Volume Calculator — Free Cube, Sphere, Cylinder & More | AllInOneTools
Home›Math›Volume Calculator
■ 3D Geometry

Volume Calculator

Calculate the volume and surface area of 8 common 3D shapes. See visual diagrams, formulas, and step-by-step solutions.

■Cube
●Sphere
◍Cylinder
△Cone
▭Rect. Prism
△Pyramid
◑Hemisphere
◦Torus
📑 Step-by-Step Solution

Related Calculators

▢Area△Pythagorean△TrianglexnExponent%Percentage📐Logarithm

Volume Formulas for 3D Geometric Shapes

Volume measures the amount of three-dimensional space enclosed within an object. It is fundamental to engineering, manufacturing, shipping, construction, chemistry, and everyday life. Whether you are calculating how much water fills a pool, how much concrete to pour for a foundation, or how much material a container can hold, volume calculations are essential. All volume measurements are expressed in cubic units (cubic meters, cubic feet, liters, gallons, etc.).

All 8 Volume Formulas

Cube: V = s3,  SA = 6s2

Sphere: V = (4/3)pi*r3,  SA = 4*pi*r2

Cylinder: V = pi*r2*h,  SA = 2*pi*r(r+h)

Cone: V = (1/3)*pi*r2*h
  SA = pi*r(r + sqrt(r2+h2))

Rectangular Prism: V = l*w*h
  SA = 2(lw + lh + wh)

Pyramid: V = (1/3)*base_area*h
  (square base: V = (1/3)*s2*h)

Hemisphere: V = (2/3)*pi*r3
  SA = 3*pi*r2

Torus: V = 2*pi2*R*r2
  SA = 4*pi2*R*r
  R = major radius, r = tube radius

Practical Applications

In construction, volume calculations determine quantities of concrete, fill dirt, gravel, or excavation requirements. Shipping companies use cubic volume (dimensional weight) to calculate freight costs. Chemistry and medicine require precise volume measurements for solutions, dosages, and reactions. HVAC engineering uses room volume to size heating and cooling systems. Aquariums and pools need volume for water treatment calculations. Even cooking uses volume measurements (cups, liters, tablespoons).

Volume Unit Conversions
1 cubic meter = 1,000 liters = 264.17 gallons. 1 cubic foot = 7.481 gallons = 28.317 liters. 1 liter = 1,000 cubic centimeters = 0.264 gallons. When converting cubic units, cube the linear factor: 1 foot = 12 inches, so 1 cubic foot = 1,728 cubic inches (12 x 12 x 12).

Frequently Asked Questions

What is volume? ▾
Volume is the amount of 3D space inside a closed surface. It is measured in cubic units (m3, ft3, cm3) or capacity units (liters, gallons).
What is the difference between volume and capacity? ▾
Volume refers to the space an object occupies. Capacity refers to how much a container can hold. They measure the same thing but use different units: cubic meters vs liters.
Why does the sphere formula use 4/3? ▾
The 4/3 comes from integrating the area of circular cross-sections along the radius using calculus. It means a sphere fills exactly 2/3 of its circumscribing cylinder.
Why do cones and pyramids have 1/3? ▾
A cone is exactly 1/3 the volume of a cylinder with the same base and height. Similarly, a pyramid is 1/3 the volume of a prism with the same base and height. This is proven by Cavalieri's principle.
How do I convert cubic meters to liters? ▾
1 cubic meter = 1,000 liters. Multiply cubic meters by 1,000. Example: 0.5 m3 = 500 liters. 1 liter = 1,000 cm3 = 1 dm3.
What is surface area vs volume? ▾
Volume measures the space inside (cubic units). Surface area measures the total area of the outer surface (square units). A ball's volume is how much air it holds; surface area is how much leather covers it.