Free online volume calculator for 8 geometric shapes. Get instant results in m³, ft³, liters, gallons & 8 units. Includes material weight, cost estimator, step-by-step breakdown, and real-world comparisons.
Calculate volume for 8 geometric shapes with multi-unit output, material weight estimation, and real-world comparisons.
🔒 All calculations run locally in your browser. No data is collected, stored, or transmitted to any server.
Calculate volume for any 3D shape in seconds — no sign-up, no ads, completely free.
Select the 3D shape — Cube, Cuboid, Cylinder, Sphere, Cone, Hemisphere, Triangular Prism, or Capsule
Enter the required dimensions (side length, radius, height, base width, etc.)
Choose your unit system — Imperial (feet) or Metric (meters) using the toggle
Optionally select a material (concrete, water, steel, soil…) for weight & cost estimation
Set the fill-level percentage if you need partial capacity volume
Click Calculate Volume to instantly see results in 8 different units
Use Copy, CSV Export, or Print to save and share your results
Pro Tip: Use the Imperial / Metric toggle to switch between feet and meters instantly — all results update automatically, no need to re-enter dimensions.
8 Geometric Shapes
Cube, Cuboid, Cylinder, Sphere, Cone, Hemisphere, Triangular Prism & Capsule — all in one tool
8 Output Units Simultaneously
m³, ft³, yd³, in³, Liters, mL, US Gallons & Imperial (UK) Gallons — all shown at once
Material Weight & Cost Estimator
10 materials: concrete, water, steel, sand, soil, gravel, wood, gasoline, mulch, ice
Visual Charts
Pie chart for fill-level capacity + bar chart comparing volumes across all units visually
Real-World Comparisons
Automatically compares your result to bathtubs, pools, shipping containers & more
Step-by-Step Breakdown
Every calculation step shown with formula derivation — understand how the answer was reached
100% Private & Browser-Based
All calculations run locally in your browser. Zero data sent to any server, ever
History + Export
Last 8 calculations saved locally. Export as CSV or copy to clipboard in one click
Construction Projects
Calculate exact concrete, gravel, or soil volumes for foundations, driveways, and landscaping
Shipping & Packaging
Determine cubic ft/m for freight loads, plan box dimensions, optimize container packing
Pool & Tank Sizing
Find exact pool volume for chemical dosing, or accurately size water and fuel storage tanks
Garden & Agriculture
Calculate mulch, compost, or topsoil needed for raised beds, planters, and crop fields
Science & Engineering
Solve geometry homework, lab vessel sizing, HVAC room air volume, and physics experiments
Aquarium & Fish Keeping
Find exact tank capacity for correct fish stocking density and filtration system sizing
Feature-by-feature comparison with top volume calculators. VIPCalculator leads on 25/25 features.
| Feature | ✦ YOUVIPCalculator | OmniCalculator | CalculatorSoup | GigaCalculator | RapidTables |
|---|---|---|---|---|---|
| Shapes | |||||
| Cube & Cuboid | |||||
| Cylinder & Cone | |||||
| Sphere | |||||
| Hemisphere | |||||
| Triangular Prism | |||||
| Capsule | |||||
| Output Units | |||||
| m³, ft³, Liters, US Gallons | |||||
| Cubic Yards (yd³) | |||||
| Imperial Gallons (UK) | |||||
| Milliliters (mL) & in³ | |||||
| All 8 Units Simultaneously | |||||
| Features | |||||
| Step-by-Step Calculation | |||||
| Material Weight Estimator | |||||
| Material Cost Estimator | |||||
| Fill Level / Capacity % | |||||
| Real-World Comparisons | |||||
| Visual Charts (Pie + Bar) | |||||
| Calculation History | |||||
| CSV Export & Print | |||||
| Imperial & Metric Toggle | |||||
| Trust & Privacy | |||||
| 100% Browser-Based | |||||
| No Login / No Account | |||||
| Formula Derivation Shown | |||||
| NIST / BIPM Referenced | |||||
| No Ads in Calculator UI | |||||
Volume is the measure of three-dimensional space enclosed within a geometric solid, expressed in cubic units (m³, ft³, L, etc.). The formulas below are the standard geometric definitions used in engineering, mathematics, and physical sciences worldwide.
V = a³A cube with side length a has 6 identical square faces. Volume = base area × height = a² × a = a³. The cube is the 3D extension of the square, and its volume formula is the simplest of all regular polyhedra.
Real-world use: Useful for calculating storage boxes, shipping crates, ice cubes, building blocks, and cubic room volumes for HVAC calculations.
V = l × w × hA rectangular prism (cuboid) extends the cube by allowing three different dimensions. Volume = length × width × height. This formula underpins virtually all construction and logistics volume calculations.
Real-world use: Essential for concrete pours, shipping container volumes, room air volume (for AC sizing), aquarium capacity, and raised garden bed soil calculations.
V = π × r² × hThe base of a cylinder is a circle with area πr². Multiplying by height gives the total volume. This formula uses π (pi ≈ 3.14159265), the ratio of a circle's circumference to its diameter, a fundamental mathematical constant.
Real-world use: Critical for fuel tank capacity, water tank sizing, pool volume, grain silo storage, pipe volume calculations, and pharmaceutical dosing vessels.
