How to Calculate Volume (3D Shapes & Practical Uses)

Volume measures how much three-dimensional space an object occupies. You need it when ordering concrete for a slab, filling a raised garden bed with soil, sizing a water tank, figuring out how much mulch to buy, or determining whether your luggage fits airline size limits.

This guide covers volume formulas for every common 3D shape, unit conversions between systems, the water displacement method for irregular objects, and practical worked examples. For instant calculations, try our Free Volume Calculator.

Cube

A cube has six identical square faces. Think of dice, storage cubes, and shipping boxes with equal dimensions.

Formula:

$V = s^3$

Where s is the length of one side.

Example: A storage cube measures 2 feet on each side.

• Volume = 2 x 2 x 2 = 8 cu ft

Rectangular Prism (Box)

This is the most common volume calculation. Shipping boxes, rooms, swimming pools, raised beds, and concrete slabs are all rectangular prisms.

Formula:

$V = length \times width \times height$

Example: A raised garden bed is 8 feet long, 4 feet wide, and 1.5 feet deep. How much soil do you need?

• Volume = 8 x 4 x 1.5 = 48 cu ft
• One bag of soil is typically 1.5 cu ft, so you need 48 / 1.5 = 32 bags

Example: A concrete slab for a shed pad is 12 ft x 10 ft x 4 inches (0.333 ft).

• Volume = 12 x 10 x 0.333 = 40 cu ft
• Convert to cubic yards: 40 / 27 = 1.48 cu yd (order 1.5 cu yd to be safe)

Cylinder

Cylinders include pipes, water tanks, round columns, cans, silos, and hot tubs.

Formula:

$V = \pi r^2 h$

Where r is the radius and h is the height (or length, if the cylinder is on its side).

Example: A cylindrical water tank has a diameter of 4 feet and a height of 6 feet. How many gallons does it hold?

• Radius = 4 / 2 = 2 feet
• Volume = 3.14159 x 2 x 2 x 6 = 75.40 cu ft
• Convert to gallons: 75.40 x 7.48 = 563.99 gallons

Example: A concrete column (sonotube) has a 12-inch diameter and is 4 feet tall.

• Radius = 6 inches = 0.5 feet
• Volume = 3.14159 x 0.5 x 0.5 x 4 = 3.14 cu ft
• For 8 columns: 3.14 x 8 = 25.13 cu ft = 0.93 cu yd

Sphere

Spheres apply to basketballs, globes, water droplets, and dome calculations.

Formula:

$V = \frac{4}{3} \pi r^3$

Example: A decorative garden sphere has a diameter of 18 inches. What is its volume?

• Radius = 9 inches
• Volume = (4/3) x 3.14159 x 9 x 9 x 9 = 3,053.63 cu in
• Convert to cu ft: 3,053.63 / 1,728 = 1.77 cu ft

Hemisphere (half sphere):

$V = \frac{2}{3} \pi r^3$

A dome-shaped planter with a 2-foot diameter: V = (2/3) x 3.14159 x 1 x 1 x 1 = 2.09 cu ft

Cone

Cones appear in funnels, piles of gravel or sand, Christmas trees, and traffic cones.

Formula:

$V = \frac{1}{3} \pi r^2 h$

A cone has exactly one-third the volume of a cylinder with the same base and height.

Example: A conical pile of gravel has a base diameter of 10 feet and a height of 6 feet. How many cubic yards is that?

• Radius = 5 feet
• Volume = (1/3) x 3.14159 x 5 x 5 x 6 = 157.08 cu ft
• Convert: 157.08 / 27 = 5.82 cu yd

Pyramid

Pyramids with a rectangular base appear in roofing (hip roofs), architectural features, and storage hoppers.

Formula (rectangular base):

$V = \frac{1}{3} \times base\ area \times height$

$V = \frac{1}{3} \times l \times w \times h$

Example: A hopper has a rectangular opening of 4 ft x 3 ft and tapers to a point 5 feet below.

• Volume = (1/3) x 4 x 3 x 5 = 20 cu ft

Triangular Prism

Triangular prisms show up in A-frame structures, tent volumes, and wedge-shaped containers.

Formula:

$V = \frac{1}{2} \times base \times height_{triangle} \times length$

Example: An A-frame attic space has a triangular cross-section with a base of 12 feet, a peak height of 6 feet, and runs 25 feet long.

• Cross-section area = 0.5 x 12 x 6 = 36 sq ft
• Volume = 36 x 25 = 900 cu ft

The Displacement Method (Irregular Objects)

Not every object has a clean geometric shape. Rocks, engine parts, sculptures, and organic forms require a different approach.

How it works:

1. Fill a container with water and mark the level.
2. Submerge the object completely.
3. Mark the new water level.
4. The volume of water displaced equals the volume of the object.

