3D Geometry Calculators
Calculate volume, surface area, and other properties of 3D shapes
Cube Calculator
Sphere Calculator
Cylinder Calculator
Cone Calculator
Pyramid Calculator
Rectangular Prism
3D Geometry Formulas Reference
| Shape | Volume | Surface Area | Other Properties |
|---|---|---|---|
| Cube | V = a³ | A = 6a² | Space diagonal: a√3 |
| Sphere | V = (4/3)πr³ | A = 4πr² | Circumference: 2πr |
| Cylinder | V = πr²h | A = 2πr(r + h) | Lateral area: 2πrh |
| Cone | V = (1/3)πr²h | A = πr(r + l) | Slant height: l = √(r² + h²) |
| Square Pyramid | V = (1/3)a²h | A = a² + 2al | Slant height: l = √(h² + (a/2)²) |
| Rectangular Prism | V = lwh | A = 2(lw + lh + wh) | Space diagonal: √(l² + w² + h²) |
Applications of 3D Geometry
Real-World Applications
- Architecture and construction (volume calculations for materials)
- Manufacturing (packaging design, container capacity)
- Physics and engineering (fluid dynamics, structural analysis)
- Computer graphics and game development
Academic Importance
- Foundation for advanced mathematics and physics
- Essential for STEM education and careers
- Develops spatial reasoning and problem-solving skills
- Basis for calculus and multivariable mathematics
Frequently Asked Questions
How do I calculate the volume of irregular 3D shapes?
For irregular shapes, you can use methods like the displacement method (for solids) or break the shape down into regular components whose volumes you can calculate separately and then sum together.
What's the difference between lateral and total surface area?
Lateral surface area includes only the sides of a 3D shape, excluding the base(s). Total surface area includes all surfaces - the lateral area plus the area of the base(s).
Why is π (pi) used in so many 3D geometry formulas?
Pi is the ratio of a circle's circumference to its diameter. It appears in formulas involving spheres, cylinders, and cones because these shapes have circular cross-sections or bases.
How accurate are these calculators?
Our calculators provide precise mathematical calculations based on the formulas. The accuracy of your results depends on the accuracy of the measurements you input.
Can I calculate 3D geometry properties for shapes not listed here?
We've covered the most common 3D shapes. For other shapes like toruses, ellipsoids, or more complex polyhedrons, specialized formulas would be needed which we may add in future updates.