Density Calculator - Find Density, Mass & Volume Easily

Density, Mass & Volume Calculator

Solve the density triangle formula: find Density ($\rho$), Mass ($m$), or Volume ($V$).

Choose Unknown Variable to Solve: Calculate Density ($\rho = m \div V$) Calculate Mass ($m = \rho \times V$) Calculate Volume ($V = m \div \rho$)

Density ($\rho$ in kg/m³):

Mass ($m$ in kg):

Volume ($V$ in m³):

Calculated Density

0.00 kg/m³

In Grams per cm³ (g/cm³)

0.00 g/cm³

In Pounds per Gallon (lb/gal)

0.00 lb/gal

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Density Calculator: Find Density, Mass & Volume with Physics Formulas

In physics and materials science, density ($\rho$) is a measure of how tightly matter is packed together within a given space. Defined formally as mass per unit volume, it explains why dense objects like lead sink in water, while less dense objects like wood or ice float.

Our free Density, Mass & Volume Calculator enables students, engineers, and scientists to compute any missing variable instantly using standard metric and imperial units.

The Density Formula and Triangle

The fundamental mathematical relationship connecting density, mass, and volume is expressed by the equation:

Core Equation:
$$\mathbf{\rho = \frac{m}{V}}$$
Where:
• $\rho$ (Density): Measured in kilograms per cubic meter ($\text{kg/m}^3$) or grams per cubic centimeter ($\text{g/cm}^3$).
• $m$ (Mass): The quantity of matter, measured in kilograms ($\text{kg}$) or grams ($\text{g}$).
• $V$ (Volume): The three-dimensional space occupied, measured in cubic meters ($\text{m}^3$) or liters ($\text{L}$).

Algebraic Variations for Solving Any Parameter

To Find	Formula	Required Inputs	Standard Unit
Density ($\rho$)	$\rho = m \div V$	Mass ($m$) & Volume ($V$)	$\text{kg/m}^3$ or $\text{g/cm}^3$
Mass ($m$)	$m = \rho \times V$	Density ($\rho$) & Volume ($V$)	$\text{kg}$ or $\text{g}$
Volume ($V$)	$V = m \div \rho$	Mass ($m$) & Density ($\rho$)	$\text{m}^3$ or $\text{L}$

Densities of Common Materials

Different substances possess unique densities under standard atmospheric conditions ($20^\circ\text{C}$ and $1\text{ atm}$):

• Pure Water: $1,000\text{ kg/m}^3$ ($1.0\text{ g/cm}^3$)
• Aluminum: $2,700\text{ kg/m}^3$ ($2.7\text{ g/cm}^3$)
• Iron / Steel: $7,850\text{ kg/m}^3$ ($7.85\text{ g/cm}^3$)
• Gold: $19,300\text{ kg/m}^3$ ($19.3\text{ g/cm}^3$)
• Air (at sea level): $1.225\text{ kg/m}^3$

Worked Example: Finding Mass from Density and Volume

Problem: Weight of a Solid Gold Bar

Scenario: A pure gold ingot measures dimensions yielding a volume of $0.002\text{ m}^3$ ($2,000\text{ cm}^3$). Given gold's density is $19,300\text{ kg/m}^3$, what is its total mass?

Solution:
1. Identify knowns: $\rho = 19,300\text{ kg/m}^3$, $V = 0.002\text{ m}^3$.
2. Apply formula: $m = \rho \times V$.
3. $m = 19,300 \times 0.002 = 38.6\text{ kg}$.
The gold bar has a mass of 38.6 kilograms (approx. 85 lbs).

Frequently Asked Questions (FAQs)

Does temperature affect density?

Yes. As substances heat up, their particles thermal-expand, increasing volume and thereby decreasing density (with water behaving uniquely near its freezing point). Conversely, cooling increases density.

What is relative density (specific gravity)?

Specific gravity is the dimensionless ratio of a substance's density compared to the density of pure water at $4^\circ\text{C}$. If a material has a specific gravity greater than 1, it sinks in water.

How do you convert $\text{g/cm}^3$ to $\text{kg/m}^3$?

To convert from grams per cubic centimeter to kilograms per cubic meter, simply multiply the value by $1,000$. (Example: $2.5\text{ g/cm}^3 \times 1,000 = 2,500\text{ kg/m}^3$).