?? Geometry

Volume Calculator

Calculate the volume and surface area of any 3D shape. Choose from 12 shapes, pick your units, and get instant results.

Select shape
Length unit
Cube Volume = a³  |  Surface Area = 6a²
?? Volume——
?? Surface Area——
Calculation details

Volume formulas for all shapes

Volume measures the amount of 3D space an object occupies, expressed in cubic units (cm³, m³, etc.). Surface area is the total area of all outer surfaces, expressed in square units.

?? Cube
V = a³
SA = 6a²
?? Rectangular Box
V = l × w × h
SA = 2(lw + lh + wh)
?? Sphere
V = (4/3)pr³
SA = 4pr²
??? Cylinder
V = pr²h
SA = 2pr² + 2prh
?? Cone
V = (1/3)pr²h
SA = pr² + prv(r²+h²)
?? Square Pyramid
V = (1/3)b²h
SA = b² + 2bv(h²+(b/2)²)
?? Hemisphere
V = (2/3)pr³
SA = 3pr²
?? Torus
V = 2p²Rr²
SA = 4p²Rr
?? Unit conversions

1 m³ = 1,000,000 cm³ = 1,000 L. 1 L = 1,000 mL = 1,000 cm³. 1 ft³ = 1,728 in³ = 28.317 L. 1 gallon ˜ 3.785 L.

?? Torus (R and r)

R = major radius (distance from centre of tube to centre of torus). r = minor radius (radius of the tube). A donut has R > r.

?? Frustum

A frustum is a cone or pyramid with the top cut off. It has a larger base radius (R), smaller top radius (r), and height (h). Common shape for buckets and cups.

?? Ellipsoid

An ellipsoid has three semi-axes: a, b, c. V = (4/3)pabc. A sphere is a special case where a=b=c=r. Approximates the shape of many natural objects.

Frequently asked questions

Volume = (4/3) × p × r³. For a sphere with radius 5 cm: V = (4/3) × p × 125 ˜ 523.6 cm³. Surface area = 4pr² ˜ 314.2 cm². Enter the radius in the calculator above and click Calculate.
Volume measures the 3D space inside a shape (cubic units: cm³, m³). Surface area measures the total area of all outer faces (square units: cm², m²). For a box: volume tells you how much it can hold; surface area tells you how much material is needed to make it.
Calculate the volume in cm³ first: V = p × r² × h. Then divide by 1,000 to convert cm³ to litres (1 L = 1,000 cm³). For a cylinder radius 10 cm, height 30 cm: V = p × 100 × 30 ˜ 9,425 cm³ ˜ 9.4 litres.
A frustum is the shape between two parallel cuts of a cone or pyramid — like a bucket or truncated cone. It has a large base radius (R), small top radius (r), and height (h). Volume = (p × h / 3) × (R² + Rr + r²).
?? Related tools
?Triangle CalcArea & angles sStd DeviationStatistics %PercentageQuick % math