Surface Area Calculator - Cube, Sphere, Cylinder & Cone
Calculate the total surface area of a cube, sphere, cylinder, or cone. Enter dimensions and get the result instantly with the formula used.
Select a 3D shape, enter its measurements, and the calculator returns the total surface area with the relevant formula.
Surface Area Calculator - Cube, Sphere, Cylinder & Cone
Calculate the total surface area of a cube, sphere, cylinder, or cone. Enter dimensions and get the result instantly with the formula used.
About the surface area calculator
Surface area is the total area of all the outer faces of a three-dimensional object. Calculating surface area is essential in many practical contexts: determining how much paint is needed to coat a tank, how much material is required to wrap a gift, how much sheet metal goes into a pipe, or how much fabric covers a tent. The surface area calculator handles the four most commonly encountered solid shapes: cube, sphere, cylinder, and cone.
A cube has six identical square faces. If each side has length a, the area of one face is a² and the total surface area is 6a². For example, a dice with a side of 1.5 cm has a surface area of 6 × 1.5² = 13.5 cm². The formula is straightforward but easy to get wrong if you confuse side length with volume or edge count.
A sphere has no edges or vertices — its entire surface is a smooth, curved shell. The surface area of a sphere with radius r is 4πr². Archimedes proved this remarkable result by showing that the surface area of a sphere equals the lateral surface area of the circumscribed cylinder. For a basketball with a radius of 12 cm, the surface area is 4π × 144 ≈ 1809.6 cm².
A cylinder consists of two circular bases and a curved lateral surface. The area of each base is πr², and the lateral surface, when unrolled, is a rectangle of width 2πr and height h, giving an area of 2πrh. The total surface area is 2πr² + 2πrh = 2πr(r + h). A can of soup with r = 3.5 cm and h = 11 cm has a total surface area of 2π × 3.5 × (3.5 + 11) ≈ 318.9 cm².
A cone has one circular base and a curved lateral surface that tapers to a point (apex). The slant height l = √(r² + h²) is the distance from the apex to the rim of the base along the slope. The lateral surface area is πrl, and the base area is πr². Total surface area = πr(r + l). An ice cream cone with r = 2.5 cm and h = 10 cm has a slant height of √(6.25 + 100) ≈ 10.31 cm and a total surface area of π × 2.5 × (2.5 + 10.31) ≈ 100.6 cm².
All four formulas give results in square units — the same unit of length squared. If you enter dimensions in centimetres, the surface area is in cm². Keep your units consistent within a single calculation. The calculator works with any positive real number, so you can use metric or imperial measurements as long as you apply the same unit throughout.
Surface area examples
Four worked examples — one for each shape — with real dimensions and verified results.
| Shape & Dimensions | Surface Area | Formula used |
|---|---|---|
| Cube: side = 1.5 cm | 13.5 cm² | SA = 6 × 1.5² = 6 × 2.25 = 13.5 cm². A standard six-sided die. |
| Sphere: radius = 12 cm | ≈ 1809.56 cm² | SA = 4π × 12² = 4π × 144 ≈ 1809.56 cm². Basketball surface area. |
| Cylinder: radius = 3.5 cm, height = 11 cm | ≈ 318.86 cm² | SA = 2π × 3.5 × (3.5 + 11) = 2π × 3.5 × 14.5 ≈ 318.86 cm². A typical soup can. |
| Cone: radius = 2.5 cm, height = 10 cm | ≈ 100.55 cm² | Slant height l = √(2.5² + 10²) ≈ 10.308 cm. SA = π × 2.5 × (2.5 + 10.308) ≈ 100.55 cm². An ice cream cone. |
How to use the surface area calculator
- Click the button for the shape you want to calculate: Cube, Sphere, Cylinder, or Cone.
- Enter the required dimensions. Cube needs one side length; Sphere needs radius; Cylinder needs radius and height; Cone needs radius and height.
- Click Calculate Surface Area. The total surface area appears with the formula applied.
- Use the example buttons below the table to load a pre-filled example for any shape.
- Click Reset to clear all fields and select a different shape.
Surface area FAQ
What is the difference between surface area and volume?
Surface area is the total area of the outer faces of a 3D solid, measured in square units (cm², m², in²). Volume is the amount of space the solid encloses, measured in cubic units (cm³, m³, in³). For a cube of side 3 cm, the surface area is 54 cm² while the volume is 27 cm³.
What units does the surface area calculator use?
The calculator uses whatever units you enter for the dimensions. If you enter centimetres, the result is in square centimetres (cm²). If you enter metres, the result is in square metres (m²). There is no built-in unit conversion, so make sure all inputs use the same unit.
How is the slant height of a cone calculated?
The slant height l is the straight-line distance from the apex (tip) of the cone to any point on the rim of the base. By the Pythagorean theorem, l = √(r² + h²), where r is the base radius and h is the vertical height. The calculator computes slant height automatically from r and h.
Why is the sphere surface area formula 4πr²?
Archimedes showed that the curved surface of a sphere equals the lateral surface of the cylinder that exactly wraps around it (same radius and height equal to the sphere's diameter 2r). That cylinder's lateral area is 2πr × 2r = 4πr². This elegant equality is one of the most celebrated results in classical geometry.
Can I calculate surface area in imperial units?
Yes. Enter dimensions in inches, feet, or yards and the result will be in square inches, square feet, or square yards respectively. Just keep all inputs in the same unit. The formulas are unit-agnostic.
Does the cone formula include the base?
Yes. The formula used here is total surface area = πr(r + l), which includes both the circular base (area πr²) and the lateral curved surface (area πrl). If you only need the lateral surface area — for example, for an open-ended conical funnel — the answer is πrl, which equals the total minus the base area πr².