How do I find the volume of an irregular shape?

For complex shapes, decompose them into simpler shapes and sum the volumes. Example: an L-shaped room is two rectangles. A shed with a pitched roof is a rectangle plus a triangular prism. For truly irregular shapes, water displacement is the practical method: submerge the object in a known volume of water and measure the volume increase (Archimedes' principle).

How many gallons are in a cubic foot?

One cubic foot = 7.4805 US gallons. Equivalently, one gallon = 0.1337 cubic feet = 231 cubic inches = 3.785 liters. This conversion is essential for pool volume (in gallons for chemical dosing), tank sizing, and any fluid containment calculation.

What is the formula for cylinder volume?

V = π × r² × h, where r is the radius and h is the height. Equivalently, V = π × (d/2)² × h where d is the diameter. Example: a cylinder 10 cm diameter and 20 cm tall: V = π × 5² × 20 = 1,570.8 cm³ = 1.571 liters. Common error: using diameter instead of radius — always halve the diameter first.

How do I calculate the volume of a cone vs a cylinder?

A cone with the same base and height as a cylinder holds exactly 1/3 the volume. Cylinder: π × r² × h. Cone: (1/3) × π × r² × h. This is a fundamental geometric relationship — a cylinder can be filled exactly three times with a same-dimension cone. The same 1/3 relationship holds for pyramids vs rectangular prisms.

📐Math Tools

How Much Does This Shape Hold? Volume Calculator

How much does this shape hold?

What This Does

Volume measures the three-dimensional space enclosed by a shape — how much liquid it can hold, how much material it contains, or how much space it occupies. Whether you're calculating how much concrete to order, how many gallons a fish tank holds, the volume of a shipping box, or solving a geometry problem, the formula depends on the shape. The most common volumes: a rectangular box (length × width × height), a cylinder (π × radius² × height), a sphere (4/3 × π × radius³), a cone (1/3 × π × radius² × height), a pyramid (1/3 × base area × height), and a triangular prism (0.5 × base × height × length). Each shape has a distinct formula, and mixing up formulas is the most common source of calculation errors. Unit conversion is frequently necessary in practice — you might measure dimensions in inches but need the result in cubic feet, gallons, or liters. This calculator accepts dimensions in any unit, converts automatically, and displays results across multiple unit systems simultaneously: cubic inches, cubic feet, cubic yards, cubic centimeters, cubic meters, US gallons, US quarts, and liters. Practical applications: aquarium volume in gallons, swimming pool volume for chemical dosing, concrete volume for construction, capacity of storage tanks and containers, shipping box volume for logistics, and geometric problems in education.

When Should You Use This?

→Calculating aquarium or fish tank volume in gallons to dose chemicals correctly
→Finding concrete, mulch, or fill volume for construction and landscaping
→Measuring container capacity for storage, shipping, or manufacturing
→Converting between cubic units (cubic feet to gallons, liters to cubic inches)
→Solving geometry homework or exam problems involving 3D shapes
→Estimating swimming pool or hot tub volume for maintenance chemicals

Example Scenario

Tom has a cylindrical rain barrel: 24 inches diameter, 36 inches tall. Radius = 12 inches. Volume = π × 12² × 36 = π × 144 × 36 = 16,286 cubic inches = 9.43 cubic feet = 70.5 gallons. He can now calculate how many days of garden watering this provides and what size pump he needs to empty it.

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Volume Calculator

9 shapes · instant multi-unit conversion · real-world comparisons

Calculate the volume of any 3D shape and instantly convert to liters, gallons, cubic feet, or any other unit. Compare shapes, model scaling scenarios, and download your results.

Select Shape

Formula: V = L × W × H

A box with six rectangular faces. The most common shape in everyday life — shipping boxes, rooms, containers.

Unit:

Length (in)

Width (in)

Height (in)

About the Volume Calculator

Volume is the measure of how much three-dimensional space an object occupies. Whether you're sizing a fish tank, calculating how much concrete to pour, estimating the capacity of a storage container, or solving a math problem, volume calculation is one of the most practical real-world skills in geometry.

