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). Understanding volume helps optimize designs and estimate costs accurately.

Different shapes have different formulas: cubes use s³, spheres use (4/3)πr³, cylinders use πr²h, cones use (1/3)πr²h, and rectangular prisms use l×w×h. Note that a cone's volume is exactly 1/3 of a cylinder with the same base and height - a beautiful geometric relationship!

This calculator supports common 3D shapes and automatically applies the correct formula with step-by-step calculations. It's perfect for homework, construction planning, container design, or any project requiring volume measurements. Remember: 1 liter = 1000 cm³ = 0.001 m³.

How To Use

  1. Select 3D Shape.
  2. Enter dimensions.
  3. Click Calculate.

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 between cubic meters and liters?+

1 m³ = 1000 liters. To convert: multiply m³ by 1000 to get liters, or divide liters by 1000 to get m³. 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. This relationship is fundamental in calculus and geometry.

How much does a cubic meter of water weigh?+

1 m³ of water = 1000 liters = 1000 kg (1 metric ton). This is by design - the kilogram was originally defined as the mass of 1 liter of water. Useful for calculating water tank weights, shipping costs, or structural loads.

Can I calculate volume for irregular shapes?+

Break them into regular shapes and sum volumes. For example, a capsule is a cylinder + two hemispheres (which together make a sphere). Calculate each part separately, then add. This calculator handles basic shapes; combine results for complex objects.

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.

About

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). Understanding volume helps optimize designs and estimate costs accurately.

Different shapes have different formulas: cubes use s³, spheres use (4/3)πr³, cylinders use πr²h, cones use (1/3)πr²h, and rectangular prisms use l×w×h. Note that a cone's volume is exactly 1/3 of a cylinder with the same base and height - a beautiful geometric relationship!

This calculator supports common 3D shapes and automatically applies the correct formula with step-by-step calculations. It's perfect for homework, construction planning, container design, or any project requiring volume measurements. Remember: 1 liter = 1000 cm³ = 0.001 m³.

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