Volume Calculator
Free online Volume Calculator with step-by-step solutions. 100% client-side, no data upload.
Select Shape & Enter Dimensions
Results
Sphere
\(V = \frac{4}{3}\pi r^3\)
Select a shape and enter dimensions to see the result.
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Volume Calculator
⚡ Volume is the measure of the amount of space occupied by a three-dimensional object.
What is Volume?
Volume quantifies the capacity of a container or the space a solid occupies. For regular shapes, volume can be computed using well-known formulas.
Formulas
- Sphere — \(V = \frac{4}{3}\pi r^3\)
- Cone — \(V = \frac{1}{3}\pi r^2 h\)
- Cube — \(V = a^3\)
- Cylinder — \(V = \pi r^2 h\)
- Rectangular Tank — \(V = lwh\)
- Capsule — \(V = \pi r^2 h + \frac{4}{3}\pi r^3\)
- Spherical Cap — \(V = \frac{1}{3}\pi h^2 (3R - h)\)
- Conical Frustum — \(V = \frac{1}{3}\pi h (r^2 + rR + R^2)\)
- Ellipsoid — \(V = \frac{4}{3}\pi abc\)
- Square Pyramid — \(V = \frac{1}{3}a^2 h\)
- Tube — \(V = \pi \frac{d_1^2 - d_2^2}{4} l\)
History
Archimedes discovered sphere/cylinder volumes. Euclid gave proofs for pyramids. Cavalieri developed indivisibles. Newton/Leibniz created calculus for integration.
Applications
Engineering (tanks, pipes), architecture, medicine, environmental science, everyday life.
🔒 Client-side only⚡ Web Worker processing🌐 Works offline🛡️ Zero server logs
Frequently Asked Questions
Got questions about volume? We've got answers.
What is volume?
Volume is the measure of the amount of space occupied by a three-dimensional object.
How many shapes are supported?
11 shapes: Sphere, Cone, Cube, Cylinder, Rectangular Tank, Capsule, Spherical Cap, Conical Frustum, Ellipsoid, Square Pyramid, and Tube.
What is the Spherical Cap rule?
Fill any two of the three fields. The third will be computed automatically.
Is this calculator private?
Yes. All calculations run locally in your browser. No data is transmitted or stored on any server.