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Volume Calculator

Calculate volume for any 3D shape

Volume

30 cu ft

Surface Area

62 sq ft

Formula

V = l × w × h

Units

Volume

30 cu ft

V = l × w × h

Surface Area

62 sq ft

Measurements Comparison

Volume (cu ft)30
Surface Area (sq ft)62

V = l × w × h

Volume Conversions

1 m³

1,000 liters

1 ft³

7.48 gallons

1 gallon

3.785 liters

1 liter

1,000 cm³

Related calculators

Area CalculatorCalculate 2D areasConcrete CalculatorConcrete neededSphere CalculatorSphere volume and areaCylinder CalculatorCylinder calculationsCone CalculatorCalculate cone volume, surface area, lateral area, and slant height from radius and height. Shows step-by-step geometry formulas for homework and engineering.Pyramid CalculatorCalculate pyramid volume and surface area for square, rectangular, or triangular bases. Shows slant height, lateral area, and all step-by-step formulas.

Formulas Used

Box Volume

V = length × width × height

The volume of a rectangular box (cuboid) is length times width times height.

Where:

length= Length of the box
width= Width of the box
height= Height of the box

Sphere Volume

V = (4/3)πr³

The volume of a sphere is four-thirds times pi times the radius cubed.

Where:

r= Radius of the sphere
π= Pi, approximately 3.14159

Cylinder Volume

V = πr²h

The volume of a cylinder is pi times radius squared times height.

Where:

r= Radius of the circular base
h= Height of the cylinder

Example Calculations

1Box Volume: 5 × 3 × 2

Inputs

ShapeBox
Length5
Width3
Height2

Result

Volume30
Surface Area62
FormulaV = l × w × h

Volume = 5 × 3 × 2 = 30. Surface Area = 2 × (5×3 + 3×2 + 2×5) = 2 × (15 + 6 + 10) = 62.

2Sphere Volume: Radius 2

Inputs

ShapeSphere
Radius2

Result

Volume33.51
Surface Area50.27
FormulaV = (4/3)πr³

Volume = (4/3) × π × 2³ = (4/3) × π × 8 = 33.51. Surface Area = 4 × π × 2² = 4 × π × 4 = 50.27.

Frequently Asked Questions

Q

How do I calculate volume?

Volume formulas vary by shape. Box: length × width × height. Sphere: (4/3)πr³. Cylinder: πr²h. Cone: (1/3)πr²h.

  • Box/cuboid: V = length × width × height
  • Sphere: V = (4/3)πr³ (e.g., r=5: V ≈ 523.6 cubic units)
  • Cylinder: V = πr²h (e.g., r=3, h=10: V ≈ 282.7 cubic units)
  • Cone: V = (1/3)πr²h (exactly 1/3 of a cylinder with same base and height)
  • Pyramid: V = (1/3) × base area × height
ShapeFormulaExample (dimensions)Volume
Cubes³s = 464 cubic units
Boxl × w × h5 × 3 × 230 cubic units
Sphere(4/3)πr³r = 3≈113.1 cubic units
Cylinderπr²hr = 2, h = 10≈125.7 cubic units
Cone(1/3)πr²hr = 2, h = 10≈41.9 cubic units
Q

What units should I use?

Use consistent units throughout. If measuring in meters, volume will be in cubic meters (m³). The calculator can convert between units.

  • All dimensions must use the SAME unit (don’t mix feet and inches)
  • Metric: mm³, cm³, m³ — Imperial: in³, ft³, yd³
  • For liquids: 1 m³ = 1,000 liters; 1 ft³ = 7.48 gallons
  • Construction: cubic yards (1 yd³ = 27 ft³) for concrete, gravel, soil
  • Shipping: cubic feet or CBM (cubic meters) for cargo volume
Q

How do I convert volume units?

1 m³ = 1,000 liters = 1,000,000 cm³. 1 ft³ = 7.48 gallons. 1 gallon = 3.785 liters.

  • 1 m³ = 1,000 liters = 1,000,000 cm³ = 35.3147 ft³
  • 1 ft³ = 7.48052 US gallons = 28.3168 liters
  • 1 yd³ = 27 ft³ = 764.555 liters = 201.97 US gallons
  • 1 US gallon = 3.78541 liters = 231 in³
  • 1 liter = 61.0237 in³ = 0.001 m³
UnitLitersUS GallonsCubic Feet
1 cm³0.001 L0.000264 gal0.0000353 ft³
1 liter1 L0.264 gal0.0353 ft³
1 ft³28.317 L7.481 gal1 ft³
1 yd³764.6 L201.97 gal27 ft³
1 m³1,000 L264.17 gal35.31 ft³
Q

What is the difference between volume and capacity?

Volume measures the 3D space an object occupies. Capacity refers to how much a container can hold. They use the same units but describe different concepts.

