Understanding Density Calculations
Density is a fundamental physical property that describes how much mass is contained within a specific volume. In physics and chemistry, it is represented by the Greek letter rho (ρ). Understanding density is crucial for determining if an object will float, identifying unknown substances, and engineering products across various industries.
The Density Formula
Density (ρ) = Mass (m) / Volume (V)
To use this worksheet calculator, you need two measurements:
- Mass: The amount of matter in the object (usually measured in grams or kilograms).
- Volume: The amount of space the object occupies (usually measured in cubic centimeters, milliliters, or liters).
Common Material Densities
| Material |
Density (g/cm³) |
| Water (at 4°C) |
1.00 |
| Aluminum |
2.70 |
| Steel/Iron |
7.87 |
| Gold |
19.32 |
| Lead |
11.34 |
Step-by-Step Worksheet Example
Problem: A rectangular block of wood has a mass of 450 grams. Its volume is measured to be 600 cm³. What is the density of the wood?
- Identify Mass: m = 450 g
- Identify Volume: V = 600 cm³
- Apply Formula: ρ = 450 / 600
- Calculate: ρ = 0.75 g/cm³
- Interpretation: Since 0.75 is less than the density of water (1.0 g/cm³), this wood block will float.
Buoyancy and the "Float Test"
The principle of buoyancy states that if an object's density is lower than the density of the fluid it is placed in, it will float. If its density is higher, it will sink. This is why a heavy aircraft carrier made of steel floats (it has a large volume of air inside, making its average density lower than water), while a small pebble sinks immediately.
function calculateDensity() {
var mass = parseFloat(document.getElementById('massValue').value);
var mUnit = document.getElementById('massUnit').value;
var volume = parseFloat(document.getElementById('volumeValue').value);
var vUnit = document.getElementById('volumeUnit').value;
var resultDiv = document.getElementById('densityResult');
var resultText = document.getElementById('resultText');
var compList = document.getElementById('comparisonList');
if (isNaN(mass) || isNaN(volume) || volume <= 0 || mass <= 0) {
alert('Please enter valid positive numbers for both mass and volume.');
return;
}
// Convert everything to Grams
var massInGrams = mass;
if (mUnit === 'kg') massInGrams = mass * 1000;
if (mUnit === 'lb') massInGrams = mass * 453.592;
if (mUnit === 'oz') massInGrams = mass * 28.3495;
// Convert everything to Cubic Centimeters (cm3)
var volumeInCm3 = volume;
if (vUnit === 'm3') volumeInCm3 = volume * 1000000;
if (vUnit === 'L') volumeInCm3 = volume * 1000;
if (vUnit === 'in3') volumeInCm3 = volume * 16.3871;
var densityGcm3 = massInGrams / volumeInCm3;
var densityKgm3 = densityGcm3 * 1000;
resultDiv.style.display = 'block';
resultText.innerHTML = '
' + densityGcm3.toLocaleString(undefined, {maximumFractionDigits: 4}) + ' g/cm³';
var buoyancyText = "";
if (densityGcm3 < 1.0) {
buoyancyText = "This object is
and will float.";
} else if (Math.abs(densityGcm3 – 1.0) < 0.01) {
buoyancyText = "This object has
in water.";
} else {
buoyancyText = "This object is
and will sink.";
}
compList.innerHTML =
'In SI Units: ' + densityKgm3.toLocaleString(undefined, {maximumFractionDigits: 2}) + ' kg/m³' +
" + buoyancyText + " +
'
' + mass.toLocaleString() + ' ' + mUnit + ' / ' + volume.toLocaleString() + ' ' + vUnit + ' = ' + densityGcm3.toLocaleString(undefined, {maximumFractionDigits: 4}) + ' g/cm³ (converted)';
}