Surface Area Calculator

Calculate surface area of common 3D shapes including sphere, cylinder, and cone.

By Konstantin Iakovlev · Updated September 2026 · Source: Khan Academy

Surface Area

150.00

Calculation

Formula6 x side^2
Surface Area150.00 sq units

Use the Surface Area Calculator above to calculate your results. Enter your values and see instant results — all calculations run in your browser.

Disclaimer: This calculator is for informational purposes only. Results are estimates based on the information you provide and the assumptions described on this page.

How It Works

Cubes, spheres, cylinders, and cones each have a total outer surface that this tool measures in a single step. Engineers and builders rely on those figures for everyday decisions, from sizing the sheet metal a part will consume to estimating how much paint or coating a structure needs.

Behind each result is the standard geometric formula for the shape. A cube with side 's' has 6s². A sphere's surface area (A) equals 4πr², where 'r' is the radius. A cylinder uses 2πrh + 2πr², which adds the two circular bases to the curved side wall, with 'r' as the radius and 'h' as the height. A cone follows πr(r + √(h² + r²)), combining its circular base with the slanted lateral surface, again with 'r' as the radius and 'h' as the height.

Accurate output depends on entering every measurement in the same unit, since mixing units throws off the final number. Watch the distinction between diameter and radius as well: the radius is half the diameter, and swapping the two is the usual source of error. Note also that the values here represent total surface area including the bases, so check whether your project actually calls for the lateral surface alone.

Example: Calculating Paint for a Cylindrical Water Tank

  1. 1 A construction company needs to repaint a cylindrical water tank. The tank has a radius of 5 meters and a height of 12 meters. The paint costs $35 per square meter.
  2. 2 Using the cylinder formula (2πrh + 2πr²): A = 2 * π * 5m * 12m + 2 * π * (5m)² = 120π m² + 50π m² = 170π m² ≈ 534.07 m².
  3. 3 The total surface area of the water tank is approximately 534.07 square meters.
  4. 4 To calculate the total paint cost, multiply the surface area by the paint cost per square meter: 534.07 m² * $35/m² = $18,692.45. That total includes the bottom of the tank; if the tank sits on a foundation and the base is not painted, subtract πr² = 78.54 m² to get 455.53 m², or 455.53 m² × $35/m² = $15,943.55.

Source: Khan Academy · Last updated: September 2026

Frequently Asked Questions

How do I calculate the surface area of a cylinder?
The total surface area of a cylinder is 2*pi*r^2 + 2*pi*r*h, where r is the radius and h is the height. The first term covers the two circular ends, and the second is the lateral surface (the curved side). For an open-top cylinder, use pi*r^2 + 2*pi*r*h.
What is the surface area of a sphere?
The surface area of a sphere is 4*pi*r^2, where r is the radius. For example, a sphere with a 5-inch radius has a surface area of 4 x 3.14159 x 25 = 314.16 square inches.
How is surface area different from volume?
Surface area measures the total area of the outside of a 3D shape (in square units), while volume measures the space inside (in cubic units). Surface area determines how much material you need to cover an object, while volume determines how much it can hold.

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