What is the formula for the volume of a cylinder?

The volume of a cylinder is V = π × r² × h, where r is the radius of the circular base and h is the height. If you know the diameter instead of the radius, divide the diameter by 2 to get the radius first. For example, a cylinder with a 3-foot radius and 5-foot height has a volume of π × 9 × 5 ≈ 141.37 cubic feet.

How do I find the volume of a cylinder with the diameter?

When you know the diameter, use V = π × (d/2)² × h, or equivalently V = (π × d² × h) / 4. Simply enter the diameter in the calculator and select "Use Diameter" — the tool divides by 2 automatically before computing. For a cylinder with a 10-inch diameter and 12-inch height, the volume is π × 25 × 12 ≈ 942.48 in³.

What is the surface area of a cylinder?

A cylinder has three surface components: two circular bases (each with area π × r²) and one lateral (side) surface that unrolls into a rectangle with area 2π × r × h. Total surface area = 2πr² + 2πrh. Lateral surface area alone = 2πrh, which is useful when calculating the material needed to wrap the side of a tank or pipe without the top and bottom caps.

What is the difference between radius and diameter in cylinder calculations?

The radius is the distance from the center of the circular base to its edge, while the diameter is the full width across the circle — exactly twice the radius. Because the volume formula uses r², using the diameter directly (without halving it first) would give a result 4× too large. Most engineering drawings specify diameter, while most math formulas use radius, so it is important to know which you have.

What are real-world uses for cylinder volume calculations?

Cylinder volume calculations are used whenever you need to know how much a round container holds. Common examples include water tanks and pressure vessels (industrial and residential), grain silos and oil drums, concrete columns and piers, pipes and culverts (to find flow capacity or fill volume), and food cans (to check net volume or fill levels). Engineers also use surface area to estimate paint, insulation, or wrapping material needed for cylindrical objects.

How many gallons are in a cylinder?

One cubic foot holds approximately 7.48 US gallons. Multiply the cylinder's volume in cubic feet by 7.48 to convert. For example, a cylinder 2 feet in radius and 4 feet tall has a volume of π × 4 × 4 ≈ 50.27 ft³, which equals about 376 gallons. This is particularly useful for sizing rain barrels, above-ground pools, and storage tanks.

What is the volume of a hollow cylinder (pipe or tube)?

To find the volume of a hollow cylinder (like a pipe or tube), subtract the volume of the inner cylinder from the outer: V = π × h × (R² − r²), where R is the outer radius and r is the inner radius. For a steel pipe 10 feet long with outer diameter 4 inches (R = 2 in) and inner diameter 3.5 inches (r = 1.75 in): V = π × 120 × (4 − 3.0625) ≈ 355 cubic inches. This calculation is used in plumbing for pipe capacity, material quantity for manufacturing, and flow rate calculations.

How does cylinder volume relate to cone and sphere volume?

A classic result from geometry: a cylinder, a cone, and a hemisphere with the same radius and height have volumes in the ratio 3:1:2. Specifically, a cone has exactly 1/3 the volume of a cylinder with the same base and height (V = ⅓πr²h), and a sphere has 2/3 the volume of the circumscribed cylinder (V = 4/3πr³ for the sphere). Archimedes discovered this relationship for the sphere and considered it his greatest achievement — it is engraved on his tombstone as a sphere inscribed in a cylinder.

Cylinder Volume Calculator — Volume & Surface Area

Calculates cylinder volume in cubic feet, liters, and gallons, plus lateral and total surface area.

How to Use This Cylinder Volume Calculator

This cylinder volume calculator returns the volume in cubic feet, cubic yards, cubic meters, liters, and US gallons, plus lateral surface area, base area, and total surface area. Enter the radius (or diameter) and the height, then select the units for each dimension. Toggle between "Use Radius" and "Use Diameter" at the top depending on which measurement you have. All inputs support inches, feet, yards, meters, and centimeters — no manual conversion needed.

For volume in cubic feet specifically, you can also try our cubic feet calculator, which covers rectangular, cylindrical, and other shapes in one tool. For the area of the triangular cross-sections or slanted cuts in geometry problems, see our triangle area calculator.

Cylinder Volume Formula (V = πr²h)

The standard formula for cylinder volume is:

V = π × r² × h

Where r is the radius of the circular base and h is the height (or length) of the cylinder. If you know the diameter d, substitute r = d / 2, giving:

V = π × (d/2)² × h = (π × d² × h) / 4

Step-by-Step Example

Measure the radius (or diameter) of the circular base
Measure the height of the cylinder
Square the radius: r²
Multiply by π (≈ 3.14159) and the height: π × r² × h
Convert to desired volume unit as needed

Example: a cylinder with a 2-foot radius and 5-foot height has volume V = π × 4 × 5 ≈ 62.83 ft³ ≈ 470.00 US gallons.

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Surface Area of a Cylinder

A cylinder has two distinct surface area components:

Lateral surface area — the curved side, equal to 2πrh. Imagine unrolling it into a flat rectangle of width 2πr (the circumference) and height h.
Base area — each circular end has area πr². A closed cylinder has two bases, adding 2πr² to the total.
Total surface area — lateral + 2 bases = 2πrh + 2πr².

Surface area is critical for material estimation: coating, painting, or insulating a cylindrical tank requires knowing the lateral area; fabricating end caps requires knowing the base area. An open-top cylinder (like a bucket) needs only lateral area plus one base.

Surface Area Example

A cylinder with r = 1.5 ft and h = 4 ft has lateral area = 2 × π × 1.5 × 4 ≈ 37.70 ft², base area ≈ 7.07 ft², and total surface area ≈ 51.84 ft².

Converting Cylinder Volume to Gallons and Liters

Once you have the volume in cubic feet, convert to other units using these factors:

1 ft³ = 7.4805 US gallons
1 ft³ = 28.3168 liters
1 ft³ = 0.0283168 m³
1 ft³ = 1,728 in³
1 ft³ = 0.037037 yd³

For construction projects involving cylindrical piers or columns, the concrete slab calculator handles rectangular pours, while this calculator covers any round form. Knowing gallons is particularly useful for sizing pumps, storage tanks, and cisterns.

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Common Cylinder Volume Applications

Cylinder volume calculations appear across many fields:

Tanks and cisterns — size a water storage tank or rain barrel for a given capacity
Pipes and ducts — calculate fill volume or flow capacity for a length of pipe
Concrete columns — estimate ready-mix or bag concrete needed for a cylindrical pour
Cooking and food science — find the volume of cylindrical pots, cans, or mixing vessels
Industrial drums — verify capacity (a standard 55-gallon drum is about 22.5 in diameter × 33.5 in tall)
Pool and spa calculations — above-ground round pools are essentially short, wide cylinders

Sources & References

Volume of a Cylinder — Math Is Fun — Math Is Fun
Volume — Khan Academy — Khan Academy

Cylinder Volume Calculator