Geometry Tool
Volume Calculator
Calculate volume of common 3D shapes.
Σ The Formula
Cube: V = s³ | Sphere: V = (4/3)πr³ | Cylinder: V = πr²h | Cone: V = (1/3)πr²h
Real World Examples
Water Tank
Cylinder: r=5m, h=10m → V = 785.4 m³
Basketball
Sphere: r=12cm → V = 7238.2 cm³
Shipping Box
Prism: l=30cm, w=20cm, h=15cm → V = 9000 cm³
Ice Cream Cone
Cone: r=4cm, h=12cm → V = 201.06 cm³
# About This Calculator
Volume measures the 3D space inside an object - how much it can hold. Measured in cubic units (cm³, m³, liters), volume is essential for determining capacity, material needs, shipping costs, and countless engineering calculations.
Volume calculations are crucial in manufacturing (material costs), shipping (package sizes), construction (concrete needed), fluid dynamics (tank capacity), cooking (ingredient measurements), and medicine (dosages).
Formulas Used
- Cube: $V = s^3$
- Rectangular Prism: $V = l \times w \times h$
- Cylinder: $V = \pi r^2 h$
- Sphere: $V = \frac43 \pi r^3$
- Cone: $V = \frac13 \pi r^2 h$
How To Use
- Select your **Shape** from the dropdown.
- Enter the required dimensions (Radius, Height, etc.).
- Click **Calculate Volume**.
Frequently Asked Questions
What's the difference between volume and capacity?+
Volume is the 3D space an object occupies (measured in cm³, m³). Capacity is how much a container can hold (measured in liters, gallons). They're related: 1 liter = 1000 cm³. A box might have volume 2000 cm³ and capacity 2 liters.
How do I convert cubic meters to liters?+
1 m³ = 1000 liters. To convert: multiply m³ by 1000 to get liters. For example, a 2m³ tank holds 2000 liters. A 500L container is 0.5 m³.
Why is a cone's volume 1/3 of a cylinder?+
Geometric proof shows that 3 identical cones exactly fill a cylinder with the same base and height. So cone volume = (1/3) × cylinder volume = (1/3)πr²h.
How much does water weigh per volume?+
1 m³ of water measures 1000 liters and weighs 1000 kg (1 metric ton). 1 liter weighs 1 kg. This makes estimating weight for tanks very easy!
Can I calculate volume for irregular shapes?+
Not with this simple tool. For irregular shapes (like a rock), you typically use 'water displacement': submerge it in water and measure how much the water level rises.
Is Volume Calculator free to use?+
Yes, Volume Calculator on Matheric is completely free to use. We believe in accessible education and utility for everyone.