Measure the skin of any 3D shape.
Pick a shape, enter its dimensions, and see the total surface area, the volume, the surface-area-to-volume ratio, and the exact formula worked out with your own numbers.
The shape
Units are generic (u). Areas come out in square units, volumes in cubic units.
The shape you are measuring
What this means
Key numbers
Same shape, different sizes
Scale every dimension by the same factor. Surface area grows with the square of the scale, volume with the cube, so the surface-area-to-volume ratio drops as the shape gets bigger.
| Scale | Surface area | Volume | SA : V ratio |
|---|
Surface area, explained
Surface Area Formulas
Cube: SA = 6s². Sphere: SA = 4πr². Cylinder: SA = 2πr² + 2πrh (two circles + lateral). Cone: SA = πr² + πr×l (base + lateral, where l is slant height). Rectangular Prism: SA = 2(lw + lh + wh). Surface area measures the total outer area of a 3D object.
Lateral vs Total Surface Area
Lateral surface area excludes the base(s), measuring only the sides. Total surface area includes all faces. For painting a cylinder (without lids), use lateral area (2πrh). For wrapping a gift box, use total surface area. The distinction matters for practical material estimation.
Surface Area to Volume Ratio
The surface area to volume ratio is important in biology (cell size limits), engineering (heat dissipation), and chemistry (reaction rates). Smaller objects have higher SA:V ratios. This is why crushed ice melts faster than an ice block, more surface area is exposed.
Practical Surface Area Applications
Surface area calculations determine how much paint, wallpaper, fabric, wrapping paper, or coating material you need. In manufacturing, surface area affects material costs. In engineering, it affects heat transfer, aerodynamics, and structural loads.
Common questions
How do I calculate slant height for a cone?
Slant height l = √(r² + h²), where r is the radius and h is the vertical height. This calculator computes the slant height automatically from the dimensions you provide.
What is the surface area of a half sphere (hemisphere)?
Total surface area of a hemisphere = 3πr² (curved surface 2πr² + flat base πr²). If you only need the curved part (like a dome), use 2πr².
How much paint do I need for a cylindrical tank?
Calculate the surface area in square feet, then divide by the paint coverage rate (typically 350-400 sq ft per gallon). Decide whether to include the top, bottom, or just the lateral surface.
What is the most efficient shape for packaging?
A sphere has the least surface area for a given volume, making it the most material-efficient shape. However, cubes and rectangular prisms are more practical for stacking and shipping.
Results are geometric estimates. Round measurements and real-world irregularities (seams, overlaps, waste) mean you should add a margin before ordering paint, wrap or material.