Volume Calculator | Sphere, Cylinder & Cone

Q: How do I calculate volume of a sphere, cylinder, or cone?

Each shape has an exact formula. Sphere: V=43πr3V = 4 / 3 r^3V=34πr3 Cylinder: V=πr2hV = r^2 hV=πr2h Cone: V=13πr2hV = 1 / 3 r^2 hV=31πr2h Enter dimensions in any of 11 units (miles to angstroms). Results display in your unit cubed.

Q: Is ellipsoid volume exact or approximate?

Ellipsoid volume is exact: V=43πabcV = 4 / 3 abcV=34πabc (a, b, c = semi-axes). Unlike ellipsoid surface area, no approximation is needed.

Volume Calculator: Formula Reference & Tips

Enter dimensions for any of 10 solids, results update live. Use the Calculation tab to see the formula with your values substituted, and the Theory tab for geometric background. Trusted by students and educators for geometry and capacity work.

Quick Workflow

Choose Shape

10 solids: sphere, cone, cube, cylinder, rectangular tank, capsule, spherical cap, frustum, ellipsoid, square pyramid.

Units & Input

Each field has a unit dropdown (m, ft, in, etc.). Spherical cap: provide any two of r, R, h.

Step-by-Step

Calculation tab: formula + substitution. Theory tab: geometric explanation for the selected shape.

Schematic

3D diagram highlights the focused dimension. Copy Results for reports or spreadsheets.

Volume Calculator: Sphere, Cylinder, Cone & More

Free volume calculator for sphere, cone, cube, cylinder, rectangular tank, capsule, spherical cap, frustum, ellipsoid, pyramid. Step-by-Step Calculation with full formula substitution. 11 length units. Trusted by students and educators. No sign-up.

What This Volume Calculator Does

Purpose & Use Cases

This volume calculator computes the volume of 10 common 3D solids. Use it to calculate volume of a sphere, cylinder volume formula, cone volume, or any supported shape. Enter dimensions in 11 length units (miles to angstroms). Ideal for geometry homework, capacity estimates, packaging, and learning how to find volume. The Step-by-Step Calculation shows the exact formula with your values substituted.

Shapes:

Sphere, cone, cube, cylinder, rectangular tank, capsule, spherical cap, conical frustum, ellipsoid, square pyramid.
Output:

Volume in your chosen unit cubed (e.g. m³, ft³).

Volume Formulas by Shape

Sphere

Volume of a sphere:

V = \frac{4}{3}\pi r^3

Use radius or diameter; d = 2r so

V = \frac{\pi d^3}{6}

Cylinder

Volume of a cylinder:

V = \pi r^2 h

Base area πr² times height.

Cone

Volume of a cone:

V = \frac{1}{3}\pi r^2 h

One-third of the cylinder with same base and height.

Cube

Volume of a cube:

V = a^3

Edge length cubed.

Rectangular Tank

Volume of a rectangular prism:

V = lwh

Length times width times height.

Capsule

Volume of a capsule:

V = \pi r^2 h + \frac{4}{3}\pi r^3

Cylinder plus full sphere (two hemispherical caps).

Spherical Cap

Volume of a spherical cap:

V = \frac{\pi h^2(3R-h)}{3}

with ball radius R and cap height h. Provide any two of r, R, h to derive the third.

Conical Frustum

Volume of a frustum:

V = \frac{1}{3}\pi h(r_1^2 + r_1 r_2 + r_2^2)

with top radius r₁, bottom radius r₂, height h.

Ellipsoid

Volume of an ellipsoid:

V = \frac{4}{3}\pi abc

with semi-axes a, b, c. Exact formula.

Square Pyramid

Volume of a square pyramid:

V = \frac{1}{3}a^2 h

One-third base area times height.

How to Use This Calculator

Compute the volume of any supported 3D solid in a few steps:

Select a Shape:

Choose from sphere, cone, cube, cylinder, rectangular tank, capsule, spherical cap, conical frustum, ellipsoid, or square pyramid using the shape selector.
Enter Dimensions:

Fill in the required measurements for your shape. Each field has its own unit dropdown (miles, feet, inches, meters, cm, mm, and more). For a spherical cap, enter any two of r, R, and h, the third is derived automatically.
Read the Volume:

The result appears in your chosen unit cubed (e.g., ft³, m³) and updates live as you type. No need to press a button.
View the Calculation Tab:

Switch to the Calculation tab to see the exact formula with your values substituted step by step, useful for homework or double-checking.
Explore the Theory Tab:

The Theory tab provides geometric background for each shape, including derivation notes, edge cases, and relationships between shapes.

Volume Calculator FAQ

How do I calculate volume of a sphere, cylinder, or cone?

Each shape has an exact formula. Sphere:

V = \frac{4}{3}\pi r^3

Cylinder:

V = \pi r^2 h

Cone:

V = \frac{1}{3}\pi r^2 h

Enter dimensions in any of 11 units (miles to angstroms). Results display in your unit cubed.

What shapes can I find the volume of?

Sphere, cone, cube, cylinder, rectangular tank, capsule, spherical cap, conical frustum, ellipsoid, and square pyramid. For sphere, radius or diameter, the other auto-updates. For spherical cap, enter any two of r, R, and h.

Is ellipsoid volume exact or approximate?

Ellipsoid volume is exact:

V = \frac{4}{3}\pi abc

(a, b, c = semi-axes). Unlike ellipsoid surface area, no approximation is needed.

Can I use feet, inches, or meters?

Yes. Each dimension has its own unit selector: miles, yards, feet, inches, km, m, cm, mm, µm, nm, angstroms. Volume displays in that unit cubed (e.g. ft³, m³).

Mathematical Reference Note

Calculation Logic: This tool uses standard mathematical algorithms. While we strive for accuracy, errors in logic or user input can result in incorrect data.

Verification: Results should be cross-checked if used for important academic, professional, or personal calculations.

Standard Terms: This tool is provided free of charge and as-is. CalcRegistry provides no warranty regarding the accuracy or fitness of these results for your specific needs.