced concrete (density ~2,400 kg/m³) weighs 4,800 kg (4.8 metric tonnes).

What is the difference between total surface area and lateral surface area?

Lateral Surface Area (LSA) measures only the area of the curved sides or perimeter faces excluding the top and bottom bases. Total Surface Area (TSA) includes the lateral area plus the area of all bases (e.g., for a cylinder, TSA = 2πrh + 2πr²).

3D Geometry & Volume Calculator Online — Cylinders, Cones, Tanks & Prisms

Free online 3D geometry and volume calculator. Compute volume, surface area, capacity in litres & gallons, and material weight for 19 shapes including cylinders, cones, spheres, frustums, prisms, and horizontal liquid dipstick tanks.

⚡ Interactive Calculation Engine Active

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How to Use 3D Geometry & Volume Calculator

Select a solid geometry category (Curved Solids, Prisms & Cubes, Pyramids, or Tanks & Silos) and choose from 19 shapes including Cylinders, Cones, Spheres, Frustums, Torus, Cuboids, and Horizontal Cylindrical Tanks.
Select your preferred measurement unit: Meters (m), Centimeters (cm), Millimeters (mm), Feet (ft), Inches (in), or Yards (yd).
Enter the dimensional parameters (radii, heights, lengths, widths). For horizontal tanks, adjust the interactive dipstick liquid depth slider.
Select a solid or liquid material (Water, Concrete, Steel, Aluminum, Timber, PLA/PETG, Soil, Gasoline) to automatically calculate net physical mass in kg, tonnes, and lbs.
Inspect the computed 3D wireframe preview, SI volume (m³), holding capacity (Litres, US Gallons, UK Gallons, ft³, bbl), and total surface area.
Review the step-by-step geometric derivations and export the complete volumetric specification as a CSV file.

Volumetric & Spatial Geometry in Engineering and Science

Volumetric calculations govern fluid storage design (chemical sumps, water reservoirs, pressurized silos), civil construction budgeting (concrete batch volumes, excavation soil tonnage), thermal heat exchange (surface-area-to-volume ratio), and logistics cargo containerization.

Liquid Storage Tanks, Dipstick Calibration & Ullage

Industrial tanks storing petroleum, milk, or chemicals require nonlinear dipstick volume charts because cylindrical cross-sections expand and contract nonlinearly with liquid depth. Our calculator provides instantaneous circular segment integration to accurately calibrate liquid inventories.

Frequently Asked Questions

How do you calculate the volume and capacity of a cylinder?: The volume of a cylinder is calculated using the formula V = π × r² × h, where r is the base radius and h is the height. To convert volume to liquid capacity: 1 cubic meter (m³) equals 1,000 Litres or approximately 264.172 US liquid gallons. Total surface area is given by A = 2πr(r + h).
What is a frustum and how is its volume computed?: A frustum is a truncated cone (or pyramid) formed by cutting off the apex with a plane parallel to the base. The volume of a conical frustum with top radius r, bottom radius R, and vertical height h is V = (1/3) × π × h × (R² + r² + R×r). Its slant height is s = √((R - r)² + h²).
How is the liquid volume calculated in a partially filled horizontal cylindrical tank?: For a horizontal cylinder of radius R and length L filled to depth h (h ≤ 2R), the cross-sectional liquid area is a circular segment: A_seg = R² × arccos((R - h)/R) - (R - h) × √(2Rh - h²). The total liquid volume is V_liquid = A_seg × L. This calculator computes exact dipstick liquid holding volumes and ullage (empty headspace).
What is Cavalieri’s Principle in 3D geometry?: Cavalieri’s Principle states that if two three-dimensional solids have the same height and equal cross-sectional areas at every level parallel to their bases, their total volumes are equal. This fundamental theorem proves why right prisms/cylinders and oblique prisms/cylinders of identical base and height share the exact same volume formula.
How do you calculate the mass/weight of a 3D solid from its volume?: The mass is calculated using the physical density relationship: Mass (kg) = Volume (m³) × Density (kg/m³). For example, a 2 m³ solid block made of reinforced concrete (density ~2,400 kg/m³) weighs 4,800 kg (4.8 metric tonnes).
What is the difference between total surface area and lateral surface area?: Lateral Surface Area (LSA) measures only the area of the curved sides or perimeter faces excluding the top and bottom bases. Total Surface Area (TSA) includes the lateral area plus the area of all bases (e.g., for a cylinder, TSA = 2πrh + 2πr²).