What is the Volume Calculator?
Volume is the quantification of the three-dimensional space a substance or shape occupies. By convention, the volume of a container represents its fluid capacity—how much liquid or gas it is able to hold—rather than the amount of space the physical container itself displaces.
Our Volume Calculator allows you to rapidly calculate the exact volume for 11 of the most common three-dimensional geometric shapes. Simply select your shape, choose your input unit (metric or imperial), and enter your dimensions. The calculator instantly provides the volume and converts it into common fluid capacities like Liters and US Gallons.
The Shapes & Volume Formulas
In mathematics, the volumes of precise geometric shapes can be calculated using well-defined formulas derived from basic principles or integral calculus. Below are the formulas utilized by our calculator.
Sphere
A sphere is a perfectly round three-dimensional object where every point on the surface is an equal distance (the radius, r) from the center point.
Where r is the radius of the sphere.
Cone
A cone is a solid that tapers smoothly from a flat circular base to a common vertex (the apex). The formula below applies to finite right circular cones.
Where r is the base radius and h is the height.
Cube
A cube is bounded by six square faces, all meeting at right angles. It is a special instance of a rectangular parallelepiped.
Where a is the length of any edge.
Cylinder
A right circular cylinder consists of two parallel circular bases of equal size, connected by a curved surface perpendicular to the bases.
Where r is the base radius and h is the cylinder's height.
Rectangular Tank (Prism)
A rectangular tank (or rectangular prism) is essentially a generalized cube where the length, width, and height can all be different measurements.
Where l is length, w is width, and h is height.
Capsule
A capsule consists of a primary central cylinder with two hemispherical ends. Its volume is exactly equal to the volume of a cylinder plus the volume of a full sphere.
Where r is the radius and h is the height of the cylindrical portion only.
Conical Frustum
A conical frustum is the part of a cone that remains after its top has been sliced off by a plane parallel to its base. Everyday examples include buckets and drinking glasses.
Where r is the top radius, R is the bottom radius, and h is the height.
How to Use This Calculator
- Select your shape: Choose from the dropdown menu (e.g., Sphere, Cylinder, Conical Frustum).
- Choose your unit format: Use the toggle to switch between Metric (meters, centimeters) and Imperial (feet, inches) units.
- Enter dimensions: Fill in the fields matching your shape's parameters (like radius and height).
- Calculate: Click the "Calculate Volume" button.
- Review capacities: Check the resulting breakdown to see your volume in standard cubic units alongside common fluid measurements like Liters and Gallons.
Frequently Asked Questions
The standard International System of Units (SI) measurement for volume is the cubic meter (m³). For smaller measurements, liters (L) or cubic centimeters (cm³) are commonly used. In the imperial system, cubic feet (ft³) and gallons are standard.
Volume refers to the amount of three-dimensional space an object occupies, usually measured in cubic units (like cm³ or ft³). Capacity refers to the amount of substance (usually fluid or gas) a container can hold, typically measured in liters or gallons. Mathematically, the inner volume of a container is equal to its capacity.
For objects without a defined geometric formula, volume can be estimated using water displacement. If you submerge an object in a graduated cylinder filled with a known volume of water, the increase in the water level equals the volume of the irregular object.
A tube is essentially a hollow cylinder. To find the volume of the material making up the tube (not the fluid inside), you calculate the volume of the outer cylinder and subtract the volume of the inner cylinder. The formula is Volume = π × ((d1² - d2²) / 4) × length, where d1 is the outer diameter and d2 is the inner diameter.
When building tanks, swimming pools, or containers (like cylinders or rectangular prisms), the primary goal is often to understand how much liquid they can hold. Converting cubic meters or cubic feet directly into Liters or US Gallons gives a practical, real-world understanding of the container's fluid capacity.