Surface Area Calculator
Calculate the surface area and volume of 3D shapes: sphere, cube, cylinder, cone, and rectangular prism. See also Area of Circle Calculator and Area of Rectangle Calculator.
How to Calculate Surface Area
Surface area is the total area of all faces or surfaces of a 3D object. Each shape has its own formula. For a sphere, it depends only on the radius. For prisms and cylinders, you add the areas of the bases and the lateral (side) surfaces. This calculator handles five common 3D shapes and also computes the volume for each.
Surface Area Formulas
Sphere: SA = 4πr²
Cube: SA = 6s²
Cylinder: SA = 2πr(r + h)
Cone: SA = πr(r + √(r² + h²))
Rectangular Prism: SA = 2(lw + lh + wh)
Example
Find the surface area of a sphere with radius 5:
SA = 4πr²
SA = 4 × π × 25
SA ≈ 314.1593 square units
Volume = (4/3)πr³ = (4/3) × π × 125 ≈ 523.5988 cubic units
Surface Area Reference Table
| Shape | Dimensions | Surface Area | Volume |
|---|---|---|---|
| Sphere | r = 1 | 12.5664 | 4.1888 |
| Sphere | r = 5 | 314.1593 | 523.5988 |
| Sphere | r = 10 | 1256.6371 | 4188.7902 |
| Cube | s = 1 | 6.0000 | 1.0000 |
| Cube | s = 5 | 150.0000 | 125.0000 |
| Cube | s = 10 | 600.0000 | 1000.0000 |
| Cylinder | r=3, h=5 | 150.7964 | 141.3717 |
| Cylinder | r=5, h=10 | 471.2389 | 785.3982 |
| Cone | r=3, h=4 | 75.3982 | 37.6991 |
| Cone | r=5, h=12 | 282.7433 | 314.1593 |
| Rect. Prism | 2×3×4 | 52.0000 | 24.0000 |
| Rect. Prism | 5×6×8 | 236.0000 | 240.0000 |
Frequently Asked Questions
What is surface area?
Surface area is the total area of all the outer surfaces of a 3D object. It is measured in square units. Think of it as the amount of wrapping paper needed to cover the object completely.
What is the difference between surface area and volume?
Surface area measures the outside of a 3D shape (in square units), while volume measures the space inside (in cubic units). A balloon's surface area is the rubber material; its volume is the air inside.
What is lateral surface area?
Lateral surface area is the area of only the sides of a 3D shape, excluding the top and bottom bases. For a cylinder: lateral SA = 2πrh. For a cone: lateral SA = πr × slant height.
Which shape has the smallest surface area for a given volume?
A sphere has the smallest surface area for any given volume. This is why bubbles are spherical — nature minimizes surface tension (surface area) for the enclosed air (volume).
What is the slant height of a cone?
The slant height is the distance from the tip of the cone to any point on the edge of the base, measured along the surface. It is calculated as l = √(r² + h²), where r is the base radius and h is the vertical height.