What is the relationship between volume and capacity?

Volume is the 3D space a shape occupies (in cubic units like m^3 or ft^3). Capacity is the amount it holds, often in fluid units (liters, gallons). They are the same measurement: 1 liter = 1 cubic decimeter (dm^3) = 1,000 cm^3. 1 US gallon = 231 in^3 = 3.785 liters.

Why is a cone volume one-third of a cylinder?

Archimedes proved this geometrically: any cone fits exactly one-third of the volume of its enclosing cylinder (same base and height). Similarly, a sphere fits exactly two-thirds of its enclosing cylinder. These elegant 1/3 and 2/3 ratios arise from calculus integration.

How do I convert cubic feet to gallons?

1 cubic foot = 7.4805 US gallons. So divide cubic feet by 7.4805 to get US gallons, or multiply by 7.4805 to convert gallons to ft^3. For liters: 1 ft^3 = 28.317 liters.

What is displacement in engines?

Engine displacement is the total volume swept by all pistons (cylinder volume x number of cylinders). A 2.0L engine has cylinders with combined swept volume of 2,000 cm^3 = 2 liters. Larger displacement generally means more power potential.

Volume Calculator — Calculover

Shape & Dimensions

Shape

Unit

Volume

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Enter dimensions above

Volume & Surface Area Formulas

Shape	Volume	Surface Area
Cube	`V = s³`	`SA = 6s²`
Rect. Prism	`V = l×w×h`	`SA = 2(lw+lh+wh)`
Sphere	`V = (4/3)πr³`	`SA = 4πr²`
Cylinder	`V = πr²h`	`SA = 2πr²+2πrh`
Cone	`V = (1/3)πr²h`	`SA = πr²+πrl, l=√(r²+h²)`
Pyramid	`V = (1/3)×base×h`	`SA = base + ½×perimeter×slant`
Torus	`V = 2π²Rr²`	`SA = 4π²Rr`
Capsule	`V = πr²(4r/3+h)`	`SA = 2πr(2r+h)`

Volume Converter

Value

From

Converted Volume

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Enter a value to convert

Result

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In Liters

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Select the Shape

Choose from box (rectangular prism), sphere, cylinder, or cone.

Enter the Dimensions

Provide the required measurements: length/width/height for a box, radius for a sphere, radius and height for a cylinder or cone.

Read the Volume

The calculated volume is displayed with unit-cubed notation and a step-by-step solution.

Box Volume

V = l × w × h

Multiply length, width, and height to get the volume of a rectangular prism.

Sphere Volume

V = (4/3)πr³

Four-thirds pi times the radius cubed gives the volume of a sphere.

Cylinder Volume

V = πr²h

Pi times the radius squared times the height gives the volume of a cylinder.

About this calculation · Accuracy & Methodology

Shape	Formula	Variables
Box	l × w × h	length, width, height
Sphere	(4/3)πr³	radius
Cylinder	πr²h	radius, height
Cone	(1/3)πr²h	radius, height
Triangular Prism	½bh × l	base, height, length

Volume The amount of three-dimensional space enclosed by a solid shape, measured in cubic units.

Rectangular Prism A box-shaped solid with six rectangular faces; also called a cuboid.

Sphere A perfectly round solid where every point on the surface is equidistant from the center.

Cylinder A solid with two parallel circular bases connected by a curved surface.

Cone A solid with a circular base that tapers to a single point (apex); its volume is one-third of the corresponding cylinder.

V = 5,184 in³ (3.0 ft³) — a standard large shipping carton

Why Volume Matters

Volume calculations are critical in shipping (box dimensions determine cost), manufacturing (material volume drives raw-material estimates), civil engineering (concrete pours require precise cubic-yard quantities), and medicine (dosage calculations may depend on body volume). Accurate volume computation prevents waste, reduces costs, and ensures structural integrity.

The Cone-Cylinder-Sphere Relationship

A cone, a cylinder, and a sphere all with the same radius and height (where the sphere's diameter equals the height) have a beautiful volume ratio of 1 : 3 : 2. Archimedes considered this relationship one of his greatest discoveries. It means a cone is exactly one-third the volume of the cylinder that encloses it, and a sphere is exactly two-thirds of that cylinder.

What 3D shapes does this calculator support?+

This calculator handles common solid shapes including cubes, rectangular prisms, cylinders, cones, spheres, pyramids, and more. Select your shape and enter the required dimensions for instant volume computation.

How is volume different from surface area?+

Volume measures the three-dimensional space inside a solid (in cubic units), while surface area measures the total area of all outer faces (in square units). Volume tells you capacity; surface area tells you how much material covers the outside.

How do I calculate the volume of a cylinder?+

Multiply pi times the radius squared times the height. A cylinder with radius 3 and height 10 has a volume of about 282.74 cubic units. This formula is widely used for tanks, pipes, and containers.

Can I use this for estimating material quantities?+

Yes, this calculator is practical for estimating concrete volume for footings, soil needed for garden beds, water capacity of tanks, and fill material for any regularly-shaped space. Convert cubic units as needed for purchasing.

What units does the volume calculator use?+

The calculator works with whatever linear units you enter. If you input measurements in feet, the result is in cubic feet; in meters, the result is in cubic meters. Use a unit converter to translate between cubic units if needed.

Volume Calculator

Volume & Surface Area Formulas

How to Use This Calculator

Select the Shape

Enter the Dimensions

Read the Volume

Formula & Methodology

Volume Formulas for Common Solids

Key Terms

Real-World Examples

Shipping Box

Basketball

Volume Calculations in Design and Engineering

Why Volume Matters

The Cone-Cylinder-Sphere Relationship

Frequently Asked Questions

Volume Calculator

Volume & Surface Area Formulas

How to Use This Calculator

Select the Shape

Enter the Dimensions

Read the Volume

Formula & Methodology

Volume Formulas for Common Solids

Key Terms

Real-World Examples

Shipping Box

Basketball

Volume Calculations in Design and Engineering

Why Volume Matters

The Cone-Cylinder-Sphere Relationship

Frequently Asked Questions

Related Calculators

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