This calculator supports 9 of the most common 3D shapes — from simple boxes and cylinders to more complex ellipsoids and toruses — and converts the result into 11 different units instantly. You can enter measurements in any linear unit (inches, feet, centimeters, meters, millimeters, or yards) and receive output in every volume unit simultaneously.

The scenarios tab shows how volume scales with dimension changes, which is particularly useful for engineering and design work. Because volume scales cubically, doubling all dimensions of an object produces 8 times the volume — a counterintuitive result that has major practical implications for tank sizing, shipping, and construction planning.

How Volume Calculation Works

Each shape has a unique geometric formula. For a rectangular box, volume is simply length × width × height. For curved shapes like spheres and cylinders, the constant π (pi, approximately 3.14159) appears in the formula. A cylinder's volume equals πr²h — the area of the circular cross-section multiplied by the height. A sphere's volume is ⁴⁄₃πr³. The calculator applies the appropriate formula for each shape, converts your input dimensions to a common base unit (cubic centimeters), then converts to all output units simultaneously.

Example: Sizing a Cylindrical Water Tank

Suppose you need a cylindrical tank with a radius of 2 feet and a height of 4 feet. Using V = πr²h: V = 3.14159 × (2)² × 4 = 3.14159 × 4 × 4 = 50.27 cubic feet. That equals about 376 US gallons or 1,423 liters. If you double the radius to 4 feet (keeping height at 4 feet), the volume becomes 201 cubic feet — nearly 4× as much, because radius is squared in the formula.

Common Mistakes to Avoid

Mixing units: All dimensions must be in the same unit. Don't mix feet and inches.
Diameter vs. radius: The formulas for cylinders, spheres, and cones use radius (half the diameter). If you measure the full width, divide by 2 first.
Triangular prism height: The formula requires the height of the triangular cross-section, not the prism's length.
Torus confusion: The torus (donut shape) has a major radius R (center to center of tube) and a minor radius r (tube thickness). These are distinct measurements.

Frequently Asked Questions

How do I convert cubic feet to gallons?

One cubic foot equals approximately 7.48 US gallons. Multiply your cubic feet value by 7.48 to get US gallons, or by 6.23 for UK imperial gallons. This is useful for sizing water heaters, tanks, and plumbing. Our calculator performs this conversion automatically.

What's the difference between volume and capacity?

Volume refers to the amount of 3D space an object occupies, while capacity is the amount a container can hold. In practice, for a solid object the two are equal. For containers, capacity may be slightly less than geometric volume because of wall thickness. This calculator computes the geometric volume.

Why does volume change so dramatically when I scale dimensions?

Volume scales as the cube (third power) of linear dimensions. If you double all dimensions of a shape, the volume becomes 2³ = 8 times larger. This cubic relationship means small errors in measurements produce large errors in volume — a 10% error in each dimension leads to a 33% error in volume. The Scenarios tab demonstrates this scaling.

How do I calculate the volume of an irregular shape?

For irregular objects, the water displacement method works well: submerge the object in a known volume of water and measure how much the water level rises. The rise in water level times the container's cross-sectional area equals the object's volume. For digital models, CAD software computes volume directly.

What units should I use for construction projects?

In the US, concrete and fill material is typically ordered in cubic yards. One cubic yard equals 27 cubic feet or 0.765 cubic meters. Enter your dimensions in feet and read the cubic yards output. Most ready-mix concrete suppliers quote by the cubic yard.

How do I use this for aquarium or tank sizing?

For rectangular aquariums, enter length × width × height in inches and read the US gallons result. A standard 55-gallon tank is approximately 48 × 13 × 20 inches (this calculator gives 54.9 gallons from those dimensions). For rounded tanks, use the cylinder or ellipsoid shape. Note that substrate and decorations reduce actual water volume by 10–20%.

Results are for informational purposes only.