Rectangular Prism Calculator

A prism with rectangular bases faces is known as a rectangular prism. Two basic types of the rectangular prism are right rectangular prism and oblique rectangular prism. Formulas that are helpful to find the unknown parameters of a rectangular prism by providing any three known details are mentioned here. Go through the following sections and use them whenever required.

• The volume of Rectangular Prism Formula:
  • Volume V = lwh
• Surface Area of Rectangular Prism Formula:
  • Surface Area S = 2(lw + lh + wh)
• Space Diagonal of Rectangular Prism Formula:
  • Diagonal length d = √(l² + w² + h²)

Rectangular Prism Calculations:

• If the surface area, length, and width of rectangular prism are given, then
  • Height h = (S - 2lw) / (2l + 2w)
  • Diagonal length d = √(l² + w² + h²)
  • Volume V = lwh
• If the length, volume, and width of rectangular prism are given, then
  • Height h = V / lw
  • Surface Area S = 2(lw + lh + wh)
  • Diagonal length d = √(l² + w² + h²)
• If diagonal length, length, width of a rectangular prism are given, then
  • Height h = √(d² - l² - w²)
  • Volume V = lwh
  • Surface Area S = 2(lw + lh + wh)
• If volume, width, and height of a prism are known, then
  • Length l = V / wh
  • Diagonal d = √((V / wh)² + w² + h²)
  • Surface Area S = 2(lw + lh + wh)
• If diagonal length, width, height of a rectangular prism are given, then
  • Length l = √(d² - w² - h²)
  • Volume V = √(d² - w² - h²) * wh
  • Surface Area S = 2(lw + lh + wh)
• If the surface area, width, height of a prism are given, then
  • Length l = (S - 2wh) / (2w + 2h)
  • Volume V = [(S - 2wh) / (2w + 2h)] * wh
  • Diagonal d = √([(S - 2wh) / (2w + 2h)]² + w² + h²)
• If the rectangular prism height, length, diagonal are given, then
  • Width w = √(d² - h² - l²)
  • Surface Area S = 2(lh + (l +h) * (√(d² - h² - l²)))
  • Volume V = √(d² - h² - l²) * lh
• If the rectangular prism volume, height, width are known, then
  • Width w = V / lh
  • Diagonal length d = √(l² + (V / lh)² + h²)
  • Total Surface Area S = 2(lh + (l + h) * (V / lh))
• If the rectangular prism total surface area, length, height are given, then
  • Width w = (S - 2lh) / (2l + 2h)
  • Volume V = lh * (S - 2lh) / (2l + 2h)
  • Diagonal d = √(((S - 2lh) / (2l + 2h))² + l² + h²)

Where,

l is the rectangular prism length

w is the width of a rectangular prism

h is the height of a rectangular prism

V is volume

S is total surface area

d is the rectangular prism space daigonal length

Get the detailed steps to calculate the volume, total surface area, length, diagonal, width, and height of the rectangular prism easily. The steps are along the lines

Rectangular Prism Total Surface Area:

• Check the rectangular prism height, width, and length from the question.
• Once multiply combination of any two parameters.
• Sum up the obtained three product values.
• Double the result to get the total surface area.

Rectangular Prism Space Diagonal Length:

• Observe the length, height, and width of a rectangular prism.
• Square each value.
• Add the squares and apply square root to it.
• Finally, the obtained value is called space diagonal length.

Rectangular Prism Length:

• Process 1:
  • Get volume, width, and height.
  • Divide the volume by product of height, width to check the length.
• Process 2:
  • Check out the rectangular prism surface area, height, and width.
  • Subtract surface area from the double product of width, height.
  • Add up width, height and multiply it with 2.
  • Divide the result from step 2 by step 3.
• Process 3:
  • Find the diagonal length, width, and height.
  • Subtract diagonal square from width square and height square.
  • Apply square root to the output to check the length.

Rectangular Prism Volume:

• Find the rectangular prism length, width, and height.
• Multiply all three parameters to check the volume.

