Cylinder Volume Calculator
Accurate geometric volume, internal fluid capacity, surface area, and material mass for solid cylinders, hollow pipes, and partially filled tanks.
Solid Cylinder Dimensions
Hollow Pipe Dimensions
Cylinder Tank & Dip Level
Computed Volume & Capacity
785.40
cu ft
5,875.19 US gal
22,240.00 Liters
29.09 cu yd
22.24 m³
1,357,168.03 cu in
Interactive 3D Axonometric Blueprint
Solid Cylinder
Base Area
78.54 sq ft
7.30 m²
Lateral Area
314.16 sq ft
29.19 m²
Total Surface
471.24 sq ft
43.78 m²
Water Mass
49,031 lb
22,240 kg (24.52 t)
| Geometric & Physical Property | Imperial Engineering Unit | Metric Standard Unit |
|---|---|---|
| Radius (r) | 5.00 ft (60.00 in) | 1.524 m (152.4 cm) |
| Diameter (d) | 10.00 ft (120.00 in) | 3.048 m (304.8 cm) |
| Height / Length (h) | 10.00 ft (120.00 in) | 3.048 m (304.8 cm) |
| Base Circumference (2πr) | 31.42 ft | 9.58 m |
| Single Base Area (πr²) | 78.54 sq ft | 7.30 m² |
| Both Base Ends Area (2πr²) | 157.08 sq ft | 14.59 m² |
| Lateral Surface Area (2πrh) | 314.16 sq ft | 29.19 m² |
| Total Surface Area | 471.24 sq ft | 43.78 m² |
| Volume (Cubic Feet / Meters) | 785.40 cu ft | 22.24 m³ |
| Volume (Cubic Yards / Inches) | 29.09 cu yd | 1,357,168 cu in |
| Fluid Capacity (Gallons / Liters) | 5,875.19 US gal | 22,240.00 L |
| Imperial Capacity & Barrels | 4,892.12 UK gal | 139.89 bbl (oil) |
| Water Weight (Filled) | 49,031 lb (24.52 tons) | 22,240 kg (22.24 tonnes) |
Mathematical Formulas & Geometric Foundations
A right circular cylinder is a three-dimensional solid formed by two congruent, parallel circular bases connected by a curved lateral surface perpendicular to both bases. The volume measures the three-dimensional space enclosed within its boundaries.
Volume Formula (Radius): V = A_base × h = π × r² × h
Volume Formula (Diameter): V = π × (d / 2)² × h = (π × d² × h) / 4
Lateral Surface Area: A_lat = 2 × π × r × h = π × d × h
Base Area (Top + Bottom): A_ends = 2 × π × r² = (π × d²) / 2
Total Surface Area: A_total = 2πr² + 2πrh = 2πr(r + h)
Volume Formula (Diameter): V = π × (d / 2)² × h = (π × d² × h) / 4
Lateral Surface Area: A_lat = 2 × π × r × h = π × d × h
Base Area (Top + Bottom): A_ends = 2 × π × r² = (π × d²) / 2
Total Surface Area: A_total = 2πr² + 2πrh = 2πr(r + h)
Specialized Cylindrical Geometries
In structural engineering, plumbing, and petrochemical processing, cylinders frequently deviate from simple solid shapes:
- Hollow Cylinder (Pipe / Conduit / Sleeve): The volume of the solid wall is calculated by subtracting the inner hollow cylinder volume from the outer cylinder volume:
V_wall = π × (R_outer² - R_inner²) × h
V_inner_flow = π × R_inner² × h - Partially Filled Horizontal Tank: Computing the liquid volume when a horizontal cylindrical tank is filled to a dip depth h requires calculating the wetted circular segment area:
θ = 2 × arccos((R - h) / R) (in radians)
A_segment = 0.5 × R² × (θ - sin(θ))
V_liquid = A_segment × L
Step-by-Step Worked Example
Consider a commercial storage silo or water cistern with a radius of 5.00 ft (or 10.00 ft diameter) and a height of 10.00 ft:
- Step 1: Calculate Base Area ($A_{ ext{base}}$):
$$A_{ ext{base}} = pi imes r^2 = pi imes (5 ext{ ft})^2 = 25pi approx 78.5398 ext{ sq ft} approx 78.54 ext{ sq ft}$$ - Step 2: Calculate Total Volume ($V$):
$$V = A_{ ext{base}} imes h = 78.5398 ext{ sq ft} imes 10 ext{ ft} = 250pi approx 785.3982 ext{ cu ft} approx 785.40 ext{ cu ft}$$ - Step 3: Convert to Fluid Gallons and Metric Liters:
