Surface Area & Volume Calculator
Calculate surface area and volume for 3D geometric shapes
Select 3D Shape
📦
Cube
Edge length
📐
Rectangular Prism
L × W × H
⚪
Sphere
Radius
🔴
Cylinder
Radius + Height
🔺
Cone
Radius + Height
🔻
Square Pyramid
Base + Height
🎪
Hemisphere
Radius
🍩
Torus
2 Radii
3D Shape Calculator: Volume & Surface Area
This tool accurately calculates the Volume and Total Surface Area for various common 3D geometric solids using their core dimensions. Results are provided with detailed step-by-step solutions.
Understanding the Calculations
A
Surface Area
The total area of the exposed outer surfaces of a 3D object. Measured in square units.
V
Volume
The amount of space a 3D object occupies, or the capacity it holds. Measured in cubic units.
Note: The calculator handles complex elements like the Slant Height (l) in cones and pyramids, which are necessary for the Area calculation but often derived from the base inputs (r and h).
Formulas for Each Shape
| Shape | Required Inputs | Volume Formula (V) | Surface Area Formula (A) |
|---|---|---|---|
| Cube | Edge (a) | V = a³ | A = 6a² |
| Rectangular Prism | l, w, h | V = lwh | A = 2(lw + wh + hl) |
| Sphere | Radius (r) | V = (4/3)πr³ | A = 4πr² |
| Cylinder | r, h | V = πr²h | A = 2πrh + 2πr² |
| Cone | r, h | V = (1/3)πr²h | A = πr² + πrl (where l = √(r² + h²)) |
| Pyramid (Square Base) | Base (a), h | V = (1/3)a²h | A = a² + 2al (where l = √(h² + (a/2)²)) |
| Hemisphere | Radius (r) | V = (2/3)πr³ | A = 3πr² |
| Torus (Donut) | Major (R), Minor (r) | V = 2π²Rr² | A = 4π²Rr |
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Surface Area Calculator – Cube, Sphere, Cylinder & Cone | Solvezi