📦 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)πr³
SA = 4πr²
🛢️ Cylinder
V = πr²h
SA = 2πr² + 2πrh
🔺 Cone
V = (1/3)πr²h
SA = πr² + πr√(r²+h²)
🔷 Square Pyramid
V = (1/3)b²h
SA = b² + 2b√(h²+(b/2)²)
☁️ Hemisphere
V = (2/3)πr³
SA = 3πr²
🍩 Torus
V = 2π²Rr²
SA = 4π²Rr
📏 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)πabc. A sphere is a special case where a=b=c=r. Approximates the shape of many natural objects.

Frequently asked questions

Volume = (4/3) × π × r³. For a sphere with radius 5 cm: V = (4/3) × π × 125 ≈ 523.6 cm³. Surface area = 4πr² ≈ 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 = π × 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 = π × 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 = (π × h / 3) × (R² + Rr + r²).
🔗 Related tools
△Triangle CalcArea & angles σStd DeviationStatistics %PercentageQuick % math