Frustum Calculator
Calculate Area & Volume for Truncated Cones & Pyramids.
Work Shown
A “Frustum” is the portion of a solid (like a cone or pyramid) that remains when its top is cut off parallel to the base. Common examples include buckets, lampshades, and drinking glasses.
The Frustum Surface Area Calculator computes the Total Surface Area (TSA), Lateral Surface Area (exposed sides), and Volume for three common frustum types: Conical, Square Pyramid, and Rectangular Pyramid.
Features
1. Multi-Shape Support: Handles Cone Frustums (buckets), Square Pyramids (monuments), and Rectangular Pyramids (hoppers).
2. Step-by-Step “Work Shown”: Unlike typical calculators, it displays the intermediate steps, such as calculating the “Slant Height” (l) before finding the area. This is invaluable for geometry students.
3. Comprehensive Outputs: Provides:
– Lateral Area: The area of the sides only (important for painting or material cost).
– Total Surface Area: Lateral Area + Top Base + Bottom Base.
– Volume: The internal capacity.
4. Dynamic Visualization: Generates a scalable diagram of the frustum shape based on inputs.
Uses
- Manufacturing: Determining the amount of sheet metal needed to fabricate a hopper or funnel.
- Packaging: Calculating the surface area for labels on tapered cups or containers.
- Education: Helping students understand solid geometry and the derivation of frustum formulas.
- Gardening: Calculating the volume of soil needed for tapered plant pots.
Tips
- Height vs. Slant Height: This calculator asks for the *vertical* height (h), which is easily measured. It then automatically calculates the *slant height* (l), which is the diagonal distance up the side, used in the area formula.
- Units: Ensure top and bottom radii are in the same units (e.g., inches). The result will be in square units (e.g., in²).
- Bucket Area: If you are calculating the area of an open bucket, use the “Lateral Area” + “Bottom Area”. Do not use “Total Surface Area” as that includes the open top.
FAQs
What is the formula for a Cone Frustum?
Lateral Area = , where is bottom radius, is top radius, and is slant height. Total Area adds and .
How do I find Slant Height?
Using the Pythagorean theorem: . This calculator performs this step for you automatically.
Can I calculate a full cone?
Yes, simply set the Top Radius () to 0. The calculator will treat it as a standard cone.
Why define Rectangular Pyramid width and length?
A rectangular frustum has two different slant heights (one for the width sides, one for the length sides). The calculator computes both to find the accurate total lateral area.
Final Words
Frustums are everywhere in design and engineering. Accurately calculating their surface area requires multiple steps involving trigonometry and algebra. This tool simplifies the process to a few inputs, providing instant, accurate results for fabrication or study.
