Volume Calculator
Select shape & enter dimensions
Select Shape
Box
Sphere
Cylinder
Cone
Pyramid
Cube
Ellipsoid
Torus
Ad · 300x250
Select a 3D shape and enter its dimensions to calculate volume.
Volume
0cm³
Formula
DimensionsValue
Volume
Volume in other units
Ad · 728x90
Volume Formulas for Every 3D Shape
Volume measures the three-dimensional space an object occupies, expressed in cubic units (cm³, m³, ft³, in³, liters, gallons). Every shape has its own formula derived from geometric principles, many going back to Archimedes.
Box (Cuboid): V = l × w × h
Sphere: V = (4/3) × π × r³
Cylinder: V = π × r² × h
Cone: V = (1/3) × π × r² × h
Square Pyramid: V = (1/3) × l × w × h
Cube: V = s³
Ellipsoid: V = (4/3) × π × a × b × c
Torus: V = 2 × π² × R × r²
Sphere: V = (4/3) × π × r³
Cylinder: V = π × r² × h
Cone: V = (1/3) × π × r² × h
Square Pyramid: V = (1/3) × l × w × h
Cube: V = s³
Ellipsoid: V = (4/3) × π × a × b × c
Torus: V = 2 × π² × R × r²
Volume vs Area
Area measures 2D space (square units). Volume measures 3D space (cubic units). A cone is 1/3 the volume of a cylinder with the same base and height — Archimedes proved this by showing 3 conefuls fill the cylinder exactly.
Unit Conversions
1 m³ = 1,000 liters = 1,000,000 cm³. 1 ft³ = 1,728 in³ = 7.481 gallons = 28.317 liters. 1 US gallon = 231 in³ = 3.785 liters. Always cube the linear factor when converting volume units.
Real-World Uses
Aquarium capacity, concrete for foundations, paint and fuel tank volumes, shipping container sizes, medical IV bag volumes, and cooking conversions all require volume calculations.
Cone = 1/3 Cylinder
A cone with the same base radius and height as a cylinder has exactly 1/3 its volume. Similarly, a pyramid has 1/3 the volume of a rectangular prism with the same base and height.
Volume Questions
What is volume and how is it measured?+
Volume is the amount of 3D space a shape occupies. It is measured in cubic units: cubic centimeters (cm³), cubic meters (m³), cubic inches (in³), cubic feet (ft³). For liquids, volume is measured in liters (1 L = 1,000 cm³) or gallons (1 US gallon = 231 in³ = 3.785 L). Volume is a scalar quantity — it has magnitude but no direction.
What is the volume formula for a sphere?+
V = (4/3) × π × r³, where r is the radius. Example: sphere with radius 5 cm. V = (4/3) × 3.14159 × 125 ≈ 523.6 cm³ (about 0.52 liters). The formula was discovered by Archimedes, who proved a sphere fits inside a cylinder (same diameter and height) at exactly 2/3 of the cylinder's volume. For diameter d: r = d/2, so V = πd³/6.
Why is the volume of a cone one-third of a cylinder?+
A cone and cylinder with the same base and height satisfy V_cone = (1/3) × V_cylinder. This was proved by Archimedes and can be demonstrated physically: filling a cone-shaped cup exactly 3 times fills a cylinder of the same base and height. The same 1/3 relationship applies to a pyramid vs a rectangular prism. Both proofs use the method of exhaustion (calculus before calculus).
How do I convert between volume units?+
Volume conversions cube the linear factor. Since 1 m = 100 cm, then 1 m³ = 100³ = 1,000,000 cm³. Key conversions: 1 m³ = 1,000 liters. 1 ft³ = 1,728 in³. 1 ft³ = 28.317 liters. 1 US gallon = 3.785 liters. 1 imperial gallon = 4.546 liters. 1 barrel (oil) = 42 US gallons = 158.99 liters.
What is the volume of a cylinder?+
V = π × r² × h, where r is the radius of the circular base and h is the height. Example: cylinder with radius 3 cm and height 10 cm. V = π × 9 × 10 ≈ 282.7 cm³. This formula comes from multiplying the base area (πr²) by the height, because a cylinder is a stack of identical circular cross-sections. For a pipe, calculate the volume of the outer cylinder minus the inner cylinder.
How do I calculate how much water an aquarium holds?+
Use the rectangular box formula: V = length × width × height. Measure all three interior dimensions in the same unit. Example: 60 cm × 30 cm × 36 cm = 64,800 cm³ = 64.8 liters (since 1 L = 1,000 cm³). For a round aquarium, use the cylinder formula with the inner radius and water depth as height. In practice, subtract 10–20% for gravel, decorations, and the gap at the top.
What is a torus and what is its volume?+
A torus is a donut-shaped 3D solid. It has two radii: R (the major radius, from the center of the torus to the center of the tube) and r (the minor radius, the radius of the tube itself). Volume = 2π² × R × r². Example: R = 5 cm, r = 2 cm. V = 2π² × 5 × 4 ≈ 394.8 cm³. The formula derives from Pappus's centroid theorem.
What is the difference between volume and surface area?+
Volume is the 3D space inside a shape (cubic units). Surface area is the total area of all outer surfaces (square units). A cube with side 2 m: volume = 8 m³, surface area = 24 m². Volume tells you how much it holds. Surface area tells you how much material wraps the outside. They scale differently: doubling linear dimensions quadruples surface area and octuples volume.
How do I calculate the volume of a pyramid?+
For a square pyramid: V = (1/3) × base length × base width × height. Example: base 6 cm × 6 cm, height 9 cm. V = (1/3) × 36 × 9 = 108 cm³. The Great Pyramid of Giza (base ≈ 230 m × 230 m, height originally 146.5 m) has volume = (1/3) × 230 × 230 × 146.5 ≈ 2,583,283 m³ — roughly 1 billion liters of stone.
How much concrete do I need for a slab?+
Use the box formula: V = length × width × thickness. Example: slab 4 m × 6 m × 0.15 m = 3.6 m³. Add 5–10% for waste. Concrete is ordered in m³ or yd³. One cubic yard = 27 ft³ = 0.7646 m³. Standard mix density is about 2,300 kg/m³, so 3.6 m³ ≈ 8,280 kg.