  • Volume: total 3D space an object occupies (including walls)
  • Capacity: usable internal space a container can hold
  • A 12 oz can has ≈21.7 in³ total volume but 12 fl oz (21.6 in³) capacity
  • Both measured in the same units (liters, gallons, ft³)
  • Practical capacity is often 80–90% of geometric volume (due to walls, seals)

Understanding Volume Calculations

1

Volume Formulas for Common 3D Shapes

A 4-inch cube holds 64 cubic inches (4³ = 64), while a sphere with the same 4-inch diameter holds only 33.51 in³ — about 52% of the cube. This ratio is exactly π/6 ≈ 0.5236, and it stays constant regardless of size. Understanding how different shapes occupy space is essential for packing, manufacturing, and engineering design.

Cylinder volume = πr²h. A cylinder with radius 3 and height 10 contains π × 9 × 10 = 282.7 cubic units. A cone with the same base and height holds exactly 1/3 of that: 94.2 cubic units. This 3:1 ratio between cylinder and cone volumes (and between prism and pyramid volumes) is a fundamental geometric relationship proved by Archimedes around 250 BCE.

For irregular shapes, decompose into primitives: a house-shaped cross-section is a rectangle plus a triangle. A silo is a cylinder plus a hemisphere or cone cap. The Area Calculator handles the 2D base shapes; multiplying by height gives prism volumes. The Sphere Calculator handles full and partial sphere calculations.

Cone = 1/3 of Cylinder (same base & height)Cylinderπr²h282.7 units³Cone⅓πr²h94.2 units³Sphere⅔πr³523.6 units³r=3, h=10r=3, h=10r=5CylinderCone (1/3 cylinder)Sphere (4/3 πr³)
Volume formulas with example calculations in cubic units
ShapeFormulaExampleVolume
Cubes³s = 5125
Boxl × w × h8 × 4 × 396
Sphere(4/3)πr³r = 5523.6
Cylinderπr²hr = 3, h = 10282.7
Cone(1/3)πr²hr = 3, h = 1094.2
Pyramid(1/3)BhB = 16, h = 948
2

Unit Conversions for Volume

1 cubic meter = 1,000 liters = 264.17 US gallons = 35.31 cubic feet. These conversion factors are essential for construction (cubic yards for concrete), shipping (cubic meters for CBM freight), and cooking (cups and milliliters). One US gallon = 231 cubic inches = 3.785 liters.

Construction materials are typically ordered in cubic yards: 1 yd³ = 27 ft³ = 764.6 liters. A concrete slab 10 ft × 12 ft × 4 inches requires (10 × 12 × 0.333) / 27 = 1.48 cubic yards. Over-order by 5–10% for waste and uneven ground. The Concrete Calculator handles these conversions and waste factors automatically.

Aquarium and pool volumes use the rectangular formula with adjustments. A 48" × 12" × 16" fish tank holds (48 × 12 × 16) / 231 = 39.9 gallons nominal, but subtract 10–15% for substrate and decorations to get 34–36 gallons of actual water volume. The Aquarium Calculator accounts for these real-world reductions.

Volume Unit Ladder1 m³ = 1,000 L1 yd³ = 764.6 L1 ft³ = 28.32 L1 gal = 3.785 LConstruction1 yd³ = 27 ft³Concrete, gravel, soilAquariumsin³ ÷ 231 = gallonsSubtract 10-15% decor
Common volume unit conversions
FromTo LitersTo GallonsTo Cubic Feet
1 mL0.0010.0002640.0000353
1 liter10.26420.03531
1 gallon3.78510.1337
1 ft³28.3177.4811
1 m³1,000264.1735.31
3

Practical Applications

Shipping costs often depend on dimensional weight: L × W × H / 5000 (cm, for international) or / 139 (inches, for domestic US) gives kilograms-equivalent. A box 60 × 40 × 30 cm has dimensional weight 60×40×30/5000 = 14.4 kg. If the actual weight is 8 kg, the carrier charges for 14.4 kg. Optimizing box dimensions to minimize dimensional weight reduces shipping costs significantly.

Cooking volume measurements: 1 cup = 236.6 mL, 1 tablespoon = 14.79 mL, 1 teaspoon = 4.93 mL. A recipe calling for 2 cups of flour requires 473.2 mL. Scaling a recipe by 1.5× requires precise volume multiplication: 2 cups becomes 3 cups, but 2/3 cup becomes 1 cup — which is easier to measure than 1× 2/3 cup.

Swimming pool water volume determines chemical dosing. A rectangular pool 40 ft × 20 ft × 5 ft average depth holds 40×20×5 / 7.481 = 534 cubic feet = 4,000 gallons. Chlorine dosing is typically 1–3 ppm, requiring 0.13 oz of sodium hypochlorite per 1,000 gallons. The Pool Volume Calculator handles irregular pool shapes including L-shaped and kidney configurations.

  • Concrete: cubic yards — order 5–10% extra for waste
  • Shipping: dimensional weight vs. actual weight (charge the higher)
  • Aquariums: nominal volume minus 10–15% for substrate and decor
  • Pools: average depth method for sloped bottoms
  • Cooking: 1 cup = 236.6 mL, 1 tbsp = 14.79 mL

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Last Updated: Jul 4, 2026

This calculator is provided for informational and educational purposes only. Results are estimates and should not be considered professional financial, medical, legal, or other advice. Always consult a qualified professional before making important decisions. UseCalcPro is not responsible for any actions taken based on calculator results.

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