This calculator is an invaluable tool that transforms volume measurements (in cubic feet) into linear feet. This conversion is crucial for anyone needing to purchase or utilize materials based on linear dimensions, ensuring that you only buy what you need, thereby reducing waste and saving money.
Formula
For a Cuboid (Rectangular Prism)
To determine the linear feet for a cuboid:
- Linear feet along length (l): Linear feet (l) = Cubic feet / (width × height)
- Linear feet along width (w): Linear feet (w) = Cubic feet / (length × height)
- Linear feet along height (h): Linear feet (h) = Cubic feet / (length × width)
Cylinder
For cylindrical shapes:
- Linear feet around circumference: Linear feet (circumference) = (2 × π × radius × Cubic feet) / (π × radius² × height)
- Linear feet along height: Linear feet (height) = Cubic feet / (π × radius²)
Sphere
For spherical objects:
- Linear feet along diameter: Linear feet (diameter) = (6 × Cubic feet) / (π × radius³)
Helpful Table for Quick Reference
Here’s a convenient table listing common dimensions and their conversion to linear feet using the formulas provided:
| Shape | Dimensions (Cubic Feet) | Linear Feet (Length) | Linear Feet (Width) | Linear Feet (Height) |
|---|---|---|---|---|
| Cuboid | 50 ft³ | 10 ft (5×10) | 5 ft (10×10) | 1 ft (5×10) |
| Cylinder | 75 ft³ | 15 ft (10x10xπ) | — | 7.5 ft (10xπ) |
| Sphere | 100 ft³ | 5.42 ft (radius = 3) | — | — |
Note: The “—” indicates that the measurement is not applicable for that shape in the respective dimension.
Examples
Example for a Cuboid
- Given: A cuboid with a volume of 50 cubic feet, width of 10 feet, and height of 5 feet.
- To Find: Linear feet along the length.
- Calculation: Linear feet (length) = 50 ft³ / (10 ft × 5 ft) = 1 ft.
Cylinder
- Given: A cylinder with a volume of 75 cubic feet, radius of 5 feet, and height of 3 feet.
- To Find: Linear feet along the height.
- Calculation: Linear feet (height) = 75 ft³ / (π × 5² ft) ≈ 0.955 ft.
Example for a Sphere
- Given: A sphere with a volume of 100 cubic feet and a radius of 3 feet.
- To Find: Linear feet along the diameter.
- Calculation: Linear feet (diameter) = (6 × 100 ft³) / (π × 3³ ft) ≈ 7.27 ft.
These examples demonstrate how to use the formulas for different shapes to convert cubic feet measurements into linear feet, providing practical insights for handling real-life scenarios involving material measurements.
Most Common FAQs
For irregular shapes, approximate the shape to the nearest standard geometric form (cuboid, cylinder, sphere) and use the corresponding formula as closely as possible.
These calculations provide a good approximation, ensuring that material purchase is as close to the actual requirements as possible, minimizing waste.
