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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

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

Related Calculators

Area Calculator

Calculate 2D areas

Concrete Calculator

Concrete needed

Sphere Calculator

Sphere volume and area

Cylinder Calculator

Cylinder calculations

Cone Calculator

Calculate cone volume, surface area, lateral area, and slant height from radius and height. Shows step-by-step geometry formulas for homework and engineering.

Pyramid Calculator

Calculate pyramid volume and surface area for square, rectangular, or triangular bases. Shows slant height, lateral area, and all step-by-step formulas.

Related Resources

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Area Calculator

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Last Updated: Mar 26, 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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