Conical Frustum Calculator Online Free

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:

1. Identify the measurements: Determine the height (h), lower base radius (R), and upper base radius (r) of the frustum.
2. Square the radii: Calculate R², r², and R*r.
3. Apply the formula: Use the volume formula V = (1/3) π h (R² + r² + Rr).
4. 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:

1. We have h = 10 cm, R = 5 cm, r = 3 cm
2. R² = 25 cm², r² = 9 cm², R*r = 15 cm²
3. V = (1/3) π 10 * (25 + 9 + 15)
4. 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:

1. Gather measurements: Determine the lower base radius (R), upper base radius (r), and height (h) of the frustum.
2. Calculate the slant height: Use the formula s = √(h² + (R – r)²) to find the slant height.
3. Apply the surface area formula: Use SA = π (R² + r² + s (R + r)).
4. 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:

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