Volume Calculator
Cube
Rectangular Prism
Cylinder
Sphere
Cone
Triangular Prism
units
Enter dimensions to calculate volume.
Understanding Volume Calculation
Volume is a fundamental concept in geometry and physics, representing the amount of three-dimensional space an object occupies. It is measured in cubic units, such as cubic meters (m³), cubic centimeters (cm³), or cubic feet (ft³). Understanding how to calculate volume is crucial in various fields, including engineering, architecture, chemistry, and everyday tasks like cooking or filling containers.
The formula for calculating volume depends on the shape of the object. Below are the common formulas for various geometric shapes:
- Cube: A cube has six equal square faces.
Volume = side³Where 'side' is the length of one edge of the cube. - Rectangular Prism (Cuboid): A box-like shape with six rectangular faces.
Volume = length × width × heightWhere 'length', 'width', and 'height' are the dimensions of the prism. - Cylinder: A shape with two parallel circular bases connected by a curved surface.
Volume = π × radius² × heightWhere 'π' (pi) is approximately 3.14159, 'radius' is the radius of the circular base, and 'height' is the perpendicular distance between the bases. - Sphere: A perfectly round geometrical object in three-dimensional space.
Volume = (4/3) × π × radius³Where 'π' is approximately 3.14159 and 'radius' is the distance from the center to any point on the surface. - Cone: A three-dimensional geometric shape that tapers smoothly from a flat circular base to a point called the apex or vertex.
Volume = (1/3) × π × radius² × heightWhere 'π' is approximately 3.14159, 'radius' is the radius of the circular base, and 'height' is the perpendicular distance from the base to the apex. - Triangular Prism: A prism with a triangular base.
Volume = Area of Base Triangle × height of prismTo calculate the area of the base triangle, you typically need its base and height:Area = (1/2) × base_triangle × height_triangle. So, the volume becomes:Volume = (1/2) × base_triangle × height_triangle × height_prism.
Use Cases for Volume Calculation:
- Construction and Engineering: Calculating the amount of concrete needed for foundations, the capacity of tanks, or the volume of materials for excavation.
- Chemistry: Determining the volume of solutions or gases.
- Manufacturing: Designing containers, calculating material usage for products.
- Everyday Life: Measuring ingredients for cooking, determining how much liquid a container can hold, or calculating space needed for furniture.
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break;
case "rectangular_prism":
htmlContent = `
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break;
case "cylinder":
htmlContent = `
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break;
case "sphere":
htmlContent = `
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break;
case "cone":
htmlContent = `
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break;
case "triangular_prism":
htmlContent = `
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break;
}
dynamicInputsDiv.innerHTML = htmlContent;
}
function calculateVolume() {
var shapeSelect = document.getElementById("shape");
var selectedShape = shapeSelect.value;
var volume = 0;
var resultDiv = document.getElementById("result");
var pi = Math.PI;
var isValid = true;
resultDiv.innerHTML = "Enter dimensions to calculate volume.";
resultDiv.className = ""; // Reset class
try {
switch (selectedShape) {
case "cube":
var side = parseFloat(document.getElementById("side_cube").value);
if (isNaN(side) || side <= 0) throw new Error("Invalid side length. Please enter a positive number.");
volume = Math.pow(side, 3);
break;
case "rectangular_prism":
var length = parseFloat(document.getElementById("length_rp").value);
var width = parseFloat(document.getElementById("width_rp").value);
var height = parseFloat(document.getElementById("height_rp").value);
if (isNaN(length) || isNaN(width) || isNaN(height) || length <= 0 || width <= 0 || height <= 0) {
throw new Error("Invalid dimensions. Please enter positive numbers for length, width, and height.");
}
volume = length * width * height;
break;
case "cylinder":
var radius = parseFloat(document.getElementById("radius_cyl").value);
var height = parseFloat(document.getElementById("height_cyl").value);
if (isNaN(radius) || isNaN(height) || radius <= 0 || height <= 0) {
throw new Error("Invalid dimensions. Please enter positive numbers for radius and height.");
}
volume = pi * Math.pow(radius, 2) * height;
break;
case "sphere":
var radius = parseFloat(document.getElementById("radius_sph").value);
if (isNaN(radius) || radius <= 0) {
throw new Error("Invalid radius. Please enter a positive number.");
}
volume = (4/3) * pi * Math.pow(radius, 3);
break;
case "cone":
var radius = parseFloat(document.getElementById("radius_cone").value);
var height = parseFloat(document.getElementById("height_cone").value);
if (isNaN(radius) || isNaN(height) || radius <= 0 || height <= 0) {
throw new Error("Invalid dimensions. Please enter positive numbers for radius and height.");
}
volume = (1/3) * pi * Math.pow(radius, 2) * height;
break;
case "triangular_prism":
var base_triangle = parseFloat(document.getElementById("base_tp").value);
var height_triangle = parseFloat(document.getElementById("height_triangle_tp").value);
var height_prism = parseFloat(document.getElementById("height_prism_tp").value);
if (isNaN(base_triangle) || isNaN(height_triangle) || isNaN(height_prism) || base_triangle <= 0 || height_triangle <= 0 || height_prism <= 0) {
throw new Error("Invalid dimensions. Please enter positive numbers for all triangle and prism dimensions.");
}
var baseArea = 0.5 * base_triangle * height_triangle;
volume = baseArea * height_prism;
break;
default:
throw new Error("Please select a shape.");
}
resultDiv.innerHTML = "Volume: " + volume.toFixed(2) + " cubic units";
} catch (error) {
resultDiv.innerHTML = error.message;
resultDiv.className = "error";
}
}
// Initialize inputs on page load
document.addEventListener("DOMContentLoaded", updateInputs);