How do I calculate the surface area of a cube?

Surface area of a cube = 6 x side squared. Formula: SA = 6s^2. Example: a cube with side = 4 cm has SA = 6 x 16 = 96 cm squared. A cube has 6 identical square faces.

How do I calculate the surface area of a cylinder?

SA of a cylinder = 2 x pi x radius x height + 2 x pi x radius squared. The first term is the lateral surface; the second adds the two circular ends. Example: radius=3, height=10: SA = 2 x pi x 3 x 10 + 2 x pi x 9 = 188.5 + 56.55 = 245.04 square units.

What is the surface area of a sphere?

Surface area of a sphere = 4 x pi x radius squared. Example: a sphere with radius 5 cm has SA = 4 x 3.14159 x 25 = 314.16 cm squared. Interestingly, this equals exactly 4 times the area of a great circle of the same radius.

What is the difference between surface area and volume?

Surface area measures the total area of all outer surfaces of a 3D object (measured in square units). Volume measures the space enclosed inside the object (measured in cubic units). They scale differently: doubling all dimensions increases surface area by 4x but volume by 8x.

Surface Area Calculator

Select a 3D shape and enter its dimensions to calculate the surface area.

Surface Area Formulas & Reference

All shapes at a glance

Shape	Total Surface Area	Lateral SA	Variables
Cube	SA = 6s²	4s²	s = side
Rectangular Box	SA = 2(lw + lh + wh)	2(lh + wh)	l, w, h
Sphere	SA = 4πr²	4πr²	r = radius
Cylinder	SA = 2πr² + 2πrh	2πrh	r, h
Cone	SA = πr² + πrl	πrl	r, h, l = slant = √(r²+h²)

What is surface area?

Surface area is the total area of all faces (or surfaces) of a 3D object. It is measured in square units (cm², m², in², ft²). Surface area determines how much material is needed to cover or paint an object and is critical in packaging, heat transfer, and engineering design.

Worked example — Cylinder

A tin can has radius r = 4 cm and height h = 10 cm.

Lateral SA = 2πrh = 2π × 4 × 10 = 80π ≈ 251.33 cm²
Two circular ends = 2πr² = 2π × 16 = 32π ≈ 100.53 cm²
Total SA = 80π + 32π = 112π ≈ 351.86 cm²

Worked example — Cone

An ice cream cone has base radius r = 3 cm and height h = 8 cm.

Slant height l = √(r² + h²) = √(9 + 64) = √73 ≈ 8.544 cm
Lateral SA = πrl = π × 3 × 8.544 ≈ 80.50 cm²
Base = πr² = π × 9 ≈ 28.27 cm²
Total SA ≈ 108.77 cm²

Worked example — Sphere

A ball has radius r = 5 m.

SA = 4πr² = 4π × 25 = 100π ≈ 314.16 m²

Total vs. Lateral surface area

Total SA includes every face (top, bottom, sides). Lateral SA includes only the side surfaces — useful for calculating the amount of paint needed on the side of a tank, for example.

References

Weisstein, E.W. Surface Area. MathWorld — A Wolfram Web Resource.
Stewart, J. (2015). Calculus: Early Transcendentals (8th ed.). Cengage Learning. (Chapter 15: Multiple Integrals — Surface Area)
Hibbeler, R.C. (2016). Engineering Mechanics: Statics (14th ed.). Pearson. (Appendix: Geometric Properties of Solids)

Related Calculators

Surface Area for Common 3D Shapes

Surface area is the total area of all faces of a 3D object, measured in square units. A rectangular box has 6 faces: surface area = 2(lw + lh + wh). A cylinder has two circular caps plus a lateral surface: SA = 2πr² + 2πrh. A sphere: SA = 4πr². A cone: SA = πr² + πrl, where l is the slant height. Use surface area to calculate how much paint, wrapping material, or coating you need for three-dimensional objects.

Surface area calculations are critical in packaging design (minimizing material for a given volume), heat exchange (fins on radiators maximize SA for heat dissipation), biology (lung alveoli and intestinal villi increase SA for gas/nutrient absorption), and chemistry (catalyst surface area affects reaction rate). The sphere has the minimum SA for a given volume — which is why bubbles and cells are roughly spherical. Increasing SA without increasing volume is achieved by folds, branches, or fractal structures.

Surface Area Formulas

Shape	Formula	Example (r=5, h=10)
Sphere	4πr²	4π(25) ≈ 314.2 cm²
Cylinder	2πr(r+h)	2π(5)(15) ≈ 471.2 cm²
Cube	6s²	6(25) = 150 cm² (s=5)
Cone	πr(r+l)	Needs slant height l