For small objects: Use a graduated cylinder or measuring cup. If the water rises from 500 mL to 735 mL, the object’s volume is 235 mL (or 235 cu cm, since 1 mL = 1 cu cm).

For large objects: Use a rectangular container. Measure the rise in water level and multiply by the container’s length and width.

Example: You drop a rock into a rectangular aquarium (24 in x 12 in). The water rises by 0.5 inches.

• Displaced volume = 24 x 12 x 0.5 = 144 cu in

This method dates back to Archimedes, who reportedly used it to detect whether a crown was pure gold by comparing its displaced volume to a gold bar of the same weight.

Unit Conversions

Projects in different countries or industries use different units. Here are the conversions that matter most:

From	To	Multiply By
cu ft	cu m	0.02832
cu m	cu ft	35.315
cu ft	gallons (US)	7.48
gallons (US)	cu ft	0.1337
cu ft	liters	28.317
cu ft	cu yd	0.03704 (or divide by 27)
cu yd	cu ft	27
cu in	cu ft	0.000579 (or divide by 1,728)
liters	cu m	0.001
mL	cu cm	1 (exact)

Example: A pool holds 450 cu ft of water. How many gallons is that?

• 450 x 7.48 = 3,366 gallons

Example: You need 2.5 cu m of topsoil. How many cu ft is that?

• 2.5 x 35.315 = 88.29 cu ft

Practical Applications

Concrete: Measure length, width, and thickness of the slab in feet. Multiply for cubic feet. Divide by 27 for cubic yards. Concrete trucks deliver in cubic yard increments, so round up. Order 5-10% extra for spillage and uneven subgrade.

Aquariums: Multiply length x width x height in inches, then divide by 231 to get US gallons. A 48 x 12 x 18 inch tank holds (48 x 12 x 18) / 231 = 44.9 gallons. This tells you the filter size, heater wattage, and fish stocking capacity you need.

Mulch and Gravel: Measure the bed area in square feet, decide on depth (usually 2-4 inches for mulch, 3-6 inches for gravel), and multiply. A 200 sq ft bed at 3 inches deep: 200 x 0.25 ft = 50 cu ft. Bags typically contain 2 cu ft, so you need 25 bags.

Shipping and Storage: Multiply the outer dimensions of the box in inches to get cubic inches. Divide by 1,728 for cubic feet. Shipping companies use “dimensional weight” which compares this volume to actual weight and charges whichever is greater.

Swimming Pools: For rectangular pools, use length x width x average depth. Average depth = (shallow end + deep end) / 2. A 30 x 15 ft pool with depths of 3 ft and 8 ft: average depth = 5.5 ft, volume = 30 x 15 x 5.5 = 2,475 cu ft = 18,513 gallons.

Skip the Math

Our Volume Calculator supports cubes, cylinders, spheres, cones, pyramids, and more. Enter your dimensions, pick the shape, and get the volume in multiple units instantly.

Frequently Asked Questions

What is the difference between volume and capacity?

Volume describes the space an object occupies. Capacity describes how much a container can hold. They measure the same thing in different contexts. A box has a volume of 2 cu ft. A bottle has a capacity of 750 mL. In practice, the terms are interchangeable for containers, but “capacity” typically implies the container holds liquid or granular material.

How do I convert cubic feet to cubic yards for concrete?

Divide cubic feet by 27. One cubic yard equals 3 ft x 3 ft x 3 ft = 27 cu ft. If your slab requires 81 cu ft, that equals 81 / 27 = 3 cu yd. Always round up because concrete trucks can’t deliver partial fractions, and running short mid-pour is far worse than having a little extra.

Why does my pool volume calculation not match reality?

Pool shapes rarely match perfect geometric formulas. Curved walls, graduated slopes, benches, steps, and uneven depths all reduce the actual volume below the theoretical calculation. Subtract about 5-10% from your calculated volume for a more accurate estimate. For kidney-shaped or freeform pools, use the 0.45 constant: length x width x average depth x 0.45 x 7.48 for gallons.

How many bags of mulch do I need?

Measure your bed area in square feet, decide on a depth (3 inches is standard), and multiply: area x depth in feet. A 150 sq ft bed at 3 inches: 150 x 0.25 = 37.5 cu ft. If bags hold 2 cu ft each, you need 37.5 / 2 = 19 bags (round up to 20). Bulk delivery by the cubic yard is cheaper for areas over 300 sq ft.

Can I add volumes of different shapes together?

Yes. If a structure has a cylindrical base topped with a cone (like a silo with a pointed roof), calculate each shape’s volume separately and add them. A 10-ft diameter, 20-ft tall cylinder topped with a 5-ft tall cone: cylinder = 3.14159 x 25 x 20 = 1,570.80 cu ft, cone = (1/3) x 3.14159 x 25 x 5 = 130.90 cu ft, total = 1,701.70 cu ft.