Volume is the quantification of the three-dimensional space a substance occupies. The SI unit for volume is the cubic meter, or m3. By convention, the volume of a container is typically its capacity, and how much fluid it is able to hold, rather than the amount of space that the actual container displaces. Volumes of many shapes can be calculated by using well-defined formulas. In some cases, more complicated shapes can be broken down into simpler aggregate shapes, and the sum of their volumes is used to determine total volume. The volumes of other even more complicated shapes can be calculated using integral calculus if a formula exists for the shape's boundary. Beyond this, shapes that cannot be described by known equations can be estimated using mathematical methods, such as the finite element method. Alternatively, if the density of a substance is known, and is uniform, the volume can be calculated using its weight. This calculator computes volumes for some of the most common simple shapes.

Sphere A sphere is the three-dimensional counterpart of a two-dimensional circle. It is a perfectly round geometrical object that, mathematically, is the set of points that are equidistant from a given point at its center, where the distance between the center and any point on the sphere is the radius r. Likely the most commonly known spherical object is a perfectly round ball. Within mathematics, there is a distinction between a ball and a sphere, where a ball comprises the space bounded by a sphere. Regardless of this distinction, a ball and a sphere share the same radius, center, and diameter, and the calculation of their volumes is the same. As with a circle, the longest line segment that connects two points of a sphere through its center is called the diameter, d. The equation for calculating the volume of a sphere is provided below:

volume = 4 3 πr3 EX: Claire wants to fill a perfectly spherical water balloon with radius 0.15 ft with vinegar to use in the water balloon fight against her arch-nemesis Hilda this coming weekend. The volume of vinegar necessary can be calculated using the equation provided below: volume = 4/3 × π × 0.153 = 0.141 ft3 Cone A cone is a three-dimensional shape that tapers smoothly from its typically circular base to a common point called the apex (or vertex). Mathematically, a cone is formed similarly to a circle, by a set of line segments connected to a common center point, except that the center point is not included in the plane that contains the circle (or some other base). Only the case of a finite right circular cone is considered on this page. Cones comprised of half-lines, non-circular bases, etc. that extend infinitely will not be addressed. The equation for calculating the volume of a cone is as follows: volume = 1 3 πr2h