Calculate total and lateral surface area for cubes, prisms, hemispheres, cylinders, cones, spheres.
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Solid geometry
Calculate total and lateral surface area for common 3D solids
Use one general surface area calculator for boxes, cubes, spheres, hemispheres, cylinders,
cones, square pyramids, and right triangular prisms, then compare the result in both your
selected square unit and standard metric or imperial coverage units.
Shape
Rectangular prism
Use this for boxes, cartons, rooms, or any straight-sided solid with rectangular faces.
The calculator keeps the total outside area separate from the lateral or curved area so
you can decide whether to include flat ends, bases, or top and bottom faces.
Result
158 ft²
Total surface area of the rectangular prism using SA = 2(lw + lh + wh). Use
side wall area when you only need the sides or curved shell rather
than the full outside.
Side wall area
78 ft²
Top and bottom area
80 ft²
Square metres
14.68 m²
Square feet
158 ft²
How to use the result
Use the lateral area when you are covering only the sides of a box or room. Use the total surface area when you also need the top and bottom faces.
Surface area calculator for cubes, prisms, cylinders, cones, spheres, and more
A surface area calculator is most useful when it separates the full outside of a solid from the curved or lateral part you may actually need to cover. This page works as a total surface area calculator and a lateral surface area calculator for boxes, cubes, spheres, hemispheres, cylinders, cones, square pyramids, and right triangular prisms, then converts the result into practical square-metre and square-foot comparisons.
Surface area formulas by solid
Surface area is the sum of every exposed face on a three-dimensional solid. For shapes with obvious bases, such as a cylinder, cone, prism, or pyramid, users often need both the total surface area and the lateral surface area. Total surface area includes every outside face. Lateral surface area removes the base or end faces and keeps only the side shell.
That distinction is what many quick geometry pages miss. A cylinder surface area calculator should not hide the difference between the wrapped side and the two circular ends. A hemisphere surface area calculator should make clear that curved area is 2πr² but total area is 3πr² once the flat base is included. A cone surface area calculator also needs the slant height, even when the user only knows radius and vertical height.
This page keeps those cases explicit. It covers the most common classroom and planning solids, shows the formula, and breaks the total into the parts that were added together so you can see whether the answer belongs to a full shell, a side-only coating job, or a shape with separate end caps.
Cube: SA = 6s²; lateral area = 4s²
A cube has six equal square faces, with four counted in lateral area and two counted as top and bottom.
Rectangular prism: SA = 2(lw + lh + wh); lateral area = 2h(l + w)
Use this for cuboids, cartons, tanks, and room-style box geometry.
Sphere: SA = 4πr²
A sphere has one continuous curved surface and no separate bases.
Hemisphere: SA = 3πr²; curved area = 2πr²
Total area includes the circular base; curved area excludes it.
Cylinder: SA = 2πr(r + h); lateral area = 2πrh
Total cylinder area adds the wrapped side to the two circular ends.
Cone: SA = πr(r + ℓ); lateral area = πrℓ
The cone uses slant height ℓ, which can be derived from radius and vertical height.
Square pyramid: SA = b² + 2bℓ; lateral area = 2bℓ
The square base is counted separately from the four triangular faces.
Right triangular prism: SA = 2B + PL; lateral area = PL
B is the triangular base area and P is the perimeter of the triangular end.
How to calculate total surface area without double-counting
A good total surface area calculator follows the same process you would use by hand. First, identify the separate faces or curved parts. Next, calculate each part in square units. Finally, add only the surfaces that are actually exposed. This last step matters most for prisms, cylinders, cones, and composite solids because it is easy to add an internal face that should not be counted.
For a rectangular prism, the safest method is to group opposite faces: top and bottom, front and back, left and right. For a cylinder, think of a label wrapped around the side plus two circle ends. For a cone, keep the curved shell and the base circle separate. For a right triangular prism, find the two triangular ends first, then add the three rectangles that run along the prism length.
