Surface Area Calculator

Surface area is the total area of all the faces or curved surfaces of a 3D shape, like the amount of wrapping paper needed to cover it. This calculator works out each part separately, such as the two circles and curved side of a cylinder, then adds them up and shows the breakdown.

Try:

How to use the surface area calculator

  1. Choose the shape.
  2. Enter its measurements and a unit.
  3. Press Calculate to see the total and each part.

Formula

SAcylinder=2πr2+2πrhSA_{\text{cylinder}} = 2\pi r^2 + 2\pi r h
SAsphere=4πr2SA_{\text{sphere}} = 4\pi r^2

Worked example: Cylinder r=3, h=5

  • Shape: Cylinder
  • Radius (r): 3
  • Height (h): 5
  • Unit: cm

✓ Answer checked

SA=48π≈150.79645 cm2SA = 48\pi \approx 150.79645\text{ cm}^2
two circles
56.54866856.548668
curved side
94.2477894.24778
020406080two circles: 56.548667764616276two circlescurved side: 94.24777960769379curved side
How the total surface area is made up from each face or surface.
Step-by-step working (4 steps)

  1. Use the formula Surface area

    Add up the area of every surface of the cylinder.

    SA=2πr2+2πrhSA = 2\pi r^2 + 2\pi r h

  2. Area of two circles

    Work out this part.

    ≈56.548668\approx 56.548668

  3. Area of curved side

    Work out this part.

    ≈94.24778\approx 94.24778

  4. Add the parts

    The total is the sum of all the surfaces.

    SA≈150.79645 cm2SA \approx 150.79645\text{ cm}^2
Formulas used
SA=2πr2+2πrhSA = 2\pi r^2 + 2\pi r h
How this was checked
  • ✓ The factorised formula gives the same total as adding the faces.

All lengths in cm, so the area is in square cm (cm²).

Frequently asked questions

How do I find the surface area of a cylinder?

Add the two circular ends (2πr²) to the curved side, which unrolls into a rectangle of area 2πr × h.

What is the slant height of a cone?

The distance from the tip to the edge of the base: l = √(r² + h²). It is needed for the curved surface area πrl.

Is surface area the same as volume?

No. Surface area measures the outside (square units); volume measures the space inside (cubic units).

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