Surface Area Calculator

Calculate the total exterior area of seven common 3D solids, inspect the component breakdown, and export the current model to a validated Excel workbook.

Cylinder Length unit: cm Area unit: cm² 2 area components

Dimensions

Shape Choose the solid whose complete exterior surface you want to measure. Length unit Changing this unit converts every stored dimension to preserve the same physical size. Radius Required positive radius. Example: 3. Use a decimal point, not a comma. Height Required perpendicular height. Example: 8 in the selected length unit. Side length Required edge length of the cube. Example: 4. Length Required first edge of the rectangular prism. Example: 6. Width Required second edge of the rectangular prism. Example: 4. Prism height Required third edge of the rectangular prism. Example: 3. Base side a Required first side of the triangular base. Example: 3. Base side b Required second side of the triangular base. Example: 4. Base side c Required third side; all three sides must satisfy the triangle inequality. Example: 5. Prism length Required distance between the two triangular bases. Example: 10. Base side Required side length of the square base. Example: 6. Pyramid height Required vertical height from the base center to the apex. Example: 7.

Live result

Total surface area 207.3451 cm²

The two circular bases contribute 27.27% and the curved side contributes 72.73%.

Total base area56.5487 cm²

Lateral surface area150.7964 cm²

Formula usedA = 2πr² + 2πrh

Area breakdown

Component	Quantity	Area	Share
Two circular bases	2 × πr²	56.5487 cm²	27.27%
Curved lateral surface	2πrh	150.7964 cm²	72.73%

Component areas are mutually exclusive and sum to the total surface area. Percentages are calculated from unrounded values.

Which surfaces contribute most?

The curved side is the largest contributor for the startup cylinder.

How to use this surface area calculator

What this calculator does

This calculator finds the total exterior area of a sphere, cube, cylinder, cone, rectangular prism, triangular prism, or right square pyramid. It also separates meaningful components such as bases and lateral faces, so you can estimate material coverage, coating area, packaging surface, insulation, sheet stock, or paint requirements. The result is a geometric identity for the dimensions supplied; it does not add allowances for seams, overlap, cutting waste, openings, wall thickness, texture, or measurement uncertainty.

When to use it

Use it when comparing how much material different container shapes require, checking homework or engineering sketches, estimating the exposed area to paint or coat, or converting a known design between metric and U.S. customary length units. Surface area is always expressed in square units. The NIST explanation of area and volume units confirms that an area calculated from a length unit is reported in the square of that unit.

How to calculate

The calculator opens with a complete cylinder example: radius 3 cm and height 8 cm. Its results and a validated example XLSX workbook are available immediately.
Select the required Shape. Only the dimensions used by that solid remain visible.
Select a Length unit. Changing units converts the stored dimensions rather than merely relabeling them, so the physical solid and its area remain equivalent.
Replace the example dimensions with positive decimal values. Use a period as the decimal separator; grouping commas, scientific notation, signs, and unit text inside a field are rejected.
Read Total surface area, the applicable component cards, the formula, the breakdown table, and – when at least two meaningful surface categories exist – the donut chart.
Select Download Excel to export the current typed inputs, outputs, formula, and breakdown. Reset clears the demonstration and all dimension fields; export is then disabled until a complete valid set is entered again.

Input guide

Shape is required and chooses the formula. Length unit is required and applies to every dimension. Radius is required for a sphere, cylinder, or cone; increasing it has a squared effect on circular base area and also changes curved area. Height is required for a cylinder or cone and must be the perpendicular height, not a cone's slant height. Side length is the required cube edge. Length, Width, and Prism height are the three required rectangular-prism edges.

For a triangular prism, Base side a, Base side b, and Base side c are required positive triangle sides, and each pair must sum to more than the remaining side. The calculator uses Heron's formula for the triangular base; see the Heron's formula reference from Wolfram MathWorld. Prism length is the required distance between the triangular bases. For a square pyramid, Base side is the square edge and Pyramid height is the perpendicular center-to-apex height. A common mistake is entering a face slant height as the vertical height.

Output guide

Total surface area is the exact sum implied by the selected formula, displayed to four decimal places in the chosen square unit. Total base area and Lateral surface area appear only when the solid has an unambiguous base-versus-side interpretation. Area of one face appears for a cube. Slant height appears for a cone or square pyramid and is a derived length. Base perimeter appears for a triangular prism. Formula used states the active identity. The summary pills report selected shape, length unit, area unit, and component count.

The Area breakdown table lists each mutually exclusive component, its geometric quantity, its area, and its percentage share. Shares near zero indicate a comparatively minor component; they are not errors if all dimensions are positive. The donut chart repeats those same current-state categories only when two to five positive components exist, so a sphere or cube correctly uses the KPI and table instead of a one-slice chart.

Worked example

For the startup cylinder, radius r = 3 cm and height h = 8 cm. The two bases total 2πr² = 18π = 56.5487 cm². The curved side is 2πrh = 48π = 150.7964 cm². Adding them gives 66π = 207.3451 cm², exactly matching the first-open result, breakdown, chart data, and workbook checkpoints. OpenStax's surface-area treatment for common solids explains the same “bases plus unwrapped lateral surface” reasoning.

Formula notes and interpretation

Surface area is two-dimensional even though the object is three-dimensional. That distinction is why the output unit is squared, not cubed. The calculator keeps full floating-point precision in the canonical model and rounds only the displayed text; the exported workbook stores typed numeric values and applies spreadsheet number formats.

SphereA = 4πr²

CubeA = 6a²

CylinderA = 2πr² + 2πrh

ConeA = πr² + πr√(r² + h²)

Rectangular prismA = 2(lw + wh + lh)

Triangular prismA = 2Aₜ + pL

Square pyramidA = s² + s√(s² + 4h²)

Practical cautions

Measure all dimensions in one consistent unit and decide whether the project needs the complete exterior area or only an exposed subset. A closed cylinder includes two bases; an open tank may include one or none. A real coating estimate should multiply the geometric area by the product's coverage rate and then add a project-specific waste factor. For very thin or irregular objects, a simple ideal solid may not represent the true surface accurately.