Volume Calculator
Comprehensive volume calculator for common 3D shapes including cubes, rectangular prisms, spheres, cylinders, cones, and square pyramids. Select a shape and enter the required dimensions to calculate both volume and surface area using standard geometric formulas. The calculator provides step-by-step formula explanations and displays results with proper units. Perfect for students, engineers, architects, or anyone working with three-dimensional measurements. All calculations ensure consistent units and provide both volume (cubic units) and surface area (square units) results. All calculations happen instantly in your browser with complete privacy—no data is stored or transmitted.
Volume Calculator
How it works: This calculator calculates the volume and surface area of common 3D shapes. Select a shape and enter the required dimensions. The calculator uses standard geometric formulas: Cube (V = s³), Rectangular Prism (V = lwh), Sphere (V = 4/3πr³), Cylinder (V = πr²h), Cone (V = 1/3πr²h), and Square Pyramid (V = 1/3 × base² × height). Make sure all dimensions use the same unit of measurement.
What Is a Volume Calculator?
A volume calculator computes the three-dimensional space enclosed by a geometric shape. Volume is measured in cubic units (cm³, m³, ft³, in³) or converted to liquid equivalents (liters, gallons). Volume calculations are essential in engineering, construction, manufacturing, cooking, aquatics, and science — anywhere you need to know how much space or material a shape contains.
This calculator covers the most common 3D shapes: cube, rectangular prism, cylinder, sphere, cone, triangular prism, and pyramid. Enter your dimensions in any unit and get instant volume and surface area results.
How to Use This Volume Calculator
- Select your shape from the dropdown (cylinder, sphere, cube, etc.).
- Enter the required dimensions in your preferred unit (cm, m, in, ft).
- The calculator instantly shows volume and surface area with unit labels.
- For liquid capacity, note: 1 ft³ ≈ 7.48 US gallons; 1 m³ = 1,000 liters.
- For mixed units (e.g., radius in inches, height in feet), convert to a single unit first.
Worked Example: Cylindrical Water Tank
A cylindrical tank with radius = 3 ft and height = 10 ft:
Volume = π × r² × h = π × 9 × 10 = 282.74 ft³
Liquid capacity: 282.74 × 7.48 = 2,114.9 US gallons
In liters: 282.74 ft³ × 28.317 = 8,003 liters
Lateral surface area = 2πrh = 2π(3)(10) = 188.5 ft²
Total surface area (with caps) = 188.5 + 2πr² = 188.5 + 56.5 = 245 ft²
Sphere comparison: A sphere with the same 3 ft radius: V = (4/3)πr³ = (4/3)π(27) ≈ 113.1 ft³ — about 40% of the cylinder's volume.
Volume Formulas Reference
| Shape | Volume Formula | Surface Area | Example (r=3, h=10) |
|---|---|---|---|
| Cube | V = s³ | SA = 6s² | s=5: V=125, SA=150 |
| Rectangular Prism | V = l × w × h | SA = 2(lw+lh+wh) | 5×4×3: V=60, SA=94 |
| Cylinder | V = πr²h | SA = 2πr(r+h) | r=3,h=10: V≈282.7, SA≈245 |
| Sphere | V = (4/3)πr³ | SA = 4πr² | r=3: V≈113.1, SA≈113.1 |
| Cone | V = (1/3)πr²h | SA = πr(r+√(r²+h²)) | r=3,h=10: V≈94.2 |
| Triangular Prism | V = (1/2)×b×h×l | SA = bh + l(a+b+c) | Depends on triangle |
| Pyramid | V = (1/3)×base area×h | SA = base + lateral faces | Depends on base shape |
All formulas use standard mathematical constants. π ≈ 3.14159265. Results rounded to 4 significant figures.
Key Concepts: Volume vs. Surface Area and Unit Conversion
Volume vs. surface area. Volume measures the interior space of a 3D object (how much it can hold). Surface area measures the total area of all outer faces (how much material covers it). A can of paint covers surface area; a container holds volume. For real-world applications: a fish tank's capacity is its volume, but the glass needed to build it is determined by surface area.
