Volume Formulas for Cubic Feet
Reference card for every common 3D shape. Plug in dimensions in feet to get cubic feet directly.
Choosing the Right Formula
Match your object to the closest regular shape, measure in feet, then apply that shape's formula. Boxes and rooms use length × width × height. Round objects — pipes, tanks, tree wells, planting holes — use the cylinder or cone formula depending on whether the sides are straight or taper to a point. Balls, domes and rounded tanks use the sphere formula. Roof trusses, wedges and some concrete footings use the triangular prism formula. Anything that doesn't match a single shape — an L-shaped room, a garage with a bump-out — gets split into two or more regular shapes, calculated separately, then added together. The main cubic feet calculator handles the box case directly; use the cylinder calculator for round shapes.
Rectangular Box
V = L × W × H
Example: 6 × 4 × 3 ft = 72 ft³.
Cylinder
V = π × r² × h
Example: r = 1.5 ft, h = 4 ft. V = 3.14159 × 2.25 × 4 = 28.27 ft³.
Cone
V = (1/3) × π × r² × h
Example: r = 2 ft, h = 5 ft. V = (1/3) × 3.14159 × 4 × 5 = 20.94 ft³.
Sphere
V = (4/3) × π × r³
Example: r = 2 ft. V = (4/3) × 3.14159 × 8 = 33.51 ft³.
Triangular Prism
V = (1/2 × base × height of triangle) × length of prism
Example: triangle base 3 ft, triangle height 2 ft, prism length 6 ft. V = (1/2 × 3 × 2) × 6 = 18 ft³.
L-Shape
Split into two rectangular sections, calculate each separately, then add.
Example: Rectangle A = 10 × 6 × 8 = 480 ft³. Rectangle B = 4 × 5 × 8 = 160 ft³. Total = 640 ft³.
Applying These Formulas to Real Projects
These six formulas cover nearly every shape encountered in construction, landscaping and shipping. A cylindrical fence post hole, a grain bin or a water tank uses the cylinder formula. A conical pile of gravel or mulch dumped from a truck uses the cone formula — the volume is one-third of a cylinder with the same base and height, which is why loose material piles hold less than they look like they should. A sphere formula applies to a decorative water feature or a round planter. For everyday landscaping quantities, the dedicated soil, mulch and gravel calculators already build the box formula in with material-specific defaults, so you don't need to do the multiplication by hand.
Frequently Asked Questions
What's the volume of a box?
Length × width × height. Use the same unit for all three.
What's the volume of a cylinder?
π × r² × h.
What's the volume of a cone?
(1/3) × π × r² × h — one-third the volume of a cylinder with the same base and height.
What's the volume of a sphere?
(4/3) × π × r³.
What's the volume of a triangular prism?
(1/2 × base × height of triangle) × length of prism.
How do I calculate volume of an L-shape?
Split into two rectangles, calculate each volume, then add the totals.
Why use π for round shapes?
π (≈3.14159) is the ratio of a circle's circumference to its diameter. It appears in any volume formula involving a circular cross-section.
What's the difference between r and r²?
r is the radius; r² is the radius squared (r × r). The squared term reflects the area of the circular base.