Find the total and lateral surface area of common solids.
A = 2πr² + 2πrh. A cylinder with radius 5 cm and height 12 cm has a total surface area of 534.07075111 cm².
Surface area is the total area of all the outer faces of a solid. Choose a cube, rectangular prism, sphere, hemisphere, cylinder, cone, rectangular pyramid or capsule, enter the dimensions and the calculator gives the total surface area, the lateral (side) area and base area where they apply, and conversions to other units.
Surface area tells you how much paint, wrapping or material you need, while volume tells you how much it holds — see the Volume Calculator. Related: Area Calculator, Circle Calculator and Pythagorean Theorem Calculator (for slant heights).
The calculator applies the standard method step by step.
| Item | Value |
|---|---|
| Base area | 78.5398163397 |
| Lateral (side) area | 376.991118431 |
| In cm² | 534.07075111 |
| Square meters (m²) | 0.0534070751 |
| Square centimeters (cm²) | 534.07075111 |
| Square feet (ft²) | 0.5748689721 |
| Square inches (in²) | 82.7811319844 |
| Hectares | 5.3407e-6 |
| Acres | 1.3197e-5 |
| Shape | Surface area |
|---|---|
| Cylinder r5 h12 | 534.07075111 cm² |
| Sphere r5 | 314.159265359 cm² |
| Cone r3 h4 | 75.3982236862 cm² |
| Cube a5 | 150 cm² |
| Box 5×4×3 | 94 cm² |
| Shape | Formula |
|---|---|
| Cube | 6 a² |
| Rectangular prism | 2 (lw + lh + wh) |
| Sphere | 4 π r² |
| Hemisphere (solid) | 3 π r² |
| Cylinder | 2 π r (r + h) |
| Cone | π r (r + l), l = √(r² + h²) |
| Rectangular pyramid | l w + l √(h² + w²/4) + w √(h² + l²/4) |
| Capsule | 4 π r² + 2 π r h |
The total area of all the outer surfaces of a 3-D shape.
A = 4 × π × r². A sphere of radius 2 has a surface area of about 50.27.
The area of the sides only, not including the top and bottom.
π r² for the base plus π r l for the side, where l = √(r² + h²) is the slant height.
6 × a², since a cube has six identical square faces.
Surface area measures the outside (square units); volume measures the space inside (cubic units).
It uses the standard method: sphere A = 4π r² cylinder A = 2π r (r + h) cone A = π r (r + √(r² + h²)) The full working and a worked example are shown on this page.
Decimal results use standard double-precision arithmetic (about 15–16 significant digits). Tools that work with whole numbers — big numbers, factors, bases, combinations — use exact integer arithmetic, so no digits are lost.
Yes for checking your work and learning the method. The steps and formula are shown so you can understand the answer, but follow your teacher's rules about calculators in exams.
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