Volume Calculator
Calculate the volume of common three-dimensional shapes including rectangular prisms, cubes, cylinders, spheres, cones, and triangular prisms with formulas and step-by-step results.
Calculate volume
Select a three-dimensional shape, choose a measurement unit, enter its dimensions, and calculate the volume. The calculator automatically uses the matching formula and explains the calculation.
Your result
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| Shape | — |
| Unit | — |
| Dimensions | — |
| Formula | — |
| Volume | — |
Step-by-step calculation
What is volume?
Volume is the amount of three-dimensional space occupied by an object or enclosed by a solid. Unlike length, which measures one dimension, and area, which measures a two-dimensional surface, volume accounts for three dimensions.
Volume is expressed in cubic units because three lengths are combined. Common units include cubic meters (m³), cubic centimeters (cm³), cubic feet (ft³), and cubic inches (in³). The correct unit depends on the dimensions used in the calculation.
How is volume calculated?
The formula for volume depends on the geometry of the object. A rectangular prism uses three perpendicular dimensions, while a cylinder and sphere require radius measurements and formulas involving π. A cone also uses radius and height, but its volume is one-third of the corresponding cylinder with the same radius and height.
This calculator asks you to select the shape first. It then changes the input fields to match the dimensions required by that shape and applies the appropriate formula.
Rectangular Prism
Uses length, width, and height. This includes box-shaped objects with rectangular faces.
Cube
All edges have the same length, so one side measurement is sufficient.
Cylinder
Uses the radius of the circular base and the perpendicular height.
Sphere
Uses the radius measured from the center to the surface.
Cone
Uses the base radius and perpendicular height; the result includes the one-third factor.
Triangular Prism
Uses the base and height of the triangular cross-section plus the prism length.
Volume calculator example
Suppose a rectangular prism is 10 meters long, 5 meters wide, and 4 meters high. Its volume is found by multiplying the three dimensions.
Volume = Length × Width × Height
Step 2 — Substitute the dimensions
Volume = 10 × 5 × 4
Step 3 — Calculate
Volume = 200 m³
Therefore, the rectangular prism contains 200 cubic meters of volume.
Volume formulas for common shapes
V = l × w × h
Cube:
V = s³
Cylinder:
V = πr²h
Sphere:
V = ⁴⁄₃πr³
Cone:
V = ¹⁄₃πr²h
Triangular Prism:
V = ½ × b × h × L
In these formulas, V represents volume, r is radius, h is height, s is cube side length, l and w are rectangular-prism dimensions, b is the triangular base, and L is the prism length.
Understanding radius, diameter, and height
For circular solids such as cylinders, spheres, and cones, it is important to distinguish radius from diameter. The radius extends from the center of a circle to its edge, while the diameter spans the full circle through its center.
Diameter = 2 × Radius
Radius = Diameter ÷ 2
If a problem gives you a diameter instead of a radius, convert it to a radius before using a formula containing r² or r³. Entering the diameter directly as the radius would produce an incorrect result.
Why volume is measured in cubic units
When three dimensions measured in the same unit are multiplied, the unit is multiplied three times. For example, meters × meters × meters becomes cubic meters, written as m³.
This also explains why changing a measurement unit can change the numerical value substantially. A cubic-unit conversion is not the same as a simple length conversion; the conversion factor is applied in all three dimensions.
How to use the volume calculator
- Select the shape that matches the object.
- Select the unit used for your measurements.
- Enter every required dimension shown by the calculator.
- Click Calculate Volume.
- Review the formula, substitution, and final cubic-unit result.
For the most reliable result, make sure all dimensions belong to the same unit system before calculating. Do not mix meters and centimeters in a single calculation unless you first convert them consistently.
Common mistakes when calculating volume
- Using area instead of volume: area is measured in square units, while volume is measured in cubic units.
- Using diameter as radius: halve the diameter before using a radius-based formula.
- Mixing units: convert all dimensions to a consistent unit before multiplying.
- Forgetting the one-third factor: a cone has one-third the volume of a cylinder with the same radius and height.
- Using slant height as cone height: the standard cone-volume formula uses perpendicular height.
- Rounding too early: keep sufficient precision during intermediate calculations, especially when π is involved.
Volume and capacity are related but not identical
Volume describes the three-dimensional space occupied by a solid, while capacity commonly describes how much a container can hold. Capacity is often expressed in liters, milliliters, gallons, or similar units.
The same physical space can be described using different unit systems. For example, a container’s internal volume may be calculated in cubic centimeters and then converted to a capacity unit when appropriate.
Where volume calculations are used
Volume calculations are useful in geometry, construction, engineering, manufacturing, packaging, storage, architecture, science, and everyday measurement. Examples include estimating the space inside a tank, determining the material needed for a solid object, comparing container sizes, or calculating the capacity of a box-shaped package.
In technical work, the accuracy of the final volume also depends on the quality of the measurements and on whether the chosen geometric model accurately represents the real object.
When this calculator is useful
This calculator is intended for common idealized shapes: rectangular prisms, cubes, cylinders, spheres, cones, and triangular prisms. It is especially useful for learning the formulas, checking arithmetic, and obtaining a transparent calculation from known dimensions.
Irregular objects may require a different method, such as dividing the object into simpler solids, using measured displacement, or applying a specialized geometric or engineering model.
Frequently asked questions
What is the basic formula for volume?
There is no single formula for every shape. For a rectangular prism, volume is length × width × height. Other shapes use formulas based on their geometry.
What units are used for volume?
Volume is measured in cubic units such as m³, cm³, ft³, and in³. The result uses the cube of the unit entered for the dimensions.
How do I calculate the volume of a cube?
Multiply the side length by itself three times: V = s³. Only one side measurement is required because all sides of a cube are equal.
How do I calculate cylinder volume?
Use V = πr²h, where r is the radius of the circular base and h is the perpendicular height.
What is the difference between radius and diameter?
The diameter is twice the radius. If a problem gives diameter, divide it by two before entering the value into a radius field.
Why does a cone have a one-third factor?
The volume of a cone is V = ¹⁄₃πr²h. For the same base radius and height, this is one-third of the corresponding cylinder’s volume.
Can I use different units for different dimensions?
It is best to convert all dimensions to the same unit before calculating. Mixing units without conversion can produce an incorrect volume.
Does this calculator work for irregular objects?
No. It is designed for the six listed geometric shapes. Irregular objects require a suitable alternative method or a combination of simpler geometric solids.
Does the calculator show the formula and steps?
Yes. After calculation, the result includes the selected shape, dimensions, formula, numerical substitution, and final volume.