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Volume Calculator

Calculate the volume of various 3D shapes using precise mathematical formulas.

Cube Volume Calculator

Volume

What Is a Volume Calculator?

A Volume Calculator helps you find how much three-dimensional space a solid shape contains or occupies. It is useful for geometry, construction, containers, tanks, storage, shipping, liquids, and material estimates.

Volume is measured in cubic units. If length, width, and height are in feet, the result is cubic feet. If the dimensions are in centimeters, the result is cubic centimeters.

Meaning

What Is Volume?

Volume measures 3D space. A box, cylinder, sphere, cone, pyramid, capsule, or ellipsoid can all have volume because each has depth as well as length and width.

Simple box example

V=length×width×heightV=\text{length}\times\text{width}\times\text{height}

Example: a box that is 10 feet long, 5 feet wide, and 4 feet high has a volume of 200 ft^3.

Calculator Uses

What This Volume Calculator Can Do

The calculator covers common solids and keeps the calculation transparent with formulas and steps.

Common 3D solids
Calculate volume for cubes, rectangular boxes, cylinders, cones, spheres, hemispheres, pyramids, capsules, and ellipsoids.
Formula breakdown
See the formula and the substituted values used to produce the result.
Cubic unit answer
The final answer is shown in cubic units because volume measures three-dimensional space.
Practical measurement
Use it for containers, tanks, rooms, shipping boxes, storage, concrete, liquids, and geometry work.

The Math

Common Volume Formulas

Choose the formula that matches the selected 3D shape.

SolidFormulaHow to read it
CubeV=s3V=s^3s is the length of one edge.
Rectangular boxV=lwhV=lwhLength times width times height.
CylinderV=πr2hV=\pi r^2hCircular base area times height.
ConeV=13πr2hV=\frac{1}{3}\pi r^2hOne-third of a cylinder with the same base and height.
SphereV=43πr3V=\frac{4}{3}\pi r^3Uses radius from center to surface.
HemisphereV=23πr3V=\frac{2}{3}\pi r^3Half of a sphere.
PyramidV=Bh3V=\frac{Bh}{3}B is base area and h is vertical height.
CapsuleV=πr2h+43πr3V=\pi r^2h+\frac{4}{3}\pi r^3Cylinder volume plus sphere volume.
EllipsoidV=43πabcV=\frac{4}{3}\pi abca, b, and c are the three radii.

How to Use

How to Use This Volume Calculator

Select the solid, enter the dimensions, calculate, then review the cubic-unit result.

  1. 1

    Select a solid

    Choose cube, box, cylinder, cone, sphere, hemisphere, pyramid, capsule, or ellipsoid.

  2. 2

    Enter dimensions

    Use the same unit for every value in the same calculation.

  3. 3

    Calculate volume

    Click Calculate Volume to get the final cubic-unit answer.

  4. 4

    Review the steps

    Check the formula breakdown to make sure radius, height, and units are correct.

Units

Cubic Units and Liquid Conversions

Some volume answers are easier to understand when converted into liquid units.

VolumeEquivalent
1 cubic foot7.48052 gallons
1 cubic inch0.004329 gallons
1 cubic meter1000 liters
1 liter1000 cubic centimeters
1 gallon3.78541 liters
Example: 10 cubic feet is about 74.8052 gallons because 1 cubic foot is 7.48052 gallons.

Common Mistakes

Volume Calculation Mistakes to Avoid

Most volume mistakes come from confusing area with volume, diameter with radius, or slanted height with vertical height.

Mixing units
Do not combine meters, centimeters, inches, and feet in one formula unless you convert them first.
Using diameter instead of radius
Round-shape formulas use radius. If you only know the diameter, divide it by 2 first.
Using slant height
For cones and pyramids, use the true vertical height, not the slanted side.
Forgetting cubic units
Area is square units, but volume is cubic units such as ft^3, m^3, or cm^3.

Use Cases

Where Volume Calculations Are Used

Volume is a practical measurement for capacity, materials, storage, and shape analysis.

Use caseWhy volume matters
Shipping and packagingEstimate box or container capacity.
ConstructionMeasure concrete, gravel, fill, rooms, and material volume.
Tanks and liquidsEstimate how much a tank or rounded container can hold.
Engineering and designSize solids, parts, capsules, and curved forms.
School geometryPractice volume formulas and check exact steps.
Geometry Help

Frequently Asked Questions

A volume calculator finds how much three-dimensional space is inside or occupied by a solid shape.

Cube volume is side cubed.

Rectangular box volume is length times width times height.

Cylinder volume is pi times radius squared times height.

Cone volume is one-third times pi times radius squared times height.

Sphere volume is four-thirds times pi times radius cubed.

Pyramid volume is base area times height divided by 3.

Volume is measured in cubic units, such as cubic inches, cubic feet, cubic centimeters, cubic meters, liters, or gallons.

No. Area measures flat 2D space in square units, while volume measures 3D space in cubic units.

For round shapes, first convert diameter to radius by dividing by 2. Then use the correct volume formula.

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