Conical Frustum Volume Calculator

Conical Frustum Volume Formula:

\[ V = \frac{1}{3} \pi h (R^2 + R r + r^2) \]

Volume (V):

Unit Converter ▲

Unit Converter ▼

From:	To:

1. What is a Conical Frustum?

A conical frustum is the portion of a cone that lies between two parallel planes cutting it. It's what remains after cutting the top off a cone with a plane parallel to the base. Common examples include buckets, lampshades, and certain drinking glasses.

2. How Does the Calculator Work?

The calculator uses the conical frustum volume formula:

\[ V = \frac{1}{3} \pi h (R^2 + R r + r^2) \]

Where:

\( V \) — Volume (cubic units)
\( h \) — Height between the two parallel surfaces
\( R \) — Radius of the top surface
\( r \) — Radius of the bottom surface
\( \pi \) — Approximately 3.14159

Explanation: The formula accounts for the combined effect of the three areas (top circle, bottom circle, and the average area between them) multiplied by the height.

3. Applications of Conical Frustum Volume

Details: This calculation is essential in engineering (storage tanks, hoppers), architecture (domes, towers), manufacturing (molded parts), and even in everyday objects like drinking glasses and flower pots.

4. Using the Calculator

Tips: Enter all dimensions in the same units (e.g., all in cm or all in inches). Height must be positive, while radii must be non-negative. The top and bottom radii can be in any order (calculator works for both truncated cones and expanded conical shapes).

5. Frequently Asked Questions (FAQ)

Q1: What if one radius is zero?
A: If the smaller radius is zero, the shape becomes a regular cone, and the formula simplifies to the standard cone volume formula.

Q2: What if both radii are equal?
A: If R = r, the shape becomes a cylinder, and the formula simplifies to πr²h.

Q3: How accurate is this formula?
A: The formula is mathematically exact for perfect conical frustums. Real-world accuracy depends on how closely your object matches this ideal shape.

Q4: Can I use different units for different dimensions?
A: No, all dimensions must be in the same units for the calculation to be correct.

Q5: What about the surface area?
A: This calculator only computes volume. Surface area calculations require additional formulas accounting for the lateral surface.