function updateCalculatorView() {
var selection = document.getElementById("calculationType").value;
document.getElementById("densityInputs").style.display = "none";
document.getElementById("massInputs").style.display = "none";
document.getElementById("volumeInputs").style.display = "none";
document.getElementById("densityResult").innerHTML = "";
if (selection === "density") {
document.getElementById("densityInputs").style.display = "block";
} else if (selection === "mass") {
document.getElementById("massInputs").style.display = "block";
} else if (selection === "volume") {
document.getElementById("volumeInputs").style.display = "block";
}
}
function performCalculation() {
var selection = document.getElementById("calculationType").value;
var resultDiv = document.getElementById("densityResult");
var result = 0;
var outputText = "";
if (selection === "density") {
var mass = parseFloat(document.getElementById("massForDensity").value);
var volume = parseFloat(document.getElementById("volumeForDensity").value);
if (isNaN(mass) || isNaN(volume) || mass <= 0 || volume <= 0) {
resultDiv.innerHTML = "Please enter valid, positive numbers for mass and volume.";
return;
}
result = mass / volume;
outputText = "Calculated Density: " + result.toFixed(4) + " g/cm³";
} else if (selection === "mass") {
var density = parseFloat(document.getElementById("densityForMass").value);
var volume = parseFloat(document.getElementById("volumeForMass").value);
if (isNaN(density) || isNaN(volume) || density <= 0 || volume <= 0) {
resultDiv.innerHTML = "Please enter valid, positive numbers for density and volume.";
return;
}
result = density * volume;
outputText = "Calculated Mass: " + result.toFixed(4) + " grams";
} else if (selection === "volume") {
var mass = parseFloat(document.getElementById("massForVolume").value);
var density = parseFloat(document.getElementById("densityForVolume").value);
if (isNaN(mass) || isNaN(density) || mass <= 0 || density <= 0) {
resultDiv.innerHTML = "Please enter valid, positive numbers for mass and density.";
return;
}
result = mass / density;
outputText = "Calculated Volume: " + result.toFixed(4) + " cm³";
}
resultDiv.innerHTML = outputText;
}
// Initialize the view on page load
updateCalculatorView();
Understanding Density Calculations
Density is a fundamental physical property of matter that describes how much "stuff" is packed into a given space. Formally, it is defined as the mass of a substance per unit of volume. Understanding density is crucial in many fields, including physics, chemistry, engineering, and geology. A common task in science classes is completing worksheets with density problems, and this calculator is designed to help you check your answers and understand the underlying concepts.
The Density Formula
The relationship between density, mass, and volume is expressed by a simple formula:
Density (ρ) = Mass (m) / Volume (V)
In this formula:
ρ (rho) is the symbol for density, often measured in grams per cubic centimeter (g/cm³) or kilograms per cubic meter (kg/m³).
m is the mass, the amount of matter in an object, measured in grams (g) or kilograms (kg).
V is the volume, the amount of space the object occupies, measured in cubic centimeters (cm³), milliliters (mL), or cubic meters (m³). Note that 1 cm³ is equivalent to 1 mL.
Solving for Mass and Volume
By rearranging the primary formula, you can also solve for mass or volume if you know the other two variables. This is a common requirement on density calculation worksheets.
To find Mass (m): m = ρ × V
To find Volume (V): V = m / ρ
Our calculator can perform all three of these calculations for you. Simply select which variable you wish to find from the dropdown menu.
Example Calculations
Let's walk through some examples to see how the formulas work in practice. These are typical problems you might find on a worksheet.
Example 1: Calculating Density
Problem: A rock has a mass of 450 grams and a volume of 150 cm³. What is its density?
Formula: ρ = m / V
Calculation: ρ = 450 g / 150 cm³
Answer: ρ = 3.0 g/cm³
Example 2: Calculating Mass
Problem: The density of ethanol is 0.789 g/cm³. What is the mass of 200 cm³ of ethanol?
Formula: m = ρ × V
Calculation: m = 0.789 g/cm³ × 200 cm³
Answer: m = 157.8 grams
Example 3: Calculating Volume
Problem: You have a piece of gold with a mass of 96.5 grams. Knowing the density of gold is 19.3 g/cm³, what is its volume?
Formula: V = m / ρ
Calculation: V = 96.5 g / 19.3 g/cm³
Answer: V = 5 cm³
By using this calculator, you can quickly verify your answers for density worksheets and gain confidence in applying the formulas for density, mass, and volume correctly.