*Note: The unit of measurement is the cube of the input unit (e.g., cubic meters, cubic inches).
How is Volume Calculated?
Volume is the measure of three-dimensional space occupied by an object. It is quantified numerically using SI derived units (such as the cubic meter or litre) or by various imperial units (such as the gallon, quart, or cubic inch). Understanding how to calculate volume is essential in fields ranging from construction and shipping to chemistry and cooking.
Common Volume Formulas
Shape
Formula
Variables
Rectangular Prism
V = l × w × h
l=Length, w=Width, h=Height
Cylinder
V = π × r² × h
r=Radius, h=Height
Sphere
V = (4/3) × π × r³
r=Radius
Cone
V = (1/3) × π × r² × h
r=Radius, h=Height
Square Pyramid
V = (1/3) × s² × h
s=Side length, h=Height
Real-World Example: Calculating a Water Tank
Suppose you have a cylindrical water tank with a radius of 2 meters and a height of 5 meters. To find out how much water it can hold:
Identify the formula: V = π × r² × h
Square the radius: 2 × 2 = 4
Multiply by Height: 4 × 5 = 20
Multiply by Pi (≈3.14159): 20 × 3.14159 = 62.83 cubic meters
Why Volume Matters
Whether you are calculating the amount of concrete needed for a driveway or the dosage of a liquid medication, volume provides the precise capacity requirements. In shipping, volume is used to determine "dimensional weight," which affects the cost of transporting goods across the globe.
function updateFields() {
var shape = document.getElementById('shapeSelect').value;
var prismFields = document.getElementById('prismFields');
var roundFields = document.getElementById('roundFields');
var pyramidFields = document.getElementById('pyramidFields');
var heightGroup = document.getElementById('heightGroup');
// Hide all
prismFields.classList.remove('active-shape');
roundFields.classList.remove('active-shape');
pyramidFields.classList.remove('active-shape');
// Reset height display for sphere
heightGroup.style.display = 'block';
if (shape === 'prism') {
prismFields.classList.add('active-shape');
} else if (shape === 'cylinder' || shape === 'cone' || shape === 'sphere') {
roundFields.classList.add('active-shape');
if (shape === 'sphere') {
heightGroup.style.display = 'none';
}
} else if (shape === 'pyramid') {
pyramidFields.classList.add('active-shape');
}
document.getElementById('volResultBox').style.display = 'none';
}
function calculateVolume() {
var shape = document.getElementById('shapeSelect').value;
var volume = 0;
var isValid = false;
var label = "";
if (shape === 'prism') {
var l = parseFloat(document.getElementById('length').value);
var w = parseFloat(document.getElementById('width').value);
var h = parseFloat(document.getElementById('height').value);
if (!isNaN(l) && !isNaN(w) && !isNaN(h)) {
volume = l * w * h;
isValid = true;
label = "Length (" + l + ") × Width (" + w + ") × Height (" + h + ")";
}
} else if (shape === 'cylinder') {
var r = parseFloat(document.getElementById('radius').value);
var h = parseFloat(document.getElementById('roundHeight').value);
if (!isNaN(r) && !isNaN(h)) {
volume = Math.PI * Math.pow(r, 2) * h;
isValid = true;
label = "π × Radius² (" + r + ") × Height (" + h + ")";
}
} else if (shape === 'sphere') {
var r = parseFloat(document.getElementById('radius').value);
if (!isNaN(r)) {
volume = (4/3) * Math.PI * Math.pow(r, 3);
isValid = true;
label = "(4/3) × π × Radius³ (" + r + ")";
}
} else if (shape === 'cone') {
var r = parseFloat(document.getElementById('radius').value);
var h = parseFloat(document.getElementById('roundHeight').value);
if (!isNaN(r) && !isNaN(h)) {
volume = (1/3) * Math.PI * Math.pow(r, 2) * h;
isValid = true;
label = "(1/3) × π × Radius² (" + r + ") × Height (" + h + ")";
}
} else if (shape === 'pyramid') {
var s = parseFloat(document.getElementById('baseSide').value);
var h = parseFloat(document.getElementById('pyramidHeight').value);
if (!isNaN(s) && !isNaN(h)) {
volume = (1/3) * Math.pow(s, 2) * h;
isValid = true;
label = "(1/3) × Base Side² (" + s + ") × Height (" + h + ")";
}
}
if (isValid) {
document.getElementById('volValue').innerText = volume.toLocaleString(undefined, {maximumFractionDigits: 4}) + " cubic units";
document.getElementById('volSummary').innerText = "Using formula: " + label;
document.getElementById('volResultBox').style.display = 'block';
} else {
alert("Please enter valid positive numbers for all fields.");
}
}