What is the simplest cubic feet formula?

For a rectangular box: V = L × W × H, with all three measurements in feet. Multiply length, width, and height to get cubic feet.

Why is the cylinder formula π × r² × h?

A cylinder is a stack of identical circles. The area of one circle is π × r². Multiplying that area by the height gives the total volume.

Is the sphere formula always (4/3) × π × r³?

Yes. The radius is half the diameter, π is 3.14159, and the (4/3) coefficient comes from integrating circular cross-sections from one pole to the other.

How do I handle a half-sphere or hemisphere?

Calculate a full sphere with the formula above and divide by two: V = (2/3) × π × r³. This is useful for dome ceilings or domed tank tops.

What is the formula for a frustum (truncated cone)?

V = (1/3) × π × h × (R² + r² + R × r), where R is the larger radius, r is the smaller radius, and h is the height between them. This shape applies to lampshades, paper cups, and some hoppers.

Cubic Feet Formulas

Every cubic feet formula you will need, in one place. Pick the shape, plug in feet, and read the answer in cubic feet (ft³). The bottom of the page covers unit conversions and material weight factors.

Note

All formulas assume measurements are already in feet. If yours are in inches, divide by 12 first. For metric units, multiply meters by 3.28084 or centimeters by 0.0328084 to convert to feet.

Shape formulas

Rectangular cuboid (box, room, container)

Cuboid volume

V = L × W × H

Where L is length, W is width, and H is height — all in feet. Example: a closet 4 ft × 2.5 ft × 8 ft has a volume of 80 ft³.

Cube (all sides equal)

Cube volume

V = s³

= A 2 ft cube = 8 ft³

Cylinder (tank, pipe, drum)

Cylinder volume

V = π × r² × h

π is 3.14159, r is the radius (half the diameter) in feet, h is the height in feet. A drum with a 1 ft radius and 3 ft height holds 9.42 ft³.

Hollow cylinder (pipe wall)

Annular volume

V = π × (R² − r²) × h

R is the outer radius, r is the inner radius. Useful for sleeving and pipe-wall material.

Sphere

Sphere volume

V = (4/3) × π × r³

A basketball with a 0.4 ft radius holds 0.268 ft³ of air.

Hemisphere

Half-sphere volume

V = (2/3) × π × r³

Cone

Cone volume

V = (1/3) × π × r² × h

The (1/3) factor is exact — a cone is one-third the volume of a cylinder with the same radius and height.

Frustum (truncated cone)

Frustum volume

V = (1/3) × π × h × (R² + r² + R × r)

Triangular prism

Triangular prism volume

V = ½ × b × h_t × L

b is the triangle base, h_t is the triangle height (perpendicular to the base), L is the prism length.

Square pyramid

Pyramid volume

V = (1/3) × b² × h

Capsule (cylinder with two hemisphere ends)

Capsule volume

V = π × r² × (h + (4/3) × r)

Trapezoidal prism

Trapezoidal prism volume

V = ½ × (a + b) × h × L

a and b are the two parallel sides of the trapezoid cross-section, h is the trapezoid height, L is the prism length.

Irregular shapes

For any shape that is not in this list, divide it into simpler pieces (rectangular cuboids, cylinders, triangular prisms), calculate each one, and add the cubic feet together. Our irregular shape calculator automates this.

Length unit conversions

Get all measurements into feet first
Convert to feet	Conversion factor	Worked example
Inches → feet	÷ 12	36 in ÷ 12 = 3 ft
Yards → feet	× 3	4 yd × 3 = 12 ft
Centimeters → feet	× 0.0328084	100 cm × 0.0328084 = 3.28 ft
Meters → feet	× 3.28084	2 m × 3.28084 = 6.56 ft
Millimeters → feet	× 0.00328084	500 mm × 0.00328084 = 1.64 ft

Volume unit conversions

Convert cubic feet to other volume units
From cubic feet	Conversion factor	Worked example
Cubic inches	× 1,728	1 ft³ = 1,728 in³
Cubic yards	÷ 27	27 ft³ = 1 yd³
Cubic meters	× 0.0283168	100 ft³ = 2.832 m³
Liters	× 28.3168	1 ft³ = 28.32 L
US gallons	× 7.48052	1 ft³ = 7.48 gal
UK gallons	× 6.2288	1 ft³ = 6.23 imp gal
US quarts	× 29.9221	1 ft³ = 29.92 qt
Board feet	× 12	1 ft³ = 12 board ft
Acre-feet	÷ 43,560	43,560 ft³ = 1 ac-ft
Bushels (US)	× 0.8036	10 ft³ = 8.04 bushels

Material weight from cubic feet

Multiply your cubic feet by the average density (in pounds per cubic foot) to get total weight. Densities vary by moisture content and packing, so treat these as planning numbers.

Pounds per cubic foot for common materials
Material	Conversion factor	Worked example
Water	× 62.43	10 ft³ × 62.43 = 624.3 lb
Concrete (cured)	× 150	5 ft³ × 150 = 750 lb
Topsoil (loose)	× 75	4 ft³ × 75 = 300 lb
Mulch (bark)	× 18	20 ft³ × 18 = 360 lb
Gravel	× 105	8 ft³ × 105 = 840 lb
Dry sand	× 100	6 ft³ × 100 = 600 lb
Oak (seasoned)	× 47	3 ft³ × 47 = 141 lb
Pine (dry)	× 30	3 ft³ × 30 = 90 lb

Project-specific formulas

Concrete bag yield

Bagged concrete

80 lb bag = 0.6 ft³ • 60 lb bag = 0.45 ft³ • 40 lb bag = 0.30 ft³

Divide your cubic feet total by the yield per bag to get the bag count.

Sauna heater sizing

Sauna heater

kW = ft³ × 0.04

For a 200 ft³ sauna, 200 × 0.04 = 8 kW.

HVAC airflow

Required CFM

CFM = (room ft³ × air changes per hour) ÷ 60

Pool gallons

US gallons

Gallons = ft³ × 7.48052

Subwoofer net internal volume

Sub box

Net ft³ = External ft³ − driver displacement − port volume − bracing

Quick reference card

1 ft³ = 1,728 in³ = 0.0283 m³ = 28.32 L = 7.48 US gal
1 yd³ = 27 ft³ = 0.7646 m³ = 202 US gal
1 m³ = 35.3147 ft³ = 1,000 L = 264 US gal
1 acre-foot = 43,560 ft³ = 325,851 US gal
1 bushel (US) = 1.2445 ft³