Volume Calculator
Calculate Volume for 10+ Geometric Shapes with Complete Formulas and Unit Conversions
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Volume Calculators for Common Shapes
Select your shape and enter dimensions. Results display instantly with unit conversions.
What is Volume?
Volume quantifies the three-dimensional space a substance occupies. Expressed in cubic units (like cubic meters, cubic feet, or liters), volume differs from area (2D) by adding depth. The SI unit for volume is the cubic meter (m³), though practical applications commonly use liters, gallons, or cubic feet.
By convention, a container's volume refers to its capacity—how much fluid it holds—rather than the physical space the container itself displaces. Volume calculations are essential across countless fields: from construction and manufacturing to medicine and cooking. Engineers design reservoirs and tanks using volume formulas. Scientists measure chemical volumes precisely. Architects calculate storage and living spaces. Even household cooking relies on volume measurements.
Complex irregular shapes can be calculated using integral calculus or broken into simpler geometric components. This calculator handles the most common geometric shapes, providing instant accurate results with unit flexibility.
Key Features & Capabilities
This comprehensive volume calculator provides:
How to Use This Calculator
Step-by-Step Instructions
- Select Your Shape: Identify which geometric shape matches your object (sphere, cone, cube, etc.)
- Measure Dimensions: Carefully measure all required dimensions (radius, diameter, height, edge length, etc.)
- Choose Unit: Select the measurement unit from the dropdown (meters, feet, inches, or centimeters)
- Enter Values: Input measured dimensions into the form fields
- Click Calculate: Press the Calculate button to compute volume
- View Results: See volume instantly displayed in the selected unit
- Convert Units (Optional): Use the unit conversion table to see results in other units
Tips for Accurate Calculations
- Consistent Units: All measurements must use the same unit. Mix meters with feet carefully.
- Radius vs Diameter: Remember: radius is half diameter. If given diameter, divide by 2 first.
- Measurement Precision: More precise measurements yield more accurate volume calculations.
- Real-World Context: Consider whether you need interior volume (capacity) or exterior (displacement).
Complete Volume Formulas Reference
Basic Shapes
V = (4/3) × π × r³Where r = radius
V = (1/3) × π × r² × hWhere r = base radius, h = height
V = a³Where a = edge length
V = π × r² × hWhere r = radius, h = height
V = l × w × hWhere l = length, w = width, h = height
V = (1/3) × a² × hWhere a = base edge, h = height
V = π × r² × (h + 4r/3)Where r = radius, h = cylindrical height
V = (4/3) × π × a × b × cWhere a, b, c = three semi-axes
V = (1/3) × π × h × (r² + r×R + R²)Where r = top radius, R = bottom radius, h = height
V = π × (d₁² - d₂²) / 4 × lWhere d₁ = outer diameter, d₂ = inner diameter, l = length
Understanding Each Shape
Sphere
A perfectly round 3D object where all points are equidistant from center. Examples: balls, planets, bubbles. Sphere has no edges or flat surfaces.
Cone
Tapers smoothly from circular base to point (apex). Examples: ice cream cones, traffic cones, funnel. Measured by base radius and height from base to apex.
Cube
Regular 6-sided object with equal edge lengths. Examples: dice, storage boxes, Rubik's cubes. All angles are 90 degrees. Volume = edge³.
Cylinder
Two parallel circular bases connected by curved surface. Examples: cans, drums, pipes, water bottles. Measured by radius and height between bases.
Rectangular Tank
Box with rectangular base (not necessarily square). Examples: aquariums, storage containers, rooms. Volume = length × width × height.
Square Pyramid
Square base tapering to apex point. Examples: Egyptian pyramids, roof peaks. Measured by base edge length and height from base to apex.
Capsule
Cylinder with hemispherical ends. Examples: pills, medical capsules, some storage containers. Combines cylinder and sphere volumes.
Ellipsoid
3D oval shape with three different axes. Examples: footballs, eggs, planets. Generalization of sphere with different radii in three directions.
Conical Frustum
Cone with top cut off by parallel plane. Examples: traffic cones (if top removed), buckets, lampshades. Two circular bases of different sizes.
Tube/Pipe
Hollow cylinder (outer minus inner). Examples: pipes, tubes, hollow containers. Measured by outer diameter, inner diameter, and length.
Volume Unit Conversions
Convert volumes between different measurement systems using these relationships:
| Unit | Cubic Meters | Liters | Cubic Feet | Gallons (US) |
|---|---|---|---|---|
| 1 Cubic Meter | 1 | 1,000 | 35.315 | 264.17 |
| 1 Liter | 0.001 | 1 | 0.03531 | 0.2642 |
| 1 Cubic Foot | 0.02832 | 28.32 | 1 | 7.481 |
| 1 Gallon (US) | 0.003785 | 3.785 | 0.1337 | 1 |
| 1 Cubic Inch | 0.00001639 | 0.01639 | 0.0005787 | 0.004329 |
| 1 Milliliter | 0.000001 | 0.001 | 0.00003531 | 0.0002642 |
Quick Conversion Guide
- Cubic Meters to Liters: Multiply by 1,000
- Liters to Cubic Meters: Divide by 1,000
- Cubic Feet to Cubic Meters: Multiply by 0.02832
- Gallons to Liters: Multiply by 3.785
- Cubic Inches to Cubic Centimeters: Multiply by 16.387
Worked Examples
Example 1: Sphere - Basketball
Problem: A basketball has diameter 24 cm. Find its volume.
Given: d = 24 cm, so r = 12 cm
V = (4/3) × π × r³
V = (4/3) × 3.14159 × 12³
V = (4/3) × 3.14159 × 1,728
V ≈ 7,238 cm³ or 7.24 liters
Example 2: Cylinder - Water Tank
Problem: Cylindrical tank: radius 2 meters, height 5 meters. Find volume in liters.
Given: r = 2 m, h = 5 m
V = π × r² × h
V = 3.14159 × 4 × 5
V = 62.83 m³
V ≈ 62,830 liters
Example 3: Rectangular Tank - Aquarium
Problem: Aquarium: length 3 ft, width 2 ft, height 2.5 ft. Find volume in gallons.
V = l × w × h
V = 3 × 2 × 2.5
V = 15 cubic feet
Converting to gallons: 15 × 7.481 ≈ 112.2 gallons
Example 4: Cone - Ice Cream Cone
Problem: Cone with base radius 2 inches, height 5 inches. Find volume.
V = (1/3) × π × r² × h
V = (1/3) × 3.14159 × 4 × 5
V = (1/3) × 62.83
V ≈ 20.94 cubic inches
Example 5: Rectangular Tank - Pool
Problem: Swimming pool: 10 m × 5 m × 2 m. Find volume in cubic meters and liters.
V = l × w × h
V = 10 × 5 × 2 = 100 m³
Convert to liters: 100 × 1,000 = 100,000 liters
Frequently Asked Questions
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Whether you're designing containers, planning construction, analyzing scientific data, or solving geometry problems, this comprehensive volume calculator handles 10 common shapes with instant results and automatic unit conversions. Fast, accurate, completely free.