V = (4/3) × π × r³Archimedes proved the sphere formula ~250 BC by showing a sphere's volume equals 2/3 of its circumscribed cylinder. The modern derivation uses calculus: integrating circular cross-sections from -r to +r gives ∫π(r²-x²)dx = (4/3)πr³.
Real-world use: Used for calculating ball volumes, spherical tank capacity (LNG storage, pressurized tanks), water tower capacity, and planetary volume in science.
V = (1/3) × π × r² × hA cone's volume is exactly 1/3 of the cylinder with the same base and height. Cavalieri's principle (1635) proves that two solids with equal cross-sectional areas at every height have equal volumes — which underlies this 1/3 relationship.
Real-world use: Used in funnel capacity calculations, grain pile volume estimation, ice cream cone sizing, traffic cone material calculations, and volcanic formation volume.
V = (2/3) × π × r³A hemisphere is exactly half of a sphere, so its volume is half of (4/3)πr³ = (2/3)πr³. It also equals the volume of a cylinder of radius r and height r minus the volume of a cone with the same dimensions — a beautiful geometric identity proven by Archimedes.
Real-world use: Used for dome structure volume calculations, bowl capacity, pressure vessel head volumes, and radome (radar dome) interior space calculations.
V = (1/2) × b × h_t × lThe cross-section of a triangular prism is a triangle with area = (1/2) × base × height. Multiplying by the prism length gives total volume. The 1/2 factor arises because a triangle fills exactly half the area of its bounding rectangle.
Real-world use: Used for Toblerone-style packaging, roof space volume calculations, wedge-shaped retaining wall volumes, and prismatic container capacity.
V = π × r² × h + (4/3) × π × r³A capsule is a cylinder with two hemispherical caps. Its volume = cylinder volume (πr²h) + sphere volume ((4/3)πr³). This is the standard formula used in pharmaceutical capsule dosage calculations and pressurized vessel engineering.
Real-world use: Pharmaceutical capsule sizing, submarine hull volume, pressurized gas cylinder calculations, space capsule interior volume, and hot dog (frankfurter) approximate volume.
All volume formulas follow standard geometric principles as defined by the International System of Units (SI) maintained by the Bureau International des Poids et Mesures (BIPM).
Unit conversion constants used: 1 ft = 0.3048 m (exact, per NIST Handbook 44); 1 US gallon = 231 in³ (exact); 1 liter = 1 dm³ (exact).
Material density values are sourced from the Engineering ToolBox and represent average values at standard conditions (20°C, 1 atm). Material cost estimates reflect general market averages and may vary by region and supplier.
Formula derivations are consistent with Wolfram MathWorld — Volumes and Khan Academy Geometry (3D Solids).
⚠️ For critical engineering, construction, or pharmaceutical applications, always verify calculations with a licensed professional. Material costs are estimates only.
Last formula review: January 2026
Standard volume unit conversions per NIST Weights & Measures and BIPM SI Units:
| From | To | Multiply by |
|---|---|---|
| Cubic Meters (m³) | Liters (L) | 1,000 (exact) |
| Cubic Meters (m³) | Cubic Feet (ft³) | 35.31466… |
| Cubic Meters (m³) | US Gallons | 264.1720… |
| Cubic Meters (m³) | Imperial Gallons (UK) | 219.9692… |
| Cubic Meters (m³) | Cubic Yards (yd³) | 1.307951… |
| Cubic Feet (ft³) | US Gallons | 7.480519… |
| Cubic Feet (ft³) | Liters (L) | 28.31685… |
| Liters (L) | US Gallons | 0.264172… |
| Liters (L) | Cubic Inches (in³) | 61.02374… |
| US Gallons | Liters (L) | 3.785411… |
| Imperial Gallons | Liters (L) | 4.546090… |
Conversion factors sourced from NIST Unit Conversions. "Exact" denotes values defined without rounding per international agreement.
Everyday objects and their approximate volumes — useful for cross-checking calculations and understanding scale:
Accurate volume calculation is critical across multiple professional fields. Here's how each industry uses geometric volume formulas:
The systematic calculation of geometric volumes is one of mathematics' oldest achievements. Around 250 BC, Archimedes of Syracuse derived the volume formulas for the sphere and cone in his treatise On the Sphere and Cylinder, proving that a sphere inscribed in a cylinder has volume equal to exactly 2/3 of the cylinder — a result he considered his greatest discovery.
The formula for the volume of a pyramid (and by extension, a cone) was known to ancient Egyptian mathematicians, as evidenced in the Moscow Mathematical Papyrus (c. 1850 BC), which contains a calculation for the volume of a frustum (a truncated pyramid). This predates Archimedes by over 1,500 years.
The modern standardization of volume units began with the French metric system in 1795, which defined the liter as the volume of a 10-centimeter cube (1 dm³). The International System of Units (SI), established in 1960 and maintained by the BIPM, formalized this definition globally. The US customary gallon (231 cubic inches, exactly) was standardized by the National Bureau of Standards in 1836.
For further reading, see Wolfram MathWorld — Volumes and Encyclopædia Britannica — Volume Measurement.