ToolkitBook
Calculate the volume of any 3D geometric shape instantly. Select from eleven shapes including spheres, cylinders, cones, cubes, and pyramids with various base types. Enter radius and height for curved shapes, edge lengths for prisms, or base measurements plus height for pyramids. The tool displays volume, surface area, and the formula used for each calculation. Engineers determine tank capacities, contractors estimate concrete for foundations, and students verify homework answers. Enter any unit consistently—results appear in corresponding cubic units. All processing runs locally in your browser.
Click the shape button that matches your measurement scenario. The interface organizes eleven shapes into three categories: curved surfaces (spheres, ellipsoids, cylinders, cones, elliptic cones), prisms (cubes, cuboids), and pyramids (triangular, square, rectangular, polygonal bases). When you select a shape, a diagram appears showing which dimensions you need to enter, and the formula displays above the input fields.
Each shape requires specific measurements. For spheres, enter the radius—distance from center to surface. For cylinders and circular cones, enter radius and perpendicular height. For cubes, enter one side length. For cuboids, enter three perpendicular edge lengths. For ellipsoids, enter three semi-axes measured from center to surface. For pyramids, enter base dimensions plus the perpendicular height from base to apex, not the slant height along the triangular face.
Enter all dimensions in the same unit—meters, feet, inches, or centimeters. The calculator preserves your unit choice: enter feet, get cubic feet in the result. Mixed units require manual conversion before entry. For liquid capacity, convert cubic measurements to liters or gallons afterward. One cubic meter equals 1000 liters; one cubic foot equals approximately 7.48 US gallons.
The primary result shows volume in large text. Below this, additional measurements appear based on shape type. Spheres display surface area and circumference. Cylinders show lateral and total surface area. Cubes and cuboids display surface area and diagonals. Cones show slant height for surface material calculations. These secondary measurements help with coating, wrapping, and fitting tasks.
Tanks and containers: Calculate storage capacity for water tanks, silos, hoppers, and shipping containers. For irregular tanks, divide into simpler shapes, calculate each separately, then sum the volumes.
Construction materials: Determine concrete quantities for foundations, columns, and slabs. Calculate excavation volumes for earthmoving estimates. Room volume affects heating and ventilation sizing.
Manufacturing: Determine material displacement for casting and molding. Calculate container capacity for packaging design. Volume affects product pricing and material planning.
DIY projects: Plan aquarium capacity for fish stocking. Determine planter box soil requirements. Calculate custom tank or container volumes for home projects.
For cylinders and cones, ensure you measure perpendicular height, not slant height along the angled surface. Height must be measured straight from base to top. For circular shapes, verify whether you have radius (center to edge) or diameter (edge to edge through center)—enter radius, dividing diameter by two if necessary.
For containers with walls, decide whether you need internal volume for capacity or external volume for displacement. Measure inside dimensions for capacity; outside dimensions for displacement. Wall thickness affects results significantly for small containers.
Real objects rarely match perfect geometric shapes. For slight irregularities, take multiple measurements and use averages. For significant irregularities, divide the object into simpler shapes that the calculator can handle individually.
Sphere: V = (4/3) × π × r³ (r = radius)Ellipsoid: V = (4/3) × π × a × b × c (a, b, c = semi-axes)Cylinder: V = π × r² × h (r = radius, h = height)Cone: V = (1/3) × π × r² × h (r = radius, h = height)Elliptic Cone: V = (1/3) × π × a × b × h (a, b = semi-axes, h = height)Cube: V = s³ (s = side length)Cuboid: V = l × w × h (l = length, w = width, h = height)Triangular Pyramid: V = (1/3) × Base Area × hSquare Pyramid: V = (1/3) × s² × h (s = base side, h = height)Rectangular Pyramid: V = (1/3) × l × w × hPolygonal Pyramid: V = (1/3) × Base Area × h