Volume Calculator
Calculate the volume and surface area of 3D shapes including cubes, spheres, cylinders, cones, pyramids, and more. Choose your shape and enter dimensions.
V = l × w × hResults
Volume
400 cm³
Select Shape
Enter Dimensions
Calculated Results
Volume
400
cm³
Surface Area
340
cm²
Formula Used
V = l × w × h
Volume Formulas Reference
| Shape | Volume Formula | Surface Area Formula |
|---|---|---|
| Cube | V = s³ | SA = 6s² |
| Rectangular Prism | V = lwh | SA = 2(lw + lh + wh) |
| Sphere | V = (4/3)πr³ | SA = 4πr² |
| Cylinder | V = πr²h | SA = 2πr(r + h) |
| Cone | V = (1/3)πr²h | SA = πr(r + √(r² + h²)) |
| Pyramid | V = (1/3)Bh | SA = B + (1/2)Ps |
| Ellipsoid | V = (4/3)πabc | SA ≈ 4π((ab^p + ac^p + bc^p)/3)^(1/p) |
Common Volume Conversions
Metric
- 1 m³ = 1,000 L = 1,000,000 mL
- 1 L = 1,000 cm³ = 1,000 mL
- 1 cm³ = 1 mL
- 1 m³ = 1,000,000 cm³
Imperial/US
- 1 ft³ = 1,728 in³
- 1 yd³ = 27 ft³
- 1 gallon (US) = 231 in³
- 1 ft³ ≈ 7.48 gallons (US)
Results
Volume
400 cm³
?How to Calculate Volume
Volume measures 3D space. Cube: side cubed. Rectangular prism: length x width x height. Sphere: (4/3) x pi x radius cubed. Cylinder: pi x radius squared x height. Cone: (1/3) x pi x radius squared x height. Pyramid: (1/3) x base area x height. Volume is expressed in cubic units.
What is Volume?
Volume is the measure of the three-dimensional space enclosed within a solid object. It quantifies how much space an object occupies and is expressed in cubic units such as cubic meters, cubic feet, liters, or gallons. Volume calculations are essential for engineering, construction, shipping, cooking, and many practical applications.
Key Facts About Volume
- Volume measures the 3D space occupied by an object, in cubic units
- Cube volume = side cubed (s to the power of 3)
- Rectangular prism = length x width x height
- Sphere volume = (4/3) x pi x r cubed
- Cylinder volume = pi x r squared x height
- Cone volume = (1/3) x pi x r squared x height (1/3 of cylinder)
- Pyramid volume = (1/3) x base area x height
- 1 liter = 1000 cubic centimeters = 0.001 cubic meters
Quick Answer
Volume measures 3D space. Cube: side cubed. Rectangular prism: length x width x height. Sphere: (4/3) x pi x radius cubed. Cylinder: pi x radius squared x height. Cone: (1/3) x pi x radius squared x height. Pyramid: (1/3) x base area x height. Volume is expressed in cubic units.
Frequently Asked Questions
Volume is the amount of three-dimensional space occupied by an object. It's measured in cubic units (like cm³, m³, or ft³). Volume tells you how much a container can hold or how much space an object takes up.
Volume measures the space inside a 3D object (in cubic units), while surface area measures the total area of all the outer surfaces (in square units). For example, volume tells you how much water a box can hold, while surface area tells you how much material you need to wrap it.
Cubic units convert by cubing the linear conversion factor. For example: 1 m³ = 1,000,000 cm³ (because 100³ = 1,000,000). 1 ft³ = 1,728 in³ (because 12³ = 1,728). 1 yd³ = 27 ft³ (because 3³ = 27).
The volume of a sphere is V = (4/3)πr³, where r is the radius. This formula comes from calculus but can be visualized as being related to the volume of a cylinder with the same radius and height equal to the diameter.
A cone's volume is exactly one-third of a cylinder with the same base and height. Cone: V = (1/3)πr²h. Cylinder: V = πr²h. This 1:3 ratio holds for any cone-to-prism or pyramid-to-prism comparison.
For irregular shapes, you can: (1) Break it into regular shapes and add volumes, (2) Use water displacement method, or (3) Use calculus integration for mathematical curves. Many real objects can be approximated using combinations of basic shapes.
Last updated: 2025-01-15
Results
Volume
400 cm³