Surface Area Calculator
This surface area calculator finds the surface area and volume of cubes, spheres, cylinders, cones, prisms and other geometric solids using standard formulas.
Calculate Surface Area
Results
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Surface area formulas for common shapes
Surface area formulas for common shapes are derived from basic geometric relationships and apply regardless of which unit of measurement is used.
Cube
Surface Area = 6a²
Volume = a³
Sphere
Surface Area = 4πr²
Volume = (4/3)πr³
Cylinder
Surface Area = 2πr(h + r)
Volume = πr²h
Cone
Surface Area = πr(r + √(r² + h²))
Volume = (1/3)πr²h
Rectangular Prism
Surface Area = 2(lw + lh + wh)
Volume = lwh
Hemisphere
Surface Area = 3πr²
Volume = (2/3)πr³
Square Pyramid
Surface Area = a(a + √(a² + 4h²))
Volume = (1/3)a²h
Capsule
Surface Area = 2πr(2r + a)
Volume = πr²((4/3)r + a)
How surface area calculations work
How surface area calculations work depends on breaking a three dimensional shape into flat or curved sections and adding the area of each section together to get a total.
Lateral surface area versus total surface area
Lateral surface area refers to the area of the sides of a shape only, while total surface area adds in the area of the top and bottom faces as well. For a cylinder, the lateral area covers just the curved side, and the total area also includes the two circular ends.
Why units matter for surface area
Why units matter for surface area comes down to consistency, since every input value must be measured in the same unit for the result to be accurate. If you enter dimensions in feet, the resulting surface area will be in square feet, and the volume will be in cubic feet.
Common uses for surface area calculations
Common uses for surface area calculations include estimating paint or material needed to cover an object, calculating heat transfer in engineering, and solving geometry problems in education. Surface area also plays a role in packaging design, where minimizing surface area can reduce material costs.
Frequently asked questions
The surface area of a cube equals six times the side length squared. The formula is written as surface area equals 6 times a squared, where a is the length of one edge of the cube.
The surface area of a sphere equals four times pi times the radius squared. The formula is written as surface area equals 4 pi r squared, where r is the radius of the sphere.
The total surface area of a cylinder equals two pi r times the quantity h plus r, where r is the radius and h is the height. This formula combines the curved side area with the area of the two circular ends.
Lateral surface area refers only to the area of the sides of a shape, excluding the top and bottom faces, while total surface area includes the lateral area plus the area of all bases. For a closed shape, total surface area represents the entire outer surface.
The total surface area of a cone equals pi r times the quantity r plus the slant height, where r is the base radius and the slant height is the square root of r squared plus h squared. This combines the circular base area with the curved lateral surface.
The unit you select does not change the calculation itself, but it determines the unit label shown with your result, such as square feet or square meters. All input values must use the same unit for the result to be meaningful.