Rectangular Prism Width:

• Process 1:
  • Observe the prism volume, height, and length.
  • Divide volume by product of length and height to get the width.
• Process 2:
  • Find out the surface area, length, and height.
  • Multiply length, height, and double it.
  • Subtract total surface area from it.
  • Add length, height, and double the sum.
  • Divide the subtracted value by the result from the above step to check width.
• Process 3:
  • Get the rectangular prism diagonal, length, and height.
  • Subtract diagonal square from the length square, and height square.
  • Apply square root to the output to know the width.

Rectangular Prism Height:

• Process 1:
  • Get the rectangular prism length, width, and surface area from the question.
  • Get the product of length, width, and 2.
  • Add double length and double width.
  • Subtract the product from the surface area.
  • Divide the result by step 3 to check the height.
• Process 2:
  • Check rectangular prism volume, width, and length.
  • Divide volume by product of length and width to obtain height.
• Process 3:
  • Get the square of diagonal, length, and width.
  • Subtract diagonal square from the length square, width square.
  • Apply square root to the result to check the height.

Example 1: Find the volume, surface area, length of a rectangular prism whose diagonal, width, and height are 10.77 cm, 6 cm, and 4 cm, respectively?

Solution:

Given that,

Rectangular Prism diagonal d = 10.77 cm

Width w = 6 cm

Height h = 4 cm

Rectangular Prism Length formula is l = √(d² - w² - h²)

l = √(10.77² - 6² - 4²)

= √(116 - 36 - 16) = √(116 - 52)

= √(64) = 8 cm

Volume formula is V = √(d² - w² - h²) * wh

V = √(10.77² - 6² - 4²) * 6 * 4

= √(116 - 36 - 16) * 24 = √(64) * 24

= 8 * 24 = 192 cm³

Surface Area S = 2(√(d² - w² - h²)(w + h) + wh)

S = 2(6 * 4 + √(10.77² - 6² - 4²) (6 + 4)

= 2(24 + 10√(116 - 36 - 16))

= 2(24 + 10√64)

= 2(24 + 10 * 8) = 2(24 + 80)

= 2(104) = 208 cm²

∴ Rectangular prism length is 8 cm, width is 6 cm, height is 4 cm, volume is 192 cm³, daigonal length is 10.77 cm, and surface area is 208 cm².

Example 2: Rectangular prism length, width, and height are 82 mm, 40 mm, 25 mm. Calculate the prism surface area, volume, and diagonal length?

Solution:

Given that,

Rectangular prism length l = 82 mm

Rectangular prism width w = 40 mm

Rectangular Prism Height h = 25 mm

Volume V = lwh

V = 82 * 40 * 25

= 82,000 mm³

Surface Area S = 2(lw + lh + wh)

S = 2(82 * 40 + 40 * 25 + 25 * 82)

= 2(3280 + 1000 + 2,050)

= 2(6,330) = 12660 mm²

Diagonal length d = √(l² + w² + h²)

d = √(82² + 40² + 25²)

= √(6724 + 1600 + 625)

= √(8,949) = 94.59 mm

∴ Rectangular prism length is 82 mm, width is 40 mm, height is 25 mm, volume is 82,000 mm³, daigonal length is 94.59 mm, and surface area is 12660 mm².

Take the help of free online calculators provided at Areavolumecalculator.com website regarding geometry or conversions.

1. How do you find the missing side of a rectangular prism when given the volume?

You can simply calculate the missing side of a rectangular prism when you have volume, other 2 sides dimensions. Divide the volume by product of given two dimensions to check the unknown side length.

2. What is the perimeter of a rectangular prism and how you calculate it?

Rectangular prism perimeter is the length of the outer line of the prism. The formula to get the prism perimeter is 2(length) + 2(width). Substitute the values in this formula and perform required arithmetic operations to get the perimeter.

3. What are the properties of a rectangular prism?

Each rectangular prism has 6 regular faces, 8 vertices, and 12 edges.

Opposite faces are in rectangle shape.

It has a rectangular cross-section.

4. What is another name for a rectangular prism?

Other name for rectangular prism is cuboid.