The Surface Area Calculator selects among common solids when the question asks for surface area of a named shape rather than every measure on a dedicated solid page. Choose the shape, enter its dimensions, and read lateral and total values where both apply.
Dedicated pages such as Sphere Calculator and Cylinder Calculator still own full volume and slant-height treatments. This page catches multi-shape surface area queries and links outward for deeper work.
Calculate the surface area of any solid
Surface area is the total area of the outer boundary of a three-dimensional object. Different shapes expose different inputs: radius for a sphere, radius and height for a cylinder, edge length for a cube. The selector switches formulas and labels without mixing shape definitions.
Results name lateral versus total when the solid has flat bases. Invalid combinations return a message instead of a partial number.
Calculate the surface area of a cube
A cube has six congruent square faces. One edge length a determines every face.
SA = 6 * a^2For a = 4:
SA = 6 * 16 = 96Calculate the surface area of a sphere
Sphere surface area uses the four pi r squared relation shared with the Sphere Calculator page.
SA = 4 * pi * r^2For r = 6:
SA = 144 * pi approx 452.39Calculate the surface area of a cylinder
Total surface area includes the curved wall and both circular ends.
SA = 2 * pi * r * (r + h)For r = 3 and h = 10:
SA = 78 * pi approx 245.04Calculate the surface area of a rectangular tank
A rectangular box uses the same six-face sum as the rectangular prism page.
SA = 2 * (l * w + l * h + w * h)For 3 by 4 by 5:
SA = 94Choose your shape and enter its dimensions
The selector lists solids such as cube, sphere, cylinder, rectangular prism, cone, capsule, conical frustum, pyramid and hemisphere cap variants used in the reference engine. Pick the shape that matches the wording of the problem, then fill only the fields that shape requires.
After the result appears, related links point to the dedicated calculator for volume or slant height when the next question goes beyond surface area alone.
Frequently asked questions
Which shapes are supported?
Common solids including cube, sphere, cylinder, box, cone, capsule and frustums per the selector list.
What is lateral surface area?
Curved or side faces only, excluding bases where applicable.
What is sphere SA for r=6?
144 * pi approx 452.39, matching the sphere page fixture.
How is this different from volume calculators?
This page foregrounds surface area across shapes; dedicated pages include volume and slant height depth.
Does a cube need three dimensions?
One edge length is enough because all edges match.
What is total SA for a cylinder?
2 * pi * r * (r + h) including both ends.
Where is hemisphere total SA?
Use Hemisphere Calculator for volume and base-inclusive total SA.
Can I compare box and tank?
Rectangular tank SA uses the same 2*(lw+lh+wh) formula as a rectangular prism.
Summary
Surface Area Calculator returns the measures named in the sections above, with substituted arithmetic for every formula and a labelled figure drawn to the entered dimensions. Worked numbers on this page match the geometry reference fixtures.