Volume Calculators
This category presents calculators describing the internal size of three-dimensional shapes. Each tool provides numerical outputs for solids such as prisms, pyramids, spheres and other curved forms.
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Cone Volume Calculator
A cone's volume depends on how its circular base and vertical height combine to enclose space within a narrowing shape.
Example use: Estimating how much sand fits inside a small cone-shaped pile.
Inputs: radius, vertical height
Outputs: shape classification, base area, vertical height, calculated volume, slant height, lateral surface area, total surface area, semi-vertical angle, solid angle
Visual: a cone showing its height, base, sloping side, and the way volume changes with height
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Conical Frustum Volume Calculator
A conical frustum forms when the top of a cone is removed, leaving two circular ends and a reduced volume between them.
Example use: Estimating how much liquid a tapered cup can hold.
Inputs: top radius, base radius, vertical height
Outputs: total volume, capacity in litres, total surface area, lateral surface area, slant height, centre of mass from base, missing top cone volume
Visual: a shortened cone with its top and base circles marked and a height line showing how volume accumulates
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Cube Volume Calculator
A cube encloses space using six equal square faces, giving a direct link between its side length and total volume.
Example use: Estimating the storage space inside a small box.
Inputs: side length
Outputs: volume, total surface area, base area, face perimeter, face diagonal, space diagonal, inscribed sphere radius, midsphere radius, circumscribed sphere radius
Visual: a cube with its diagonals and related measures highlighted
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Cylinder Volume Calculator
A cylinder's volume grows steadily as its height increases while its circular base remains fixed.
Example use: Estimating how much water fits inside a tall container.
Inputs: radius, height
Outputs: volume, surface area, lateral surface area, base area, volume to surface ratio, capacity approximate
Visual: a cylinder with its height and base marked, alongside a comparison of volume and surface area
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Ellipsoid Volume Calculator
An ellipsoid encloses space by stretching a sphere along three perpendicular directions, changing both volume and surface area.
Example use: Estimating the space inside an egg-shaped object.
Inputs: semi-axis a, semi-axis b, semi-axis c
Outputs: volume, surface area, surface area to volume ratio, global flattening, linear eccentricity
Visual: an ellipsoid with its three perpendicular lengths shown and how scaling affects volume and area
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Hemisphere Volume Calculator
A hemisphere represents half of a sphere, combining a curved outer surface with a flat circular base to define its volume.
Example use: Estimating how much fruit fits inside a half-round bowl.
Inputs: radius
Outputs: hemisphere volume, full sphere volume, curved surface area, base surface area, total surface area, hemisphere height, volumetric centroid from base, surface-to-volume ratio, moment of inertia factor, approximate mass using water density
Visual: a half-sphere with its curved surface, base circle, and volume comparison to a full sphere
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Rectangle Prism Volume Calculator
A rectangular prism encloses space using three perpendicular lengths, giving a straightforward relationship between its edges and volume.
Example use: Estimating the capacity of a box-shaped drawer.
Inputs: length, width, height
Outputs: volume, base area, lateral surface area, total surface area, volume to surface ratio, space diagonal, base perimeter, total edge length, circumscribed sphere radius, equivalent cube edge, face diagonal for length-width, face diagonal for length-height, face diagonal for width-height
Visual: a box shape with its edges, diagonals, and surface areas highlighted
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Rectangular Pyramid Volume Calculator
A rectangular pyramid encloses space by rising from a rectangular base to a single apex, forming four triangular faces.
Example use: Estimating the volume of a small decorative pyramid.
Inputs: base length, base width, vertical height
Outputs: volume, base area, base perimeter, slant height along length side, slant height along width side, corner edge length, lateral surface area, total surface area
Visual: a pyramid with its base, sloping edges, and surface areas shown for comparison
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Spherical Zone Volume Calculator
A spherical zone forms when a sphere is cut by two parallel planes, creating a curved band with two circular ends.
Example use: Estimating the volume of a rounded slice taken from a ball.
Inputs: top radius, bottom radius, height
Outputs: segment volume, corresponding sphere radius, top base area, bottom base area, segment curved surface area, segment total surface area, solid angle, slant arc length as surface distance, mean curvature, volume relative to full sphere, distance from centre to top base, distance from centre to bottom base
Visual: a curved band of a sphere with its two circular ends, height, and related distances marked
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Sphere Volume Calculator
A sphere encloses space evenly in all directions from its centre, giving a smooth relationship between its radius and volume.
Example use: Estimating the space inside a round ornament.
Inputs: radius
Outputs: volume, surface area, circumference, surface-area-to-volume ratio, volume change per one percent radius increase
Visual: a sphere with its radius marked and a comparison of how volume changes with radius
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Spherical Cap Volume Calculator
A spherical cap forms when a sphere is cut by a single plane, leaving a curved top with a circular base.
Example use: Estimating the volume of a rounded lid shape.
Inputs: base radius, cap height
Outputs: cap volume, sphere radius, curved surface area, base area, total surface area, base circumference, spherical sector volume, volume relative to sphere, polar angle
Visual: a curved top section of a sphere with its height, base circle, and related measures shown
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Square Pyramid Volume Calculator
A square pyramid encloses space using a square base and four identical triangular faces rising to a single apex.
Example use: Estimating the volume of a small square-based model.
Inputs: base side length, vertical height
Outputs: volume, base area, slant height, lateral edge length, single face area, total surface area, height-to-base ratio
Visual: a square-based pyramid with its height, sloping faces, and surface areas highlighted
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Square Pyramidal Frustum Volume Calculator
A square pyramidal frustum forms when the top of a square pyramid is removed, leaving two square ends joined by four sloping faces.
Example use: Estimating the capacity of a tapered container with a square opening.
Inputs: top side length, base side length, vertical height
Outputs: total volume, total surface area, lateral surface area, top base area, bottom base area, slant height, taper ratio, volume of removed cap
Visual: a shortened square pyramid with its top and base squares and sloping sides shown from above
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Tetrahedron Volume Calculator
A tetrahedron encloses space using four triangular faces, each meeting at sharp edges and corners.
Example use: Estimating the volume of a small triangular decoration.
Inputs: edge length
Outputs: volume, total surface area, vertical height, slant height as face height, single face area, inradius, circumradius, exradius, dihedral angle, surface area to volume ratio
Visual: a triangular pyramid with its edges, face heights, and surface areas shown
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Torus Volume Calculator
A torus encloses space in a ring shape formed by rotating a circle around an external axis.
Example use: Estimating the space inside a ring-shaped float.
Inputs: major radius, minor radius
Outputs: volume, major circumference, minor circumference, surface area, cross-sectional area, aspect ratio, surface-to-volume ratio, outer diameter, inner hole diameter
Visual: a ring shape with its outer and inner measures shown and a comparison of volume and surface area
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Triangular Prism Volume Calculator
A triangular prism encloses space by extending a triangular base along a straight length, forming three rectangular sides and two triangular ends.
Example use: Estimating the capacity of a long triangular gift box.
Inputs: base of triangle, height, prism length
Outputs: volume, base area as triangular, base perimeter, base hypotenuse, lateral surface area, total surface area, volume to surface ratio, space diagonal
Visual: a prism with its triangular end, extended length, and surface areas shown
Volume Calculators FAQs
Volume describes the internal space of a three-dimensional shape, expressed in cubic units representing total capacity.
Volume measures internal space, while surface area measures the total outer coverage of a solid. They use cubic and square units respectively.
Many volumes use base area multiplied by height. For example, a cylinder uses the expression V = πr²h to describe its internal capacity.