Since 1 cubic foot equals exactly $1,728 / 231 approx 7.48052 ext{ US liquid gallons}$:
$$ ext{Gallons} = 785.3982 imes 7.480519 approx 5,875.19 ext{ US gal}$$
Since 1 cubic foot equals $28.3168466 ext{ liters}$:
$$ ext{Liters} = 785.3982 imes 28.316847 approx 22,240.00 ext{ L}$$ - Step 4: Compute Total Surface Area:
$$A_{ ext{lat}} = 2pi(5)(10) = 100pi approx 314.16 ext{ sq ft}$$
$$A_{ ext{ends}} = 2 imes 25pi = 50pi approx 157.08 ext{ sq ft}$$
$$A_{ ext{total}} = 100pi + 50pi = 150pi approx 471.24 ext{ sq ft}$$
Standard Volumetric Equivalents Reference
Use this reference table to convert cylinder volume across standard imperial and metric engineering benchmarks:
| Standard Base Unit | Cubic Feet (ft³) | Cubic Meters (m³) | US Gallons (gal) | Liters (L) | Cubic Yards (yd³) |
|---|---|---|---|---|---|
| 1.00 Cubic Foot | 1.0000 | 0.0283 | 7.4805 | 28.3168 | 0.0370 |
| 1.00 Cubic Meter | 35.3147 | 1.0000 | 264.172 | 1,000.00 | 1.3079 |
| 1.00 US Gallon | 0.1337 | 0.003785 | 1.0000 | 3.7854 | 0.00495 |
| 100 Liters | 3.5315 | 0.1000 | 26.4172 | 100.00 | 0.1308 |
| 1.00 Cubic Yard | 27.0000 | 0.7646 | 201.974 | 764.555 | 1.0000 |
| 1 Oil Barrel (bbl) | 5.6146 | 0.1590 | 42.0000 | 158.987 | 0.2079 |
Frequently Asked Questions (FAQ)
Because radius is half the diameter ($r = d / 2$), squaring the radius yields $(d / 2)^2 = d^2 / 4$. The volume formula becomes $V = (pi imes d^2 imes h) / 4$. Alternatively, simply divide your measured diameter by 2 first to get the radius, and then apply $V = pi r^2 h$.
Exactly 7.48052 US liquid gallons fit in 1 cubic foot of volume. If you are calculating in UK (Imperial) gallons, 1 cubic foot holds approximately 6.2288 Imperial gallons. For metric capacity, 1 cubic foot contains 28.3168 liters.
Unlike a vertical cylinder where horizontal cross-sectional area remains constant from bottom to top, a horizontal cylinder widens toward the equator (middle) and narrows at the bottom and top. Consequently, the first 10% of depth holds far less volume than the middle 10% of depth. Calculating horizontal tank liquid requires the circular segment area formula: $A = 0.5 imes R^2 imes ( heta - sin heta)$.
Total volume (outer displacement) is the total geometric space bounded by the pipe's outer diameter ($pi R_{ ext{outer}}^2 h$). Inner capacity is the open volume inside the hollow core through which liquid or gas flows ($pi R_{ ext{inner}}^2 h$). The difference between outer volume and inner volume is the solid wall volume ($pi (R_{ ext{outer}}^2 - R_{ ext{inner}}^2) h$), which determines the dry weight of the pipe material.
At standard room temperature (68°F / 20°C), pure water weighs approximately 62.43 pounds per cubic foot (8.345 pounds per US gallon), or exactly 1,000 kilograms per cubic meter (1 kilogram per liter). Multiply your calculated volume in cubic feet by 62.43 (or gallons by 8.345) to determine the water payload weight.
In industrial design and tank fabrication, material costs are minimized when total surface area is lowest for a required volume. Mathematically, the optimum right circular cylinder has a height equal to its diameter ($h = 2r$ or $h / d = 1$). In this balanced state, the lateral surface area accounts for exactly two-thirds (66.7%) of total surface area, while the top and bottom bases account for one-third (33.3%).