5 × 3 × 2 cm box
2(15 + 10 + 6) = 62 cm²
The two 5 × 3 cm bases contribute 30 cm². The four side faces contribute 32 cm². Total surface area is 62 cm², or exactly 0.0062 m².
Geometry and measurement
Surface Area Calculator
Measure the outside of a closed solid, with separate base and lateral areas where they apply.
Calculate a solid's surface area
Total surface area
Choose a shape and enter its dimensions, then select Calculate.
- Lateral area (sides)
- Both bases combined
- Cone slant height
Calculations run in your browser. Press Enter to calculate. Successful results appear in this tab's Recent calculations. Ideal shapes do not include seams, waste, wall thickness, or measurement uncertainty.
Worked examples
Cone: radius 3 cm, height 4 cm
Slant height = √(3² + 4²) = 5 cm
The curved side is 15π cm² and the base is 9π cm². Together they give 24π, approximately 75.398224 cm². Using the perpendicular height 4 in place of slant height 5 would undercount the curved side.
1 ft × 6 in × 3 in box
2(12 × 6 + 12 × 3 + 6 × 3)
After converting the length to 12 inches, the total is 252 in², which is exactly 1.75 ft². Input units can differ without changing the geometry.
Formulas and calculation rules
With length l, width w, perpendicular height h, and radius r, a rectangular prism has total area 2(lw + lh + wh). Its lateral area is 2h(l + w); the two bases total 2lw. A closed cylinder has total area 2πrh + 2πr²: curved side 2πrh plus two bases 2πr².
A sphere has surface area 4πr². A right circular cone has slant height s = √(r² + h²), lateral area πrs, and total area πrs + πr². An oblique cone, a truncated cone, or a partial sphere needs a different formula.
Lengths convert to meters using exact definitions: 1 mm = 0.001 m, 1 cm = 0.01 m, 1 in = 0.0254 m, 1 ft = 0.3048 m, and 1 yd = 0.9144 m. Area conversions square the length factor. Feet and yards use international definitions, not historical survey units.
Rectangular areas and their conversions use exact rational arithmetic. Curved areas use a separate 120-significant-digit decimal context for π and square roots. A cone with a rational slant height retains that exact value. Only the final display is rounded, using half-up rounding to at most 0, 2, 4, 6, or 10 decimal places; trailing zeros are omitted. The ≈ mark identifies numerical approximation or display rounding. A positive measurement displayed as zero receives a notice. Display precision does not make physical measurements more accurate.
References: OpenStax: Volume and Surface Area for prism and cylinder geometry; OpenStax: Geometry Applications for the sphere formula; OpenStax: Surface Integrals for the right circular cone; and NIST: SI Units — Length for length definitions. See the calculation policy for shared input and rounding rules.
Common questions
How is surface area different from volume?
Surface area measures a solid's outside faces in square units. Volume measures the space inside in cubic units. Covering a box uses area; filling the box uses volume.
Does this include the top and bottom?
Yes. The main result covers the entire closed solid. A box or cylinder includes both ends; a cone includes its base. For an open cylinder without either end, use the lateral area. For a cylinder with one end, add half of the combined base area to the lateral area before rounding.
Can I enter diameter or slant height?
Convert diameter to radius by dividing by two. For a cone, enter perpendicular height, not slant height; the tool calculates slant height from the radius and perpendicular height. A tilted or oblique cone is outside this tool's scope.
Can I use this to buy wrapping material or paint?
The result is the geometric area, without overlap, seams, cutouts, material waste, or extra coats. Account for those separately. For a real object, measure the surfaces that will actually be covered.
Why is slant height shown without a squared unit?
Slant height is a distance along the cone's side. If output area is in square feet, slant height is in feet. Area and length are different measurements and use different conversion factors.