Area of Geometric Shapes Calculator
Calculate the area and perimeter of geometric shapes online: square, rectangle, triangle, circle, trapezoid, rhombus, regular hexagon and ellipse.
Maths
Calculator · Maths
Volume of Geometric Solids Calculator
The volume of geometric solids calculator lets you instantly find the volume of the most common three-dimensional shapes: cube, cuboid, sphere, cylinder, cone, square pyramid and triangular prism. Simply choose the solid, enter the relevant dimensions (side length, radius, height) and press "Calculate" — the result appears immediately. Volume measures the amount of three-dimensional space enclosed by a solid, expressed in cubic units (e.g. cm³, m³, in³). Volume calculations are essential in school geometry, civil engineering, architecture, chemistry (vessel capacity) and many areas of everyday life. The calculator uses standard mathematical formulas and rounds results to 6 decimal places.
How we calculate volume
Cube: V = a³. Cuboid: V = a·b·c. Sphere: V = (4/3)·π·r³. Cylinder: V = π·r²·h. Cone: V = (1/3)·π·r²·h. Square pyramid: V = (1/3)·a²·h. Triangular prism (right-triangle base): V = (a·b/2)·h. All results rounded to 6 decimal places.
Example: volume of a cylinder with radius 5 cm and height 10 cm
Cylinder formula: V = π·r²·h = π × 5² × 10 = π × 25 × 10 ≈ 785.3982 cm³. For a sphere with radius 4 cm: V = (4/3)·π·r³ = (4/3)·π·64 ≈ 268.0826 cm³. For a cube with side 6 cm: V = a³ = 216 cm³.
Frequently asked questions
What is volume in geometry?
Volume is the measure of three-dimensional space enclosed within a solid, expressed in cubic units such as cm³, m³ or in³. It tells you how much space an object occupies or how much liquid a container can hold.
What is the formula for the volume of a cube?
The volume of a cube is V = a³, where a is the length of one side (all sides are equal). For example, a cube with side 4 cm has volume 4³ = 64 cm³.
What is the formula for the volume of a sphere?
The volume of a sphere is V = (4/3)·π·r³, where r is the radius. For a sphere with radius 3 cm: V = (4/3)·π·27 ≈ 113.097 cm³.
What is the formula for the volume of a cylinder?
The volume of a cylinder is V = π·r²·h, where r is the base radius and h is the height. This is the area of the circular base multiplied by the height.
What is the formula for the volume of a cone?
The volume of a cone is V = (1/3)·π·r²·h, where r is the base radius and h is the height. A cone holds exactly one third of the volume of a cylinder with the same base and height.
What is the formula for the volume of a cuboid (rectangular box)?
The volume of a cuboid is V = a·b·c, where a, b and c are the three edge lengths. For example, a box measuring 2 × 3 × 4 cm has volume 24 cm³.
What is the formula for the volume of a square pyramid?
The volume of a square pyramid is V = (1/3)·a²·h, where a is the side length of the square base and h is the perpendicular height. A pyramid holds one third of the volume of a prism with the same base and height.
How do I convert cubic centimetres to litres?
1 litre = 1000 cm³. To convert cm³ to litres, divide by 1000. For example, 785 cm³ = 0.785 litres. To convert m³ to litres, multiply by 1000.
What units should I use in the calculator?
You can use any consistent unit (cm, m, mm, inches). The result will be in the cube of that unit. For example, if you enter dimensions in centimetres, the volume is in cm³. Never mix different units in one calculation.
Why does the volume of a cone equal one-third of a cylinder?
This is a fundamental result of integral calculus. If you fill a cone with sand and pour it into a cylinder of the same base radius and height, you need exactly three cones to fill the cylinder — proving the factor of 1/3 in the formula V = (1/3)·π·r²·h.
Indicative result
Results are for educational and informational purposes. The calculator applies standard geometric formulas. For engineering and construction use, apply material correction factors and industry standards.