Volume Calculator - Cube, Sphere, Cylinder & More | CalcMaster

Free online volume calculator. Calculate the volume of cubes, spheres, cylinders, cones, pyramids, and prisms. Includes surface area calculations.

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Volume Calculator

Free online volume calculator. Calculate the volume of cubes, spheres, cylinders, cones, pyramids, and prisms. Includes surface area calculations.

iAbout This Calculator

The volume calculator is your comprehensive tool for calculating the three-dimensional space occupied by various geometric shapes. Whether you're a student studying solid geometry, an engineer calculating container capacities, or a homeowner determining how much concrete or soil you need, understanding volume calculations is essential. This calculator supports seven common 3D shapes: cubes, rectangular prisms, spheres, cylinders, cones, pyramids, and triangular prisms. Each shape has its own volume formula, and our calculator handles the math instantly, providing both volume and surface area calculations. Volume measurements are fundamental in countless applications, from shipping and packaging to construction and manufacturing. Whether you're calculating the capacity of a water tank, the amount of fill dirt needed for landscaping, or the volume of a storage container, this calculator makes complex 3D geometry accessible and practical. Understanding the relationship between dimensions and volume helps in material estimation, cost calculation, and efficient space utilization.

?How to Use

1
Select the 3D shape you want to calculate from the dropdown menu: cube, rectangular prism, sphere, cylinder, cone, pyramid, or triangular prism.
2
Enter the required measurements for your selected shape. Different shapes require different inputs (side length for cube, radius for sphere, base radius and height for cylinder, etc.).
3
All measurements should be in the same unit (meters, feet, inches, etc.). The result will be in cubic units of your chosen measurement.
4
Click Calculate to see the volume result. For all shapes, the surface area will also be displayed.
5
To calculate a different shape, simply select a new shape from the dropdown and enter new measurements.
6
For pyramids, you'll need the base dimensions (length and width) plus the height. For triangular prisms, you'll need the triangle base, triangle height, and prism length.

fFormula

V_{cube} = s^3 \quad V_{sphere} = \frac{4}{3}\pi r^3 \quad V_{cylinder} = \pi r^2 h

Cube: V = side³. Rectangular Prism: V = length × width × height. Sphere: V = (4/3) × π × radius³. Cylinder: V = π × radius² × height. Cone: V = (1/3) × π × radius² × height. Pyramid: V = (1/3) × base area × height. Triangular Prism: V = (1/2) × base × height × length.

s: Side length (cube)
l, w, h: Length, width, height (rectangular prism, pyramid)
r: Radius (sphere, cylinder, cone)
h: Height (cylinder, cone, pyramid, prism)

Examples

Shipping Box Volume

Inputs: shape: rectangular-prism, length: 30, width: 20, height: 15

Volume: 9,000 cubic units

A shipping box measuring 30 × 20 × 15 cm has a volume of 9,000 cubic centimeters (30 × 20 × 15 = 9,000 cm³), or 9 liters. This helps determine packaging capacity and shipping costs based on dimensional weight.

Spherical Water Tank

Inputs: shape: sphere, radius: 2

Volume: 33.51 cubic units

A spherical water tank with a radius of 2 meters has a volume of approximately 33.51 cubic meters ((4/3) × π × 2³ ≈ 33.51 m³). This equals about 33,510 liters of water storage capacity.

Cylindrical Storage Tank

Inputs: shape: cylinder, baseRadius: 1.5, cylinderHeight: 3

Volume: 21.21 cubic units

A cylindrical tank with radius 1.5 meters and height 3 meters has a volume of approximately 21.21 cubic meters (π × 1.5² × 3 ≈ 21.21 m³). This is useful for calculating liquid storage capacity.

Ice Cream Cone Volume

Inputs: shape: cone, baseRadius: 3, cylinderHeight: 10

Volume: 94.25 cubic units

A cone with base radius 3 cm and height 10 cm has a volume of approximately 94.25 cubic centimeters ((1/3) × π × 3² × 10 ≈ 94.25 cm³). This helps understand portion sizes for conical containers.

Use Cases

Construction & Concrete Work

Calculate the volume of concrete needed for foundations, slabs, and columns. Knowing exact volumes helps order the right amount of materials and estimate costs accurately.

Shipping & Packaging

Determine box and container volumes for shipping calculations. Many carriers charge based on dimensional weight, making volume calculations essential for cost estimation.

Tank & Container Capacity

Calculate the capacity of water tanks, fuel tanks, and storage containers. Convert volume to liters or gallons to understand practical storage capacity.

Landscaping & Gardening

Determine how much soil, mulch, gravel, or sand you need. Volume calculations help you order the right quantity and avoid waste or shortages.

Education & Homework

Students can verify their solid geometry homework or understand how volume formulas work in practice. Teachers can demonstrate 3D concepts with real-time calculations.

Frequently Asked Questions

What's the difference between volume and surface area?

Volume measures the three-dimensional space inside a shape (in cubic units like m³), while surface area measures the total area of all outer surfaces (in square units like m²). Think of volume as how much water a container can hold, and surface area as how much paint you'd need to cover its outside.

How do I convert between cubic units?

To convert cubic units, cube the linear conversion factor. For example: 1 m = 100 cm, so 1 m³ = 100³ = 1,000,000 cm³. Similarly, 1 foot = 12 inches, so 1 cubic foot = 12³ = 1,728 cubic inches. Common conversions: 1 m³ = 1,000 liters; 1 gallon ≈ 3.785 liters.

Why is the sphere formula (4/3)πr³?

The sphere volume formula comes from calculus, derived by integrating circular cross-sections throughout the sphere. Archimedes originally discovered that a sphere's volume equals 2/3 of the circumscribed cylinder's volume. The (4/3)π factor naturally emerges from this relationship.

Why do cones and pyramids have a 1/3 factor?

The 1/3 factor appears because cones and pyramids taper to a point. Mathematically, when you integrate the cross-sectional areas from base to tip, you get exactly 1/3 of what a prism or cylinder with the same base and height would have. This is why V = (1/3) × base area × height for both shapes.

How accurate are these calculations?

The calculations are mathematically exact to 4 decimal places. Any small differences from hand calculations are due to rounding of π or intermediate values. For practical purposes like ordering materials, results are more than precise enough.

How do I calculate the volume of an irregular shape?

Break the irregular shape into simpler geometric shapes you can calculate. Add volumes for parts that combine, or subtract for parts cut out. For very complex shapes, you might need to use water displacement (submerge the object and measure displaced water) or 3D scanning software.

What's the relationship between a cylinder and a cone with the same dimensions?

A cone with the same base radius and height as a cylinder has exactly 1/3 the volume. This means three identical cones could fill one cylinder. This relationship is useful for quick mental calculations and understanding the geometry of tapered vs. straight-sided containers.

How do I calculate how many liters a tank holds?

First calculate the volume in cubic meters, then multiply by 1,000 to convert to liters (1 m³ = 1,000 L). Alternatively, if your measurements are in centimeters, divide the cubic centimeter result by 1,000. For gallons, divide liters by 3.785 (US gallons) or 4.546 (imperial gallons).

Conclusion

The volume calculator is an essential tool for anyone working with three-dimensional space and measurements. From construction projects requiring precise concrete calculations to shipping logistics based on container capacities, understanding volume is fundamental. Our calculator supports the most common 3D geometric shapes and provides instant, accurate results including both volume and surface area. Remember to keep your units consistent, add extra for waste when ordering materials, and break complex shapes into simpler components when needed. Whether you're a student learning solid geometry, an engineer designing containers, or a homeowner planning a project, this calculator makes 3D calculations accessible and practical.