This **surface area of a cylinder calculator** uses the **A = 2πr² + 2πrh** formula to to compute the **total surface area** of a cylindrical object.

For example, a cylinder with a **radius** of **5 cm** and a **height** of **10 cm**:

- Input:
**Radius**=**5 cm**,**Height**=**10 cm** - The calculator processes these values using the surface area formula.
- Output:
**Total surface area**≈**471.24 cm²**.

The calculator typically requires input of the cylinder’s **dimensions**, such as its **radius** (or diameter) and **height**. Once these measurements are provided, it automatically applies the appropriate formula to calculate the **total surface area**.

## Surface Area of a Cylinder Calculator

Radius | Height | Total Surface Area | Curved Surface Area | Volume | Conversion |
---|---|---|---|---|---|

2 cm | 5 cm | 87.96 cm² | 62.83 cm² | 62.83 cm³ | 0.00880 m² |

1.5 in | 4 in | 51.84 in² | 37.70 in² | 28.27 in³ | 0.0334 m² |

0.5 m | 2 m | 7.85 m² | 6.28 m² | 1.57 m³ | 7.85 m² |

10 ft | 15 ft | 1,570.80 ft² | 942.48 ft² | 4,712.39 ft³ | 145.93 m² |

20 cm | 30 cm | 6,283.19 cm² | 3,769.91 cm² | 37,699.11 cm³ | 0.628 m² |

Conversion equation used: **1 m² = 10.7639 ft² = 10,000 cm² = 1,550 in²**.

**Related Tools**

## Surface Area of a Cylinder Formula

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

**A = 2πr² + 2πrh**

Where:

**A**is the**total surface area****π**(pi) is approximately**3.14159****r**is the**radius**of the circular base**h**is the**height**of the cylinder

This formula can be broken down into two parts:

**2πr²**: This represents the area of the two circular bases (top and bottom).**2πrh**: This represents the area of the**curved lateral surface**.

Let’s work through an example:

Consider a cylinder with a **radius** of **3 meters** and a **height** of **5 meters**.

- Calculate the area of the circular bases: $$2πr² = 2 × π × 3² ≈ 56.55 m²$$
- Calculate the area of the curved surface: $$2πrh = 2 × π × 3 × 5 ≈ 94.25 m²$$
- Sum these values to get the
**total surface area**: $$56.55 m² + 94.25 m² ≈ 150.80 m²$$

The **total surface area** of this cylinder is approximately **150.80 square meters**.

## How can you find the surface area of a cylinder?

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

**Measure the radius**: Determine the**radius**of the circular base. If you have the**diameter**, divide it by**2**to get the radius.**Measure the height**: Measure the distance between the two circular bases.**Apply the formula**: Use the formula $$A = 2πr² + 2πrh$$, where**A**is the surface area,**r**is the radius, and**h**is the height.**Calculate**: Plug in the values and compute the result. Remember to keep track of your**units**!**Round as needed**: Depending on the required precision, round your answer appropriately.

## How to calculate the surface area of a tube?

The formula is:

**A = 2π(r₁² – r₂²) + 2πh(r₁ + r₂)**

Where:

**r₁**is the**outer radius****r₂**is the**inner radius****h**is the**height**of the tube

For example, if a tube has an **outer radius** of **5 cm**, an **inner radius** of **4 cm**, and a **height** of **10 cm**:

- $$A = 2π(5² – 4²) + 2π × 10 × (5 + 4)$$
- $$A ≈ 2π(25 – 16) + 2π × 10 × 9$$
- $$A ≈ 56.55 + 565.49$$
- $$A ≈ 622.04 cm²$$

A **tube** is essentially a **hollow cylinder**. To calculate its **surface area**, you need to consider both the inner and outer surfaces.

## How do you find the height of a cylinder?

If you know the **surface area** and **radius** of a cylinder, you can find its **height** using this rearranged formula:

**h = (A – 2πr²) / (2πr)**

Where **A** is the **total surface area** and **r** is the **radius**.

For instance, if a cylinder has a **surface area** of **300 cm²** and a **radius** of **5 cm**:

- $$h = (300 – 2π × 5²) / (2π × 5)$$
- $$h ≈ (300 – 157.08) / 31.42$$
- $$h ≈ 4.55 cm$$

## How to figure out the volume of a cylinder?

The formula for a cylinder’s volume is:

**V = πr²h**

Where **r** is the radius and **h** is the height.

For a cylinder with **radius** **3 cm** and **height** **8 cm**:

- $$V = π × 3² × 8$$
- $$V ≈ 226.19 cm³$$

While not directly related to **surface area**, the **volume** of a cylinder is often needed alongside surface area calculations.

## Surface area of cylinder with diameter

For a cylinder with **diameter** **10 cm** and **height** **15 cm**:

**Radius**= $$10 / 2 = 5 cm$$- $$A = 2π × 5² + 2π × 5 × 15$$
- $$A ≈ 157.08 + 471.24$$
- $$A ≈ 628.32 cm²$$

If you’re given the **diameter** instead of the **radius**, simply divide the diameter by **2** to get the radius, then proceed with the standard formula.

## Surface area of cylinder with steps

Here’s a step-by-step breakdown for finding the **surface area** of a cylinder with **radius** **4 m** and **height** **6 m**:

- Calculate the area of one circular base: $$πr² = π × 4² ≈ 50.27 m²$$
- Multiply by
**2**for both bases: $$2 × 50.27 ≈ 100.54 m²$$ - Calculate the area of the curved surface: $$2πrh = 2π × 4 × 6 ≈ 150.80 m²$$
- Sum the results: $$100.54 + 150.80 = 251.34 m²$$

The **total surface area** is approximately **251.34 square meters**.

## Surface area of cylinder square feet

For a cylinder with **radius** **2 ft** and **height** **5 ft**:

- $$A = 2π × 2² + 2π × 2 × 5$$
- $$A ≈ 25.13 + 62.83$$
- $$A ≈ 87.96 sq ft$$

When working in **square feet**, ensure all measurements are in feet before applying the formula.

## Surface area of cylinder square meters

Consider a cylinder with **radius** **1.5 m** and **height** **3 m**:

- $$A = 2π × 1.5² + 2π × 1.5 × 3$$
- $$A ≈ 14.14 + 28.27$$
- $$A ≈ 42.41 m²$$

For calculations in **square meters**, use measurements in meters.

## Curved surface area of cylinder

The formula is:

**Curved Surface Area = 2πrh**

For a cylinder with **radius** **3 cm** and **height** **7 cm**:

**Curved Surface Area**= $$2π × 3 × 7$$**Curved Surface Area**≈**131.95 cm²**.

The **curved surface area** (also known as **lateral surface area**) is the area of just the **curved side** of the cylinder, excluding the circular bases.

## Lateral surface area of a cylinder

Using the same formula as above:

For a cylinder with **radius** **5 m** and **height** **10 m**:

**Lateral Surface Area**= $$2π × 5 × 10$$**Lateral Surface Area**≈**314.16 m²**.

The **lateral surface area** is synonymous with the **curved surface area**. It represents the “wrap” around the cylinder, excluding the top and bottom.