Home/Maths/3D Volume Calculator

3D Volume Calculator

Calculate the volume of 11+ 3D shapes including spheres, cones, and tanks with this professional geometry solver.

r
🧊

Calculated Volume

523,5988

cubic units

📐 Formula

V = ⁴⁄₃πr³

🔄 Conversions

Liters (approx if meters)~523 598,776 L
Gallons (US)~138 320,136 gal

*Assuming input units are meters

Sphere Volume

A sphere is a perfectly round geometrical 3D object. The volume of a sphere is the amount of space occupied within it. It is defined centrally by its radius (the distance from the center to the surface).

Formula: V = ⁴⁄₃πr³

Cylinder Volume

A cylinder is a 3D solid that holds two parallel bases joined by a curved surface, at a fixed distance. The volume is calculated by multiplying the area of the circular base by the height.

Formula: V = πr²h

Cone Volume

A cone is a three-dimensional geometric shape that tapers smoothly from a flat base (usually circular) to a point called the apex or vertex. Its volume is exactly one-third of a cylinder with the same base and height.

Formula: V = ⅓πr²h

Cube Volume

A cube is a regular polyhedron with 6 equal square faces. Since all edges are equal in length, calculation is simple: just cube the length of any edge.

Formula: V = a³

Rectangular Tank

Also known as a rectangular prism or cuboid. It is a convex polyhedron bounded by six quadrilateral faces. The volume is found by multiplying its length, width, and height.

Formula: V = l × w × h

Capsule Volume

A capsule consists of a cylinder with hemispherical ends. To calculate the volume, you combine the volume of the cylinder part with the volume of the two hemispheres (which make a whole sphere).

Formula: V = πr²(⁴⁄₃r + a)

Spherical Cap

A spherical cap is a portion of a sphere cut off by a plane. It's like the top slicing of a ball. The volume calculation involves the height of the cap and the radius of the sphere.

Formula: V = ⅓πh²(3R - h)

Conical Frustum

A frustum is the portion of a cone that lies between two parallel planes cutting it. Think of it as a cone with the tip cut off. The volume depends on the top radius, bottom radius, and height.

Formula: V = ⅓πh(r₁² + r₂² + r₁r₂)

Ellipsoid Volume

An ellipsoid is a surface that may be obtained from a sphere by deforming it by means of directional scalings. It has three semi-axes: a, b, and c. It looks like a stretched sphere (e.g., a rugby ball).

Formula: V = ⁴⁄₃πabc

Square Pyramid

A square pyramid is a pyramid having a square base. Its volume is one-third of the product of the base area and the perpendicular height.

Formula: V = a²(h/3)

Tube Volume

A tube (or hollow cylinder) volume is the volume of metal or material that makes up the tube. It is calculated by subtracting the volume of the inner cylinder (hole) from the outer cylinder.

Formula: V = πl(R² - r²)

This geometry solver is useful for civil engineers, logistics managers, and laboratory technicians who need to calculate capacity for shapes, industrial tanks, and chemical containers.

Related Calculators

Graphical Solver

Plot and analyze functions y = f(x) with interactive graphs.

Differential Equation Solver

Solve first-order ODEs with clear steps and directional field mapping. Perfect for calculus students and engineering modeling.

Annulus Area Calculator

Calculate annulus area A = π(R² - r²) for ring shapes.

Polynomial Solver

Solve polynomial equations P(x) = 0 with graphical visualization.

Mastering 3D Measurement and Capacity

In the science category, volume is the measure of the three-dimensional space occupied by an object, liquid, or gas. This geometry solver simplifies the complex math required to calculate the internal capacity of everything from basic cubes to specialized industrial tanks. Whether you're estimating concrete for a foundation or measuring chemical displacement in a lab, accuracy is paramount.

Our tool supports 11 distinct shapes, including spheres, cones, cylinders, and industrial conduits. By selecting your shape and entering the required dimensions, you get instant, mathematically rigorous volume results.

The Mathematics of Volume

This science solver utilizes foundational volumetric proofs:

Cylinder

V = π r² h

Cone

V = 1/3 π r² h

Rectangular Prism

V = l × w × h

For comprehensive updates on 3D shape properties and industrial standards, refer to the Wolfram MathWorld Volume Guide or Britannica Science references.

Industrial Applications

Precision in the geometry solver category is vital for:

  • Logistics: Calculating "cube out" capacity in shipping containers to maximize transport efficiency and reduce fuel costs.
  • Civil Engineering: Sizing drainage pipes and retention ponds to handle peak rainwater runoff, as dictated by NIST infrastructure standards.
  • Chemistry: Scaling up reaction vessels from lab-bench test tubes to industrial-sized fermentation tanks.

Volume FAQ

What is the difference between Volume and Capacity?

Volume refers to the space an object occupies, while capacity refers to the amount of substance (like water) a container can hold. For most engineering purposes, these are considered identical.

Does this tool support Liters and Gallons?

While the primary output is in cubic units, you can use our Unit Converter to quickly translate these results into industrial liquid measurements.

How do I calculate volume for a Conical Frustum?

A conical frustum is a cone with the top cut off. The formula is V = (1/3) π h (r² + rR + R²), where r and R are the radii of the top and bottom circles.

Related Geometry Tools