Capsule Surface Area Calculator

Enter the values of base radius, height to calculate top & bottom surface area, Lateral and total surface area. For more understanding read the solved examples and formulas below.

Base radius (r)

Height (h)

Top surface area

Bottom surface area

Lateral surface area

Total surface area

The Capsule Surface Area Calculator is a powerful online calculator to help Professionals to helps them accurately design and construct capsule shapes objects. Here we have explored more with formulas and examples.

Formula:

The formula is:

$A = 4\pi r^2 + 2\pi rh$

Variables

Variable	Meaning
A	Surface Area of the capsule
$r$	Radius of the spherical ends of the capsule
$h$	Height (or length) of the cylindrical part of the capsule

Solved Examples:

Example 1:

Given:

Radius () = 3 cm
Height () = 10 cm

Calculation	Instructions
Step 1: $A = 4\pi r^2 + 2\pi rh$	Start with the formula.
Step 2: $A = 4\pi (3)^2 + 2\pi (3)(10)$	Replace $r$ with 3 cm and $h$ with 10 cm.
Step 3: $A = 4\pi (9) + 2\pi (30)$	Calculate $r^2 = 9$ and multiply $r \times h = 30$
Step 4: $A = 36\pi + 60\pi$	Multiply $4 \times 9 = 36$ and $2 \times 30 = 60$
Step 5: $A = 96\pi$	Add the two terms.
Step 6: $A \approx 301.59 \, \text{cm}^2$	Multiply by $\pi \approx 3.14159$ to get the surface area.

Answer: The surface area of the capsule is approximately 301.59 cm².

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Capsule Surface Area Calculator

Example 2:

Given:

Radius ( $r$ ) = 5 cm
Height ( $h$ ) = 8 cm

Calculation	Instructions
Step 1: $A = 4\pi r^2 + 2\pi rh$	Start with the formula.
Step 2: $A = 4\pi (5)^2 + 2\pi (5)(8)$	Replace $r$ with 5 cm and with 8 cm.
Step 3: $A = 4\pi (25) + 2\pi (40)$	Calculate $r^2 = 25$ and multiply $r \times h = 40$
Step 4: $A = 100\pi + 80\pi$	Multiply $4 \times 25 = 100$ and $2 \times 40 = 80$
Step 5: $A = 180\pi$	Add the two terms.
Step 6: $A \approx 565.49 \, \text{cm}^2$	Multiply by $\pi \approx 3.14159$ to get the surface area.

Answer: The surface area of the capsule is approximately 565.49 cm².

What is Capsule Surface Area Calculator ?

The Capsule Surface Area Calculator used to calculate the total surface area of a capsule-shaped object. A capsule is a geometric shape that consists of a cylinder with hemispherical ends on both sides. The surface area of the capsule is made up of the surface area of the cylindrical part and the surface areas of the two hemispherical ends.

The formula $A = 4\pi r^2 + 2\pi rh$ calculates this total surface area by adding the surface area of the two hemispheres (which together form a full sphere) and the surface area of the cylindrical part.

Final Words:

Capsule Surface area calculation are essential in certain fields like pharmacology, engineering etc in shapes design. For accurate calculation use the calculator above and for better understanding see the solved examples.

Capsule Surface Area Calculator