Best for
Mass and capacity estimates
Use volume with density for mass, or directly for tank, pipe, and container capacity.
Engineering formula reference
Volume Formula Sheet
Search volume formulas for common solids used in fluid capacity, mass estimates, material takeoff, tank sizing, and engineering geometry.
3D geometry
Search volume formula sheet
Filter the formula table by shape, variable, symbol, expression, or engineering use case.
Check geometry
Inside vs outside volume
For hollow parts and tanks, confirm whether you need material volume, internal volume, or displaced volume.
Formula reference
Volume formulas with variables
| Shape | Volume formula | Variables and notes |
|---|---|---|
| Cube | V = a3 | a = side length |
| Rectangular prism | V = l w h | l = length, w = width, h = height |
| Sphere | V = (4/3)πr3 | r = radius |
| Cylinder | V = πr2h | h = height or length |
| Cone | V = (1/3)πr2h | h = perpendicular height |
| Pyramid | V = A h / 3 | A = base area |
| Triangular prism | V = A h | A = triangular base area |
| Hollow cylinder material | V = πh(R2 - r2) | R = outer radius, r = inner radius |
| Ellipsoid | V = (4/3)πabc | a, b, c = semi-axes |
How to use
Practical engineering checks
Mass estimate
m = ρ V
rho is density and V is volume.
Fluid capacity
capacity = internal volume
Use inside dimensions for tanks, pipes, and containers.
Prism volume
V = A h
A is cross-sectional area and h is length or height.
Units
volume units are cubed
Cube unit conversions before comparing values.
Definitions
Symbols and variables explained
V
Volume of the solid or enclosed space.
A
Base area or cross-sectional area.
h
Height, depth, or extrusion length depending on shape.
ρ
Density, used with volume to estimate mass.
FAQ
Volume Formula Sheet questions
How do I use this formula sheet?
Find the shape or identity, confirm each variable definition, keep units consistent, then substitute values into the formula.
Are these formulas exact?
The basic geometry formulas are exact for ideal shapes. Rows marked approximate depend on simplified geometry, thin-wall assumptions, or ignoring radii and fillets.
Can I use these formulas for final engineering design?
Use them as calculation references. Final design should also check loads, materials, tolerances, safety factors, and any governing standards.
Related
Engineering formula sheets
Cross-Section Formula Sheet
Cross-sectional area formulas for common shapes.
Second Moment of Area Formula Sheet
Second moment of area formulas for common sections.
Surface Area Formula Sheet
Surface area formulas for common 3D shapes.
Trigonometric Identities Formula Sheet
Common trigonometric identities for engineering math.