Frustum Calculator with Height and Weight

Frustum Volume Formula:

\[ V = \frac{1}{3} \pi h (r_1^2 + r_1 r_2 + r_2^2) \]

Height:

Top Radius:

Bottom Radius:

Material Density (optional):

kg/m³

Volume: m³

1. What is a Frustum Calculator?

Definition: This calculator computes the volume of a frustum (truncated cone or pyramid) based on its height and the radii of its top and bottom bases.

Purpose: It helps in engineering, construction, and manufacturing to determine the volume and weight of frustum-shaped objects.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ V = \frac{1}{3} \pi h (r_1^2 + r_1 r_2 + r_2^2) \]

Where:

\( V \) — Volume (m³)
\( h \) — Height (m)
\( r_1 \) — Radius of top base (m)
\( r_2 \) — Radius of bottom base (m)

Weight Calculation: If material density is provided, weight is calculated as \( Weight = Volume \times Density \).

3. Applications of Frustum Calculations

Details: Used in calculating volumes for buckets, hoppers, lampshades, drinking glasses, and various architectural elements.

4. Using the Calculator

Tips: Enter the height and both radii in meters. Optionally add material density to get weight. All values must be positive numbers.

5. Frequently Asked Questions (FAQ)

Q1: What is a frustum?
A: A frustum is the portion of a solid (typically a cone or pyramid) that lies between two parallel planes cutting it.

Q2: Can I use this for square frustums?
A: No, this calculator is for circular frustums. For square/pyramidal frustums, a different formula is needed.

Q3: What are typical density values?
A: Common densities: water (1000 kg/m³), concrete (2400 kg/m³), steel (7850 kg/m³).

Q4: How accurate is the calculation?
A: The calculation is mathematically precise for perfect frustums. Real-world objects may vary slightly.

Q5: Can I calculate partial frustums?
A: No, this calculates the full volume between the two circular bases.