Calculate mass when you know the volume of an object in cubic inches and its density in kilograms per cubic inch. Mass is a fundamental property of matter, representing its resistance to acceleration. Understanding how to convert between volume, density, and mass is crucial in various scientific and engineering applications.
This guide provides a clear explanation of the relationship between these quantities and offers practical examples to illustrate the calculation process. We will focus on determining mass in kilograms (kg), given a volume expressed in cubic inches and a density expressed in kilograms per cubic inch (kg/in³). By following the steps outlined here, you can accurately determine the mass of an object. Below, you'll find several worked examples to help solidify your understanding.
Additionally, a frequently asked questions (FAQs) section is included to address common queries and provide further clarification on the concepts discussed. This resource aims to provide a comprehensive understanding of how to calculate mass from volume and density in the specified units, making it accessible to a wide range of users.
Kilograms from Volume & Density Calculator
Calculate the mass of an object in kilograms (kg) by providing its volume in cubic inches (in³) and its density in kilograms per cubic inch (kg/in³).
Enter Object Properties
Understanding Mass, Volume, and Density
Density is an intrinsic property of a material that relates its mass to the space it occupies (volume). It tells you how much mass is packed into a given unit of volume.
The Formula
The relationship between mass, volume, and density is:
Mass (kg) = Volume (in³) × Density (kg/in³)
Where:
- Mass (kg): The amount of matter in the object, measured in kilograms.
- Volume (in³): The amount of three-dimensional space the object occupies, measured in cubic inches.
- Density (kg/in³): The mass per unit volume of the material, measured in kilograms per cubic inch.
Important Note on Units: This calculator requires density specifically in kg/in³. Densities are more commonly listed in kg/m³ or g/cm³. Ensure your density value is converted to kg/in³ before using it here. (See FAQs for conversion info).
Why is this Calculation Useful?
- Weight Estimation: Calculate the mass (and therefore weight) of objects or materials when direct weighing is difficult.
- Material Selection: Compare the mass of components made from different materials but having the same volume.
- Engineering & Design: Crucial for structural analysis, load calculations, and material specification.
- Shipping & Logistics: Estimate the mass of items based on their dimensions and material type.
Examples with Step-by-Step Solutions
Click on each example to see the calculation:
Example 1: Steel Block
Given:
- Volume = 50 in³
- Density of Steel ≈ 0.284 kg/in³ (converted from g/cm³)
Steps:
- Use Formula: Mass (kg) = Volume × Density
- Calculate: 50 in³ × 0.284 kg/in³
Result: Mass ≈ 14.2 kg
Example 2: Aluminum Component
Given:
- Volume = 120 in³
- Density of Aluminum ≈ 0.0975 kg/in³ (converted from g/cm³)
Steps:
- Use Formula: Mass (kg) = Volume × Density
- Calculate: 120 in³ × 0.0975 kg/in³
Result: Mass ≈ 11.7 kg
Example 3: Small Plastic Part
Given:
- Volume = 5 in³
- Density of a type of Plastic ≈ 0.036 kg/in³ (hypothetical/converted)
Steps:
- Use Formula: Mass (kg) = Volume × Density
- Calculate: 5 in³ × 0.036 kg/in³
Result: Mass ≈ 0.18 kg
Example 4: Large Volume, Low Density
Given:
- Volume = 1000 in³
- Density = 0.01 kg/in³ (e.g., a foam material)
Steps:
- Use Formula: Mass (kg) = Volume × Density
- Calculate: 1000 in³ × 0.01 kg/in³
Result: Mass = 10 kg
Frequently Asked Questions (FAQs)
What is Density?
Density is a measure of how tightly packed the matter is within a substance. It's defined as mass per unit volume. A small, heavy object (like a lead weight) has high density, while a large, light object (like a styrofoam block) has low density.
Where can I find material densities?
Material densities can be found in:
- Engineering handbooks (e.g., Machinery's Handbook)
- Physics and Chemistry textbooks
- Online material property databases (e.g., MatWeb, Engineering Toolbox)
- Manufacturer datasheets for specific materials
How do I convert density to kg/in³?
Common conversions include:
- From g/cm³: $ \text{Density (kg/in³)} = \text{Density (g/cm³)} \times 0.016387 \times \frac{1 \text{ kg}}{1000 \text{ g}} \times (\frac{2.54 \text{ cm}}{1 \text{ in}})^3 = \text{Density (g/cm³)} \times 0.036127 $ (Approx.)
- From kg/m³: $ \text{Density (kg/in³)} = \text{Density (kg/m³)} \times (\frac{1 \text{ m}}{39.3701 \text{ in}})^3 = \text{Density (kg/m³)} \times 1.6387 \times 10^{-5} $ (Approx.)
Can I calculate volume if I know mass and density?
Yes, by rearranging the formula: $ \text{Volume (in³)} = \frac{\text{Mass (kg)}}{\text{Density (kg/in³)}} $. Ensure you use consistent units.
Does temperature affect density?
Yes, generally density decreases as temperature increases (because volume usually expands with heat), and increases as temperature decreases. The density values used should ideally correspond to the temperature of the object, although for many solids, the change is relatively small over typical ambient temperature ranges.
