Cubic Inches Calculator
The Cubic Inches Calculator is a valuable tool for anyone needing to convert and calculate volumes in cubic inches. This unit of measurement is commonly used in various fields, including manufacturing, woodworking, automotive, and more. By using this calculator, you can quickly determine the volume of any three-dimensional space or object, helping you make informed decisions about materials, capacities, and storage.
How to Use the Cubic Inches Calculator
Using the Cubic Inches Calculator is straightforward. Simply input the dimensions of the object in inches, and the calculator will return the volume in cubic inches. The calculator can also convert volumes from cubic feet, liters, or milliliters into cubic inches.
Conversion Formulas
- Cubic Inches to Cubic Feet: Volume (cu ft)=Volume (cu in)1728\text{Volume (cu ft)} = \frac{\text{Volume (cu in)}}{1728}Volume (cu ft)=1728Volume (cu in)
- Cubic Inches to Liters: Volume (liters)=Volume (cu in)61.0237\text{Volume (liters)} = \frac{\text{Volume (cu in)}}{61.0237}Volume (liters)=61.0237Volume (cu in)
- Cubic Inches to Milliliters: Volume (ml)=Volume (cu in)×16.3871\text{Volume (ml)} = \text{Volume (cu in)} \times 16.3871Volume (ml)=Volume (cu in)×16.3871
Practical Example Table
The following table provides practical examples for calculating the volume in cubic inches for various shapes and configurations. Each example displays the dimensions and the resulting volume in both cubic inches and cubic feet, along with a real-world application.
| Shape | Dimensions (inches) | Volume Calculation | Volume (cu in) | Volume (cu ft) | Application |
|---|---|---|---|---|---|
| Cube | 5 x 5 x 5 | V = s³ | 125 | 0.072 | Ideal for calculating the capacity of a storage box measuring 5 inches on each side. |
| Rectangular Prism | 10 x 6 x 4 | V = l × w × h | 240 | 0.139 | Useful for estimating the volume of a container measuring 10 inches long, 6 inches wide, and 4 inches high. |
| Cylinder | Radius: 3, Height: 6 | V = π × r² × h | 56.55 | 0.033 | Suitable for determining the volume of a cylindrical water tank with a radius of 3 inches and height of 6 inches. |
| Sphere | Diameter: 4 | V = (4/3) × π × (r³) | 33.51 | 0.019 | Helpful for calculating the volume of a ball with a diameter of 4 inches. |
| Cone | Radius: 3, Height: 5 | V = (1/3) × π × r² × h | 15.71 | 0.009 | Useful for estimating the volume of a traffic cone with a radius of 3 inches and height of 5 inches. |
| Rectangular Prism | 12 x 10 x 8 | V = l × w × h | 960 | 0.555 | Ideal for measuring the volume of a shipping box that is 12 inches long, 10 inches wide, and 8 inches high. |
| Cube | 3 x 3 x 3 | V = s³ | 27 | 0.016 | Suitable for estimating the volume of a small gift box measuring 3 inches on each side. |
| Cylinder | Radius: 2, Height: 10 | V = π × r² × h | 125.66 | 0.072 | Useful for calculating the volume of a tall cylindrical vase with a radius of 2 inches and height of 10 inches. |
| Sphere | Diameter: 8 | V = (4/3) × π × (r³) | 268.08 | 0.155 | Helpful for determining the volume of a beach ball with a diameter of 8 inches. |
| Cone | Radius: 5, Height: 12 | V = (1/3) × π × r² × h | 78.54 | 0.045 | Ideal for calculating the volume of a conical sandcastle with a radius of 5 inches and height of 12 inches. |
Detailed Explanation of Calculations
To help you understand how to arrive at the volume calculations, let’s break down a few examples in detail:
- Example 1 – Volume of a Cube with 5 Inches on Each Side:
- Formula Used: V = s³
- Calculation: V = 5³ = 125 cubic inches.
- Conversion to Cubic Feet: Volume in cubic feet = 1251728=0.072\frac{125}{1728} = 0.0721728125=0.072 cubic feet.
- Application: This calculation is ideal for determining the capacity of a storage box measuring 5 inches on each side.
- Example 2 – Volume of a Rectangular Prism (Box) Measuring 10 x 6 x 4 Inches:
- Formula Used: V = l × w × h
- Calculation: V = 10 × 6 × 4 = 240 cubic inches.
- Conversion to Cubic Feet: Volume in cubic feet = 2401728=0.139\frac{240}{1728} = 0.1391728240=0.139 cubic feet.
- Application: This is useful for estimating the volume of a container that is 10 inches long, 6 inches wide, and 4 inches high.
- Example 3 – Volume of a Cylinder with Radius of 3 Inches and Height of 6 Inches:
- Formula Used: V = π × r² × h
- Calculation: V = 3.1416 × (3)² × 6 = 56.55 cubic inches.
- Conversion to Cubic Feet: Volume in cubic feet = 56.551728=0.033\frac{56.55}{1728} = 0.033172856.55=0.033 cubic feet.
- Application: This calculation is suitable for determining the volume of a cylindrical water tank with a radius of 3 inches and height of 6 inches.
- Example 4 – Volume of a Sphere with a Diameter of 4 Inches:
- Formula Used: V = 43×π×(r3)\frac{4}{3} × π × (r³)34×π×(r3)
- Calculation: First, find the radius: r=42=2r = \frac{4}{2} = 2r=24=2.
- Conversion to Cubic Feet: Volume in cubic feet = 33.511728=0.019\frac{33.51}{1728} = 0.019172833.51=0.019 cubic feet.
- Application: This calculation helps estimate the volume of a ball with a diameter of 4 inches.
- Example 5 – Volume of a Cone with a Radius of 3 Inches and Height of 5 Inches:
- Formula Used: V = 13×π×r2×h\frac{1}{3} × π × r² × h31×π×r2×h
- Calculation: V = 13×3.1416×(3)2×5=13×3.1416×9×5=15.71\frac{1}{3} × 3.1416 × (3)² × 5 = \frac{1}{3} × 3.1416 × 9 × 5 = 15.7131×3.1416×(3)2×5=31×3.1416×9×5=15.71 cubic inches.
- Conversion to Cubic Feet: Volume in cubic feet = 15.711728=0.009\frac{15.71}{1728} = 0.009172815.71=0.009 cubic feet.
- Application: This is useful for estimating the volume of a traffic cone with a radius of 3 inches and height of 5 inches.
- Example 6 – Volume of a Rectangular Prism Measuring 12 x 10 x 8 Inches:
- Formula Used: V = l × w × h
- Calculation: V = 12 × 10 × 8 = 960 cubic inches.
- Conversion to Cubic Feet: Volume in cubic feet = 9601728=0.555\frac{960}{1728} = 0.5551728960=0.555 cubic feet.
- Application: This calculation is ideal for measuring the volume of a shipping box that is 12 inches long, 10 inches wide, and 8 inches high.