Use this **surface area of a cuboid calculator** a **mathematical tool** designed to **compute** the **total area** of all faces of a **cuboid** (also known as a **rectangular prism**).

A cuboid is a **three-dimensional** geometric shape with **six rectangular faces**. It’s characterized by its **length** (l), **width** (w), and **height** (h). The **surface area calculator** takes these three measurements as input and **calculates** the total surface area.

For example, let’s consider a cuboid with the following dimensions:

**Length (l)**= 10 cm**Width (w)**= 5 cm**Height (h)**= 3 cm

## Surface Area of a Cuboid Calculator

Length | Width | Height | Surface Area | Conversion (if applicable) |
---|---|---|---|---|

10 cm | 6 cm | 4 cm | 248 cm² | 0.0248 m² (1 m² = 10000 cm²) |

2.5 m | 1.8 m | 3 m | 35.1 m² | 351000 cm² (1 m² = 10000 cm²) |

15 in | 9 in | 7 in | 726 in² | 5.0417 ft² (1 ft² = 144 in²) |

4 ft | 3 ft | 2.5 ft | 71 ft² | 6.5968 m² (1 m² ≈ 10.7639 ft²) |

1.2 m | 0.8 m | 0.5 m | 3.32 m² | 33200 cm² (1 m² = 10000 cm²) |

**Related Tools**

## Surface Area Of A Cuboid Calculation Formula

The **formula** for calculating the surface area of a cuboid is:

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

Where:

**l**= length**w**= width**h**= height

This formula **accounts** for all six faces of the cuboid:

- Two faces with area
**l × w**(top and bottom) - Two faces with area
**l × h**(front and back) - Two faces with area
**w × h**(left and right sides)

Consider a cuboid with dimensions:

**Length (l)**= 8 m**Width (w)**= 4 m**Height (h)**= 3 m

**Applying the formula**:

- Calculate
**lw**: 8 × 4 = 32 - Calculate
**lh**: 8 × 3 = 24 - Calculate
**wh**: 4 × 3 = 12 **Sum**these products: 32 + 24 + 12 = 68**Multiply by 2**: 68 × 2 = 136

The **surface area** of this cuboid is **136 square meters (m²)**.

## How to find the surface area of a cuboid

To find the **surface area** of a cuboid, follow these steps:

**Measure the dimensions**: Determine the**length**,**width**, and**height**of the cuboid using a**consistent unit**of measurement.**Apply the formula**: Use the formula**Surface Area = 2(lw + lh + wh)**.**Calculate each component**:- Multiply
**length by width (lw)** - Multiply
**length by height (lh)** - Multiply
**width by height (wh)**

- Multiply
**Sum the products**: Add the results from step 3.**Multiply by 2**: Double the sum to account for all six faces.**Review the result**: The final number represents the**total surface area**in**square units**.

## What is the total surface area of a cuboid

The **total surface area** of a cuboid is the **sum** of the areas of all six rectangular faces. It represents the entire outer “**skin**” of the cuboid if it were to be **unfolded** and laid flat.

The total surface area includes:

- The area of the
**top and bottom faces**(2 × length × width) - The area of the
**front and back faces**(2 × length × height) - The area of the
**left and right side faces**(2 × width × height)

This **comprehensive measurement** is crucial in various **real-world applications**, such as:

**Determining**the amount of paint needed to cover a box**Calculating**the material required for packaging**Estimating**heat loss or gain through the walls of a room

## What is the surface area of the cuboid 3 5 2?

Let’s calculate the **surface area** of a cuboid with dimensions 3, 5, and 2 units:

**Length (l)**= 5 units**Width (w)**= 3 units**Height (h)**= 2 units

Using the formula **Surface Area = 2(lw + lh + wh)**:

- Calculate
**lw**: 5 × 3 = 15 - Calculate
**lh**: 5 × 2 = 10 - Calculate
**wh**: 3 × 2 = 6 **Sum**these products: 15 + 10 + 6 = 31**Multiply by 2**: 31 × 2 = 62

The **surface area** of the cuboid 3 5 2 is **62 square units**.

## Surface Area Of A Cuboid Conversion Table

Original Dimensions | Converted Dimensions | Surface Area | Conversion Equation |
---|---|---|---|

5 ft × 3 ft × 2 ft | 1.524 m × 0.914 m × 0.610 m | 4.65 m² | 1 ft = 0.3048 m |

20 in × 15 in × 10 in | 50.8 cm × 38.1 cm × 25.4 cm | 7,742.0 cm² | 1 in = 2.54 cm |

1 yd × 2 yd × 1.5 yd | 0.914 m × 1.829 m × 1.372 m | 10.97 m² | 1 yd = 0.9144 m |

100 cm × 50 cm × 30 cm | 1 m × 0.5 m × 0.3 m | 1.9 m² | 1 cm = 0.01 m |