If you are solving a practical problem rather than a textbook question, define the job before choosing the result. Paint, insulation, wrapping, and sheet material often need the full outside. A sleeve, label, or sidewall lining often needs the lateral surface area only. The calculator's face-by-face breakdown is designed to keep that decision visible.
Worked examples for cylinder, hemisphere, and triangular prism surface area
Suppose you need the total surface area of a cylinder with radius 4 ft and height 10 ft. The wrapped side is 2πrh = 80π ft². The two circular ends contribute 2πr² = 32π ft². Total surface area is 112π ft², or about 351.86 ft². If your job only covers the side, the lateral area stays at 80π ft², or about 251.33 ft².
For a hemisphere with radius 5 ft, the curved area is 2πr² = 50π ft². The flat base adds another πr² = 25π ft². Total surface area is 75π ft², or about 235.62 ft². This is a common source of mistakes because many learners remember the curved dome but forget to ask whether the flat base belongs in the answer.
A right triangular prism with triangle base 3 ft, triangle height 4 ft, and prism length 10 ft is another good check. Each triangular end has area 0.5 × 3 × 4 = 6 ft², so both ends together contribute 12 ft². The missing triangle side is 5 ft, so the lateral area is 10 × (3 + 4 + 5) = 120 ft². Total surface area is 132 ft². Breaking the solid into ends plus side rectangles makes the formula easier to trust.
Square units, metric conversions, and when to use a specialist calculator
Surface area should always be reported in square units that match the original dimensions. If you enter feet, the first result is in square feet. If you enter metres, the result is in square metres. That seems basic, but it is one of the most common points of confusion when someone searches for a surface area formula calculator and then tries to compare the answer with a supplier quote, a material coverage sheet, or a class workbook using different units.
This page converts every total result into square metres and square feet so you can cross-check metric and imperial workflows without re-entering the shape. That makes the calculator more useful for planning paint coverage, wraps, insulation, plating, cladding, or classroom verification where the geometric setup is the same but the reporting system changes.
Use this general calculator when the object really is one clean solid. Switch to a specialist workflow once the shape includes cut-outs, wall thickness, rounded transitions, frustums, composite solids, or hidden faces. In those cases the right method is usually to break the object into simpler exposed parts rather than pretending one single solid formula still fits.
Further reading
NIST — SI Units: Area — Official NIST reference for square-unit relationships and metric area conventions.
What is the difference between total surface area and lateral surface area?
Total surface area includes every outside face of the solid. Lateral surface area excludes the base or end faces and keeps only the side shell. For a cylinder that means the wrapped side without the two circles. For a hemisphere it means the curved dome without the flat base.
How do I calculate surface area for a rectangular prism or box?
Use SA = 2(lw + lh + wh). Multiply each pair of dimensions to get the three unique face areas, add them, and double the result to account for opposite faces. If you only need the sides, use the lateral-area form 2h(l + w).
Why does a cone surface area calculator need slant height?
The curved side of a cone stretches along the slant, not straight up the vertical height. If you know the radius and vertical height, first derive slant height with ℓ = √(r² + h²), then use total surface area πr(r + ℓ) or lateral surface area πrℓ.
Does a hemisphere include the flat base in total surface area?
Yes, total surface area of a hemisphere is 3πr² because it includes the curved half-sphere plus the circular base. If the question only wants the curved shell, use 2πr² instead.
How do I find the surface area of a triangular prism?
Find the area of both triangular ends, then add the three rectangles that wrap around the prism. For a right triangular prism, total surface area can be written as 2B + PL, where B is the area of one triangular base and P is the perimeter of that triangle.
What units should surface area be written in?
Surface area is always written in square units, such as cm², m², in², or ft². If the dimensions are entered in metres, the first answer should be in square metres. If the dimensions are entered in feet, the first answer should be in square feet.
When should I stop using a general surface area calculator?
Stop when the real object is no longer one clean solid. Composite roofs, frustums, pipes with wall thickness, shapes with cut-outs, and objects with hidden contact faces usually need to be split into exposed pieces or handled with a more specific calculator.
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