Capsule Calculator

A capsule is a basic three-dimensional geometric shape having a cylinder with hemisphere ends. Other names of the capsule are spherocylinder or stadium of revolution. Here we are giving the basic formulas to calculate the capsule shape volume, surface area, radius, side length, and circumference. Check the following sections and follow them.

• Volume of a Capsule Formula:
  • Volume V = πr²((4/3)r + a)
• The Surface Area of a Capsule Formula:
  • Surface Area S = 2πr(2r + a)
• Circumference of a Capsule Formula:
  • Circumference C = 2πr

Capsule Calculations

Make use of the following additional formulas along with the formulas mentioned above to check the capsule surface area, volume, radius, side length, and circumference if any two measures are known.

• If volume, radius of the capsule are given, then
  • Side length a = (V/(πr²)) - (4r/3)
  • Circumference C = 2πr
  • Surface area S = 2πr(2r + a)
• If surface area, radius of the capsule are given, then
  • Side length a = (S / 2πr) - 2r
  • Volume V = πr²((4/3)r + (S / 2πr) - 2r)
  • Circumference C = 2πr
• If circumference, side length of a capsule are given, then
  • Radius r = C / 2π
  • Surface area S = C(C / π + a)
  • Volume V = πr²((4/3)r + a)
• If side length, radius of the capsule are known, then
  • Surface Area S = 2πr(2r + a)
  • Circumference C = 2πr
  • Volume V = πr²((4/3)r + a)

Where, a is the side length

r is the radius

V is the volume

S is the surface area

C is the circumference

A geometric solid capsule is a sphere of the radius that has been cut in half through the center, and the two ends are then separated by the cylinder of radius and side length. If you would like to check those parameters manually, here are the simple steps. We have listed some of them. Find the one that is most convenient for you to solve the questions related to capsule shape easily.

Capsule Surface Area

• Get the side length, the radius of the capsule from the question.
• Double the radius, add side length to it.
• Find the product of double radius, π.
• Multiply the values obtained from the above two steps to check surface area.

Capsule Circumference

• Check out the capsule radius from the question.
• Multiply the radius with π and 2 to see circumference.

Capsule Volume

• Make a note of the side length, radius.
• Multiply the radius with (4/3) fraction, add side length to it.
• Square the radius and multiply it with π.
• Multiply the values from step 2 & step 3 to check the volume.

Capsule Radius

• Check the circumference of the capsule.
• Divide the circumference by double the radius to obtain radius value.

Capsule Side Length

• Process 1:
  • Note down the volume, the radius of the capsule.
  • Square the radius and multiply it with π.
  • Divide the volume by the result from the above step.
  • Multiply the radius by (4/3).
  • Subtract volume division from the radius multiplication fraction to get side length.
• Process 2:
  • Get surface area, a radius of the capsule from the question.
  • Divide the surface area by the product of 2, π, and radius.
  • Subtract the double radius from the result to check Capsule Side Length.

Example 1: Calculate the capsule side length, surface area, and circumference. If the capsule volume is 340 m³, the radius is 2.5 m.

Solution:

Given that,

Volume V = 340 m³

Radius r = 2.5 m

Circumference formula is C = 2πr

= 2 * π * 2.5

= 5 π = 5 * 3.14

= 15.7 m

Side length a = (V/(πr²)) - (4r/3)

= (340/(π * 2.5²)) - ((4 * 2.5)/3)

= (340/(π * 6.25)) - (10/3)

= (340/(3.14 * 6.25)) - (3.33)

= (340/19.62) - (3.33)

= 17.324 - 3.33

= 13.99 m

Curved Surface area of the hemisphere = 2πr²

= 2 * π * 2.5²

= 2 * π * 6.25

= 12.5 * π

= 12.5 * 3.14 = 39.25 m²

Curved surface area of the cylinder = 2πra

= 2 * π * 2.5 * 13.99

= 69.96 * π = 69.95 * 3.14

= 219.643

Inner surface area of the vessel = Curved Surface area of the hemisphere + Curved surface area of the cylinder

= 219.643 + 39.25

= 258.893 m²

Surface Area S = 2πr(2r + a)

= 2 * π * 2.5 (2 * 2.5 + 13.99)

= 5 * π (5 + 13.99)

= 5 * π (18.99)

= 5 * 3.14 (18.99)

= 15.7 * 18.99

= 298.143 m²

∴ The capsule radius is 2.5 m, side length is 13.99 m, the surface area is 298.143 m², the inner surface area is 258.893 m², the circumference is 15.7 m, and the volume is 34. m³.

Example 2: The diameter of the capsule is 14 cm and the side length is 24 cm. What are the capsule total surface area, volume, and circumference?

Solution:

Given that,

Capsule side length a = 24 cm

Diameter = 14 cm

Radius r = diameter / 2 = 14 / 2 = 7 cm

Volume of the capsule V = πr²((4/3)r + a)

= π * 7² * ((4/3) * 7 + 24)

= 49 * π ((28/3) + 24)

= 49 * π (9.33 + 24)

= 49 * π (33.33)

= 49 * 3.14 (33.33)

= 5128 cm³

Surface Area S = 2πr(2r + a)

= 2 * π * 7 (2 * 7 + 24)

= 14 * π (14 + 24)

= 14 * π (38)

= 14 * 3.14 * 38

= 1,670.48 cm²

Circumference C = 2πr

= 2 * 3.14 * 7

= 43.96 cm

∴ The capsule radius is 7 cm, the diameter is 14 cm, the side length is 24 cm, the surface area is 1,670.48 cm², the circumference is 43.96 cm, and the volume is 5128 cm³.

Clarify your queries right after class and seek help on geometry concepts all at one place on Areavolumecalculator.com

1. How do you calculate the volume of a capsule?

You can compute the volume of a capsule by using its side length and radius. The basic formula is the Volume of a capsule V = πr²((4/3)r + a). Substitute the values in this formula, perform the required math operations to get the volume.

2. How do you calculate capsule fill weight?

The weight of a capsule is also known as a spherocylinder. First of all, find out the capsule radius, side length, and mean density. The formula to compute the capsule weight is M = mD * π * r² * (a - (2/3) * r). Place the values in this formula, and do further calculations to get the weight of the capsule.

3. Find the capsule side length? If the surface area is 760 mm² and the radius is 6 mm.

Surface area S = 760 mm²

Radius r = 6 mm

Side length a = (S / 2πr) - 2r

= (760 / (2 * 3.14 * 6) - 2 * 6

= (760 / 37.68) - 12 = 20.16 - 12

= 8.16 mm