Volume Calculator
This free volume calculator finds both the volume and surface area of a cube, rectangular box, sphere, cylinder, or cone. Nothing you enter is sent anywhere or stored.
How to Use It
- Choose a shape: Cube, Rectangular Box, Sphere, Cylinder, or Cone.
- Enter its dimensions.
- Volume and surface area update instantly, no submit button.
How It Works
Each shape has its own standard formulas for volume and surface area, built from whichever dimensions define that shape. A sphere only needs a radius, a cube only needs a side length, while a cylinder and cone both need a radius and a height. A cone's surface area formula also relies on its slant height, the distance along its slanted side rather than its straight vertical height, calculated internally from the radius and height using the Pythagorean theorem.
Formulas
cube volume = s³, surface area = 6 × s²
box volume = l × w × h, surface area = 2 × (lw + lh + wh)
sphere volume = (4 ÷ 3) × π × r³, surface area = 4 × π × r²
cylinder volume = π × r² × h, surface area = 2πr² + 2πrh
cone volume = (1 ÷ 3) × π × r² × h, surface area = πr² + πr × slant height
A worked example: a cube with a side length of 3 has a volume of 27 cubic units (3 cubed) and a surface area of 54 square units (6 times 3 squared, one term for each of its 6 identical faces). A cylinder with a radius of 2 and a height of 5 has a volume of about 62.83 cubic units and a surface area of about 87.96 square units.
Everything runs client-side in your browser. Nothing you enter is sent anywhere or stored.
Frequently Asked Questions
What is the difference between volume and surface area?
Volume measures how much 3D space a shape encloses, like how much water a tank can hold. Surface area measures the total area of a shape's outer surface, like how much material it takes to build, wrap, or paint it. A shape's volume and surface area answer different practical questions and generally are not equal to each other.
What is slant height for a cone, and how is it different from height?
A cone's height is the straight vertical distance from its base to its apex. Its slant height is the distance along the cone's slanted side, from the edge of the base up to the apex, which is longer than the vertical height for any real cone. Surface area needs the slant height, not the vertical height, since it is measuring the slanted surface itself.
How do I find the volume of a shape that is not listed?
Many real world objects can be approximated as a combination of the shapes here, a silo as a cylinder with a cone or sphere on top, for example, calculating each part separately and adding the volumes together.
Can you give a real-world example?
A water tank shows the difference well. Its volume tells you how much water it can hold, its capacity. Its surface area tells you how much sheet material it takes to build the tank itself, a completely different number answering a completely different question, even though both come from the same set of dimensions.