ToolkitBook
Calculate the volume of eleven different 3D shapes, including spheres, cylinders, cones, cubes, and pyramids. Input dimensions such as radius, height, or edge length to view the total volume, surface area, and the formula applied. This tool helps engineers determine tank capacities, contractors estimate concrete needs, and students check their homework. Results appear in cubic units matching your input. All processing happens locally in your browser.
Need to calculate area? Try Area Calculator.
Click the button for the shape that matches your specific scenario. The interface categorizes eleven shapes into three groups: curved surfaces (spheres, ellipsoids, cylinders, cones, and elliptic cones), prisms (cubes and cuboids), and pyramids (with triangular, square, rectangular, or polygonal bases). Once you select a shape, a diagram will illustrate the required dimensions, and the formula will appear above the input fields.
Every shape requires unique parameters. For spheres, enter the radius—the distance from the center to the surface. For cylinders and circular cones, provide the radius and the perpendicular height. For cubes, input a single side length, while cuboids require three perpendicular edge lengths. For ellipsoids, enter the three semi-axes measured from the center. For pyramids, use the base dimensions and the perpendicular height from the base to the apex (do not use the slant height along the triangular face).
Input all dimensions using a consistent unit, such as meters, feet, inches, or centimeters. The calculator preserves your selection: if you enter dimensions in feet, the result will be in cubic feet. If your measurements use mixed units, convert them to a single standard before entry. For liquid capacity, you can convert the final cubic result into liters or gallons—remember that one cubic meter equals 1,000 liters, and one cubic foot is approximately 7.48 US gallons.
The calculated volume is displayed prominently in large text. Below this, secondary measurements provide more context based on the shape. Spheres show surface area and circumference; cylinders list lateral and total surface area; and cubes and cuboids display surface area and diagonals. Cones include the slant height, which is useful for calculating surface materials. These additional values assist with tasks like coating, wrapping, or fitting components.
Tanks and containers: Determine the storage capacity for water tanks, silos, hoppers, and shipping containers. For irregular vessels, divide them into simpler geometric parts, calculate each separately, and sum the results.
Construction materials: Estimate concrete quantities for foundations, columns, and slabs, or calculate excavation volumes for earthmoving. Room volume is also essential for sizing heating and ventilation systems.
Manufacturing: Calculate material displacement for casting and molding, or design packaging based on internal capacity. Volume measurements are critical for material planning and product pricing.
DIY projects: Plan the capacity of an aquarium for fish stocking or determine the amount of soil needed for a custom planter box.
For cylinders and cones, ensure you are measuring the perpendicular height (straight from the base to the top) rather than the slant height along the angled side. For circular shapes, confirm whether you have the radius (center to edge) or the diameter (edge to edge through the center); the calculator requires the radius, so divide the diameter by two if necessary.
For containers with walls, decide if you need the internal volume (capacity) or the external volume (displacement). Use inside dimensions for the former and outside dimensions for the latter. Note that wall thickness can significantly alter results for smaller containers.
Real-world objects are rarely perfect geometric shapes. For slight irregularities, take several measurements and use the average. For more complex objects, break them down into simpler shapes and calculate each individually.
Sphere: V = (4/3) × π × r³Ellipsoid: V = (4/3) × π × a × b × cCylinder: V = π × r² × hCone: V = (1/3) × π × r² × hElliptic Cone: V = (1/3) × π × a × b × hCube: V = s³Cuboid: V = l × w × hTriangular Pyramid: V = (1/3) × Base Area × hSquare Pyramid: V = (1/3) × s² × hRectangular Pyramid: V = (1/3) × l × w × hPolygonal Pyramid: V = (1/3) × Base Area × h