Accurately calculate the Volume and Surface Area of geometric shapes. Perfect for students, engineers, and DIY projects.
Formulas Used
Volume
units³
Surface Area
units²
Volume is the measure of 3-dimensional space enclosed by a boundary. Whether you are filling a swimming pool, pouring concrete for a driveway, or packing a shipping container, understanding volume is essential. This calculator supports the most common shapes found in geometry and construction.
Volume formulas are derived from area formulas combined with a height or depth dimension. Here are the core formulas used in this calculator:
V = π × r² × hArea of the circular base (πr²) multiplied by the height.
V = (4/3) × π × r³A unique formula derived by Archimedes.
V = π × r² × (h/3)Exactly one-third of a cylinder with the same dimensions.
V = l × w × hLength times Width times Height. The standard box calculation.
Shipping costs are often calculated by "Dimensional Weight". Carriers calculate the volume of your package (Length x Width x Height) to determine how much space it takes up in the truck or plane. If you ship a large box full of feathers, you pay for the volume, not the weight.
To treat a swimming pool, you need to know exactly how many gallons of water it holds. For a rectangular pool, you calculate the volume in cubic feet (L x W x Avg Depth) and then multiply by 7.5 to get gallons. Getting this wrong leads to unsafe chemical levels.
Concrete is ordered by the "Cubic Yard". A contractor measures the driveway length, width, and slab thickness (converted to feet) to find cubic feet. They then divide by 27 to find Cubic Yards. This Volume Calculator simplifies that entire process.
Volume is the amount of space an object occupies (measured in cubic units like m³ or ft³). Capacity is the amount of liquid or substance an object can hold (measured in Liters or Gallons). For most practical purposes, they are directly convertible (1 cubic meter = 1000 Liters).
For mathematical irregular shapes, you use calculus (integration). For physical objects, you can use the 'Water Displacement Method': submerge the object in water and measure how much the water level rises. The rise in water volume equals the object's volume.
This is a geometric theorem. If you have a cylinder and a cone with the same base radius and height, exactly three cones of liquid will fill the cylinder. It relates to how the cross-sectional area decreases as you go up the height.
Multiply your cubic feet by 7.48. For example, a box with a volume of 10 cubic feet can hold roughly 74.8 gallons of water.
Surface Area is the total area of all the outer faces of a 3D object. While volume tells you how much fits *inside*, surface area tells you how much material you need to *cover* the outside (like wrapping paper or paint).