Use this online free **conical frustum calculator** designed to calculate various **measurements** related to a **cone volume of a frustum** or **conical frustum**.

A conical frustum is the portion of a cone that remains when the **top part** is cut off **parallel** to the base.

This calculator helps determine the **volume**, **surface area**, and other **dimensions** of a conical frustum given specific input parameters.

For example, if you have a conical frustum with a **lower radius** of **5 cm**, an **upper radius** of **3 cm**, and a **height** of **10 cm**, the calculator can instantly provide you with its **volume** and **surface area**. This saves time and reduces the chance of **manual calculation errors**.

## Conical Frustum Calculator

Lower Radius (R) | Upper Radius (r) | Height (h) | Volume (V) | Surface Area (SA) | Conversion Equation |
---|---|---|---|---|---|

5 cm | 3 cm | 10 cm | 513.33 cm³ | 267.04 cm² | V = (1/3) π 10 (5² + 3² + 53) |

8 in | 6 in | 15 in | 2,413.47 in³ | 754.77 in² | SA = π (8² + 6² + √(15² + (8-6)²) (8 + 6)) |

2.5 m | 1.5 m | 4 m | 52.36 m³ | 53.41 m² | V = (1/3) π 4 (2.5² + 1.5² + 2.51.5) |

10 ft | 7 ft | 20 ft | 4,561.59 ft³ | 1,131.71 ft² | SA = π (10² + 7² + √(20² + (10-7)²) (10 + 7)) |

6 mm | 4 mm | 12 mm | 603.19 mm³ | 263.89 mm² | V = (1/3) π 12 (6² + 4² + 64) |

**Related Tools**

## Conical Frustum Formula

Let’s explore each of these formulas:

### Volume **V**:

$$V = 13\pi h (r_1^2 + r_1 r_2 + r_2^2)$$

$$V = 31\pi h (r_1^2 + r_1 r_2 + r_2^2)$$

**r1**=**Radius**of the**larger base****r2**=**Radius**of the**smaller base****h**=**Height**of the**frustum**

### Lateral Surface Area **A_L**:

$$A_L = \pi (r_1 + r_2) \cdot l$$

$$A_L = \pi (r_1 + r_2) \cdot l$$

**l**=**Slant height**of the**frustum**

### Slant Height **l**:

$$l = \sqrt{h^2 + (r_1 – r_2)^2}$$

$$l = \sqrt{h^2 + (r_1 – r_2)^2}$$

### Total Surface Area **A_T** (including both bases):

$$A_T = A_L + \pi (r_1^2 + r_2^2)$$

$$A_T = A_L + \pi (r_1^2 + r_2^2)$$

## How to Calculate the Volume of a Conical Frustum?

To calculate the **volume** of a conical frustum, follow these steps:

**Identify the measurements**: Determine the**height (h)**,**lower base radius (R)**, and**upper base radius (r)**of the frustum.**Square the radii**: Calculate**R²**,**r²**, and**R*r**.**Apply the formula**: Use the volume formula**V = (1/3)**.*π*h*(R² + r² + R*r)**Compute the result**: Plug in the values and calculate the final**volume**.

For example, let’s calculate the volume of a conical frustum with **h = 10 cm**, **R = 5 cm**, and **r = 3 cm**:

- We have
**h = 10 cm**,**R = 5 cm**,**r = 3 cm** **R² = 25 cm²**,**r² = 9 cm²**,**R*r = 15 cm²****V = (1/3)***π*10 * (25 + 9 + 15)**V ≈ 513.33 cm³**

## How Do You Find the Surface Area of a Conical Frustum?

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

**Gather measurements**: Determine the**lower base radius (R)**,**upper base radius (r)**, and**height (h)**of the frustum.**Calculate the slant height**: Use the formula**s = √(h² + (R – r)²)**to find the**slant height**.**Apply the surface area formula**: Use**SA = π**.*(R² + r² + s*(R + r))**Compute the result**: Plug in the values and calculate the final**surface area**.

For example, let’s calculate the **surface area** of a conical frustum with **R = 5 cm**, **r = 3 cm**, and **h = 10 cm**:

- We have
**R = 5 cm**,**r = 3 cm**,**h = 10 cm** **s = √(10² + (5 – 3)²) = √(100 + 4) = √104 ≈ 10.20 cm****SA = π***(5² + 3² + 10.20*(5 + 3))**SA ≈ 267.04 cm²**