Surface Area Calculator

Surface Area is evaluated from Shape, Side / Radius and Width. The calculation reports Total Surface Area, Lateral Surface Area and Base Area.

Results

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About the Surface Area Calculator

Surface Area is treated here as a quantitative relation between Shape, Side / Radius, Width and Height and Total Surface Area, Lateral Surface Area and Base Area.

The calculator uses a multi formula configuration. Each reported value is read as a direct evaluation of the stored rules with the declared field formats and units.

Formula basis:
Cylinder: SA = 2pir^2 + 2pirh
Sphere: SA = 4pir^2
Cone: SA = pir^2 + pirl, where l = sqrt(r^2+h^2)

Interpret the outputs in the order shown by the result fields. Optional inputs affect only the outputs that depend on those variables.

Formula & How It Works

The calculation applies the following relations exactly as recorded in the metadata:

Cylinder: SA = 2pir^2 + 2pirh
Sphere: SA = 4pir^2
Cone: SA = pir^2 + pirl, where l = sqrt(r^2+h^2)

Each output field is produced by substituting the supplied inputs into the relevant relation and then applying the declared rounding or text format.

Worked Examples

Example 1: Painting a Storage Tank

Inputs

shape: cylinder dim1: 10 dim3: 30
Total Surface Area: 628.3185 sq units. Lateral Surface Area: 0 sq units. Base Area: 314.1593 sq units

With Shape = cylinder, Side / Radius = 10 and Height = 30 as the stated inputs, the result is Total Surface Area = 628.3185 sq units, Lateral Surface Area = 0 sq units and Base Area = 314.1593 sq units. Each value corresponds to the declared output fields.

Example 2: Gift Box Wrapping Paper

Inputs

shape: rectangular_prism dim1: 18 dim2: 12 dim3: 6
Total Surface Area: 792 sq units. Lateral Surface Area: 360 sq units. Base Area: 216 sq units

With Shape = rectangular_prism, Side / Radius = 18, Width = 12 and Height = 6 as the stated inputs, the result is Total Surface Area = 792 sq units, Lateral Surface Area = 360 sq units and Base Area = 216 sq units. Each value corresponds to the declared output fields.

Example 3: Sphere — Basketball Leather

Inputs

shape: sphere dim1: 4.7
Total Surface Area: 277.5911 sq units. Lateral Surface Area: 277.5911 sq units. Base Area: 0 sq units

With Shape = sphere and Side / Radius = 4.7 as the stated inputs, the result is Total Surface Area = 277.5911 sq units, Lateral Surface Area = 277.5911 sq units and Base Area = 0 sq units. Each value corresponds to the declared output fields.

Example 4: Cone — Ice Cream Wafer

Inputs

shape: cone dim1: 1.5 dim3: 4.5
Total Surface Area: 14.1372 sq units. Lateral Surface Area: 7.0686 sq units. Base Area: 7.0686 sq units

With Shape = cone, Side / Radius = 1.5 and Height = 4.5 as the stated inputs, the result is Total Surface Area = 14.1372 sq units, Lateral Surface Area = 7.0686 sq units and Base Area = 7.0686 sq units. Each value corresponds to the declared output fields.

Common Use Cases

  • Calculate paint coverage for a 3D object
  • Find wrapping paper needed for a gift box
  • Determine coating material for a tank
  • Compute heat dissipation area for electronics