Volume Calculator
Volume is the total amount of three dimensional space an object occupies or holds. To find the volume of any standard geometric shape, you multiply its base surface area by its height or depth. For a rectangular box, the formula is length times width times height. For a cylinder, the formula is pi times radius squared times height. For a sphere, it is four thirds times pi times radius cubed.
Dimensions
Volume
523.598776 m³
Formula Used
V = (4/3) × π × r³
Common Unit Conversions
3D View
Sphere
V = (4/3) × π × r³
Where r is the radius
Cube
V = a³
Where a is the edge length
Cylinder
V = π × r² × h
Where r is radius, h is height
Cone
V = (1/3) × π × r² × h
Where r is base radius, h is height
Rectangular Prism
V = l × w × h
Where l, w, h are length, width, height
Pyramid
V = (1/3) × Base Area × h
Where h is the height
Ellipsoid
V = (4/3) × π × a × b × c
Where a, b, c are semi-axes
Conical Frustum
V = (1/3) × π × h × (r₁² + r₁×r₂ + r₂²)
Where r₁, r₂ are top/bottom radii
Spherical Cap
V = (1/3) × π × h² × (3R - h)
Where R is ball radius, h is cap height
Torus
V = 2 × π² × R × r²
Where R is major radius, r is minor radius
Hemisphere
V = (2/3) × π × r³
Half of a sphere
How to Calculate Volume for Common 3D Shapes
Calculating volume depends entirely on the geometric shape you are working with. Below are the standard mathematical formulas used to measure capacity and space for the most common three dimensional objects.
1. Cube
A cube is a six sided shape where every edge has the exact same length. Because all sides are equal, calculating its capacity requires only one measurement.
Formula: Volume = side³
Example: A storage box with a side length of 3 feet has a total volume of 3 × 3 × 3 = 27 cubic feet.
2. Rectangular Prism (Box)
A rectangular prism has six faces that form right angles. This is the standard shape for cardboard boxes, rooms, shipping containers, and aquarium tanks.
Formula: Volume = length × width × height
Example: A room measuring 10 meters long, 8 meters wide, and 3 meters high has a volume of 240 cubic meters.
3. Cylinder
A cylinder consists of two parallel circular bases connected by a curved surface. You can use this formula for water pipes, storage tanks, and soup cans.
Formula: Volume = π × radius² × height
Example: A pipe with a radius of 2 inches and a length of 10 inches has a volume of 3.14159 × 4 × 10 = 125.66 cubic inches.
4. Sphere
A sphere is a perfectly round three dimensional object where every point on the surface is equal distance from the center point.
Formula: Volume = (4 / 3) × π × radius³
Example: A basketball with a radius of 4.7 inches has a volume of (4 / 3) × 3.14159 × 103.823 = 434.89 cubic inches.
5. Cone
A cone features a flat circular base that tapers smoothly up to a single top point called the apex. Its capacity is exactly one third that of a cylinder with the same base and height.
Formula: Volume = (1 / 3) × π × radius² × height
Example: A party hat with a base radius of 3 inches and a height of 7 inches holds (1 / 3) × 3.14159 × 9 × 7 = 65.97 cubic inches.
6. Pyramid
A regular pyramid has a polygon base and triangular sides that meet at an apex point. For a pyramid with a square base, the formula uses the base side length and vertical height.
Formula: Volume = (1 / 3) × base area × height
Example: A square pyramid with a base side of 6 feet and a height of 9 feet has a volume of (1 / 3) × 36 × 9 = 108 cubic feet.
Common Volume Units and Unit Conversions
Volume calculations use cubed distance measurements or liquid capacity units. Choosing the correct unit depends on whether you are working in metric or imperial measurement systems.
| Unit System | Standard Unit | Common Abbreviation | Conversion Equivalent |
|---|---|---|---|
| Metric | Cubic Meter | m³ | 1,000 Liters |
| Metric | Cubic Centimeter | cm³ or cc | 1 Milliliter |
| Metric | Liter | L | 1,000 Milliliters |
| Imperial | Cubic Foot | ft³ | 1,728 Cubic Inches |
| Imperial | Cubic Inch | in³ | 0.000578 Cubic Feet |
| Imperial / US | Gallon (US Liquid) | gal | 231 Cubic Inches |
When performing manual calculations, always ensure that all input dimensions are in the same unit. Mixing inches with feet or meters with centimeters will produce an incorrect answer. You can convert your linear dimensions before calculating or use a dedicated unit converter to adjust your final output.
Real World Applications of Volume Calculations
Understanding three dimensional space is vital across many industries and everyday tasks:
- Construction and Building: Calculating the exact volume of concrete needed for slab foundations, post holes, or footings avoids material waste and delays. You can plan materials better by using a concrete calculator for large building projects.
- Shipping and Logistics: Freight companies determine freight class and shipping rates based on dimensional weight, which relies on box volume measurements.
- Landscaping and Gardening: Determining how many bags of topsoil, mulch, or gravel are required to cover a garden bed at a set depth.
- Aquariums and Pools: Finding the exact water capacity in gallons or liters is necessary to correctly dose water treatments and chemicals.
- Engine Displacement: Measuring the total volume swept by all pistons in an engine block to determine engine size in cubic centimeters or liters.
How to Measure the Volume of Irregular Shapes
Not all physical objects have flat sides or clean circular bases. For odd shapes like rocks, statues, or small mechanical parts, you can use the water displacement method based on Archimedes Principle.
- Select a graduated beaker or measuring container large enough to fit the object.
- Fill the container with enough water to submerge the item completely.
- Record the initial water volume reading.
- Submerge the object fully in the water.
- Record the new water volume level.
- Subtract the initial volume from the final volume. The difference is the exact volume of the irregular object.
For liquid and density calculations, you can also compute volume if you already know the total weight and material density of an item. Dividing mass by density yields the volume, which you can quickly verify with a density calculator.
Frequently Asked Questions
What is the difference between area and volume?
Area measures the two dimensional space inside a flat shape and is expressed in square units. Volume measures the three dimensional space inside an object and is expressed in cubic units.
How do I convert cubic feet to gallons?
Multiply the total cubic feet by 7.48052. For example, a container that holds 10 cubic feet holds roughly 74.8 gallons of liquid.
Why do cone and pyramid formulas use one third?
A cone fits inside a cylinder with the same base and height, taking up exactly one third of its total volume. Similarly, a pyramid occupies one third of the volume of a prism with an identical base area and height.
How do I calculate the volume of a liquid in a partially filled tank?
For a horizontal cylindrical tank, you must calculate the area of the circular segment formed by the liquid depth and multiply that segment area by the total length of the tank.