Surface Area Calculator
Calculate the total surface area and lateral surface area of common 3D shapes: cube, rectangular box, sphere, cylinder, cone, and square pyramid.
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How to use this calculator
Cube: 6s². Box: 2(lw+lh+wh). Sphere: 4πr². Cylinder: 2πr(r+h). Cone: πr(r+l). Pyramid: b² + 2b·√((b/2)²+h²).
- 1
Select the 3D shape from the dropdown.
- 2
Enter the required dimensions: cube needs side length; cylinder needs radius and height; box needs length, width, and height.
- 3
Total surface area and lateral surface area are displayed instantly.
Frequently asked questions
Which input fields does each shape use?
Cube: only the first field (side). Sphere: only the first (radius). Cylinder and cone: first is radius, second is height. Square pyramid: first is the base edge, second is the vertical height. Rectangular box: first is length, second is width, third is height. Unused fields are ignored, though they must still hold numbers.
What counts as “lateral” surface area here?
The area without the base or bases. For a cube and a box that is the four sides, excluding top and bottom; for a cylinder it is the curved wall; for a cone and pyramid it is the slanted faces. With a 5-unit cube the lateral area is 100 against a total of 150.
Why does the sphere show no lateral area?
A sphere has one continuous surface with no separate base, so the tool prints “n/a” for lateral area and gives only the total, 4πr². For r = 5 that is 314.159265.
Does the pyramid height mean the slanted face height?
No, it is the vertical height from the base centre to the apex. The tool computes the slant height of each triangular face itself as √((b ÷ 2)² + h²). It handles square pyramids with the apex above the centre; rectangular-base or oblique pyramids are not covered.
What units do I get?
Square units of whatever length unit you typed. Enter centimetres to get cm², metres for m². Mixing units across fields gives meaningless results.
What input errors are caught?
The first dimension must be above zero. A cylinder, cone or pyramid also requires a positive second dimension, and a box requires all three to be positive. Blank or non-numeric fields return a prompt to enter a number in every field. Otherwise nothing is calculated.
Can it find volume or work backwards from an area?
No. It returns surface areas only, rounded to 6 decimals, and cannot solve for a missing dimension. For a cone’s volume and slant height, use the dedicated cone calculator.
Surface area calculator — six common solids
Formulas by shape
Surface area is the combined area of all faces. The calculator applies these formulas: cube 6s², box 2(lw + lh + wh), sphere 4πr², cylinder 2πr(r + h), cone πr(r + l) with l = √(r² + h²), and square pyramid b² + 2b·√((b ÷ 2)² + h²). It always reports total area and the area of the sides without the base or bases.
| Shape | Fields used | Total area | Lateral area |
|---|---|---|---|
| Cube | 5 | 150 | 100 |
| Rectangular box | 5, 4, 3 | 94 | 54 |
| Sphere | 5 | 314.159265 | n/a |
| Cylinder | 5, 4 | 282.743339 | 125.663706 |
| Cone | 5, 4 | 179.119857 | 100.58004 |
| Square pyramid | 5, 4 | 72.169906 | 47.169906 |
Worked examples with other sizes
A cube with side 3 has a total surface area of 54 and a lateral area of 36. A sphere of radius 6,371 gives 510,064,471.909788 square units, which in kilometres is close to the commonly quoted 510 million km² for Earth, even though the real planet is not a perfect sphere. A square pyramid with base 230 and vertical height 146 has a total area of 138,391.962195 and 85,491.962195 in its four slanted faces.
Why the table’s box and cube differ
The 5-unit cube and the 5 × 4 × 3 box share the first dimension but give 150 and 94. A box has two faces of each size: 5×4, 5×3 and 4×3, so 2(20 + 15 + 12) = 94. The box’s lateral area uses its height (the third field), 2 × 3 × (5 + 4) = 54. Remember the third field only matters for boxes.
Painting, wrapping and coating
Surface area tells you how much paint, wrap or coating a solid needs. Choose total area for a fully enclosed object and lateral area when the ends are open or covered by something else, such as a label on a can or the walls of a tank without a lid. Add a margin for waste and overlaps. The cylinder in the table, radius 5 and height 4, needs 125.663706 square units for its curved wall and 282.743339 with both lids.
Limits
These are right-angled, regular solids only: no hemispheres, frustums, prisms with other bases or partly filled shapes. The pyramid has a square base with the apex above its centre. Lengths must be positive and in one unit. Results are rounded to 6 decimal places, so treat very long outputs as display values rather than measured accuracy.
Learn more from an authoritative source:
WikipediaVolume Calculator
Calculate the volume of common 3D shapes: cube, rectangular box, sphere, cylinder, cone, pyramid, and ellipsoid.
Cone Calculator
Calculate the volume, slant height, lateral surface area, and total surface area of a cone from its base radius and height.
Sphere Calculator
Calculate radius, diameter, surface area, and volume of a sphere from any one known measurement.
Cylinder Calculator
Calculate the volume, lateral surface area, total surface area, and base area of a cylinder from its radius and height.
Percentage Difference Calculator
Calculate the symmetric percentage difference between two values — useful when neither value is a reference baseline.
Percent Error Calculator
Calculate the percent error between an experimental measurement and the accepted theoretical value, including absolute error and sign.
Results are estimates for informational purposes only and do not constitute professional financial, medical, legal, or technical advice. Read full disclaimer →