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 + Rr).
- 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