Cubic unit conversions. 1 m³ = 1,000 liters = 264.2 US gallons. 1 ft³ = 7.481 US gallons = 28.317 liters. 1 in³ = 16.387 mL. When converting between units, remember that cubic conversions are cubed: 1 m = 100 cm, so 1 m³ = 100³ cm³ = 1,000,000 cm³ (not 100 cm³).
Relationship between shape and volume efficiency. Among shapes with equal surface area, the sphere encloses the maximum volume — this is why bubbles are spherical, cells are roughly spherical, and large tanks are often cylindrical or spherical. This mathematical property, called the isoperimetric inequality, explains many natural and engineering design choices.
Tips for Accurate Volume Calculations
Use consistent units throughout. All dimensions must be in the same unit before calculating. A tank measured in feet and inches needs dimensions converted entirely to feet (or entirely to inches) first. Mixed units are the most common source of errors: a cylinder with radius in centimeters and height in meters will give a result in neither cm³ nor m³.
Account for wall thickness in containers. When calculating capacity (how much a container holds), use the interior dimensions — subtract wall thickness from external measurements. A fish tank with 0.5 cm glass and external dimensions 60×30×40 cm has interior dimensions 59×29×39 cm. The difference is small for thin walls but significant for thick concrete or steel vessels.
For irregular shapes, use the water displacement method. Fill the container with a known volume of water, then submerge the irregular object and measure how much the water level rises. The volume displaced equals the object's volume. Archimedes reportedly discovered this principle when tasked with verifying whether a crown was pure gold.
Frequently Asked Questions
How do I calculate the volume of a cylinder?
Volume of a cylinder = π × r² × h, where r is the radius and h is the height. Example: cylinder with radius 5 cm and height 20 cm: V = π × 25 × 20 = 1,570.8 cm³ ≈ 1.571 liters. For diameter (d) instead of radius: V = π × (d/2)² × h.
How do I calculate the volume of a sphere?
Volume of a sphere = (4/3) × π × r³, where r is the radius. Example: sphere with radius 10 cm: V = (4/3) × π × 1000 = 4,188.8 cm³ ≈ 4.189 liters. For a hemisphere (half sphere): V = (2/3) × π × r³.
How do I convert cubic feet to gallons?
1 cubic foot = 7.4805 US gallons. Multiply cubic feet by 7.48 to get US gallons. Example: 100 ft³ × 7.48 = 748 gallons. For UK/imperial gallons: 1 ft³ = 6.229 imperial gallons. For liters: 1 ft³ = 28.317 liters.
How do I calculate the volume of an irregular shape?
For objects that don't fit standard formulas, use water displacement: submerge the object in a graduated container of water and measure the volume increase. Alternatively, for complex 3D shapes, divide them into simpler sub-shapes (prisms, cylinders, cones), calculate each separately, and sum the volumes.
What is the formula for the volume of a cone?
Volume of a cone = (1/3) × π × r² × h. A cone has one-third the volume of a cylinder with the same base and height. Example: cone with radius 4 cm and height 9 cm: V = (1/3) × π × 16 × 9 = 150.8 cm³. The slant height (l) = √(r² + h²) is used for surface area but not volume.
How do I calculate how many gallons a fish tank holds?
Measure interior length, width, and height in inches. Multiply all three to get volume in cubic inches, then divide by 231 (1 US gallon = 231 in³). Example: 48 in × 12 in × 18 in = 10,368 in³ ÷ 231 = 44.9 gallons. Subtract ~10% for gravel and decorations to get usable water volume.
What is surface area and how does it differ from volume?
Volume is the interior space (measured in cubic units: cm³, ft³, liters). Surface area is the total area of all outer surfaces (measured in square units: cm², ft²). Volume determines capacity — how much a container holds. Surface area determines materials needed — how much glass for a tank, how much paint to coat a shape. They scale differently: doubling linear dimensions multiplies volume by 8 but surface area by only 4.
How do I calculate the volume of a pyramid?
Volume of a pyramid = (1/3) × base area × height. For a square-base pyramid: V = (1/3) × s² × h. For the Great Pyramid of Giza (s ≈ 230 m, h ≈ 138.5 m): V = (1/3) × 52,900 × 138.5 ≈ 2,441,000 m³. The (1/3) factor applies to all pyramids regardless of base shape — a cone is a pyramid with a circular base.