Cubic Meter Calculator — 9 Shape Types
Select a 3D shape, choose your input unit, enter dimensions — get volume in m³, litres, cubic feet, gallons, and more instantly
Room / Slab / Tank
Pipe / Round tank
Hopper / Funnel
Ball / Dome
Roof section / wedge
Embankment / dam
Stockpile / spire
Oil / water tank
L-pool / irregular room
Volume in All Units
Volume Breakdown
Result Summary
Detailed Breakdown
Unit Comparison
Step-by-Step Working
What Is a Cubic Metre? — Complete Volume Guide
Understanding volume measurement, formulas for every 3D shape, and how cubic metres are used in construction, shipping, and industry
A cubic metre (m³) is the SI unit of volume — the amount of three-dimensional space enclosed by a cube with sides of exactly 1 metre each. It is the standard unit for measuring volumes of concrete, water, soil, gas, cargo, and rooms across engineering, construction, and shipping worldwide.
One cubic metre is a surprisingly large amount: it contains exactly 1,000 litres of water, weighs 1,000 kg (one metric tonne) if filled with water, and is roughly the size of a standard washing machine. In shipping, 1 m³ of space is a common unit of freight — a standard 20-foot shipping container holds about 33 m³, and a 40-foot container holds about 67 m³.
The key principle for any volume calculation: multiply three measurements in the same unit. If your dimensions are in metres, the result is in m³. If in centimetres, divide by 1,000,000 to get m³. Getting the unit conversion right before multiplying saves the most common calculation mistakes.
Box / Rectangular Prism
V = L × W × H. The most common volume calculation. Used for rooms, concrete slabs, swimming pools, pits, and shipping boxes. All three dimensions must be in metres for the result to be in m³.
Cylinder
V = π × r² × h. Where r is the radius and h is the height/length, both in metres. Used for round water tanks, silos, pipe volumes, and round columns. Diameter version: V = π × (d/2)² × h.
Cone & Frustum
Cone: V = (1/3) × π × r² × h. Exactly one-third the volume of a cylinder with the same base and height. Frustum (truncated cone): V = (1/3) × π × h × (R² + Rr + r²) where R and r are top and bottom radii.
Sphere & Hemisphere
Sphere: V = (4/3) × π × r³. Hemisphere: V = (2/3) × π × r³. Used for spherical storage tanks, domes, and round balls. Note: doubling the radius increases volume by 8 times (it is cubed, not squared).
Triangular Prism
V = (½ × b × h_tri) × length. Where b is triangle base and h_tri is triangle height (perpendicular). The cross-section is a triangle; the prism has length/depth. Used for roof volumes, wedge-shaped stockpiles, and triangular channels.
Trapezoidal Prism
V = ½ × (a + b) × h × L. Where a and b are the parallel widths at top and bottom, h is the depth, and L is the length. Extremely common for road embankments, irrigation canals, dam cross-sections, and retaining walls.
Square Pyramid
V = (1/3) × L × W × H. Exactly one-third the volume of a rectangular box with the same base and height. Used for material stockpiles, pyramid-shaped hoppers, and architectural spires.
Horizontal Cylinder (partial fill)
For a fully horizontal cylinder: same as vertical. For partial fill at fraction f: V = L × r² × (θ − sin θ)/2 where θ = 2 × arccos(1 − f). Used for truck tankers, oil drums, and horizontal storage vessels.
Volume Unit Conversion — Complete Reference Table
Convert between m³, litres, cubic feet, cubic inches, US gallons, imperial gallons, and more
| From | To | Multiply by | Example |
|---|---|---|---|
| Cubic Metres (m³) | Litres (L) | × 1,000 | 2.5 m³ = 2,500 L |
| Cubic Metres (m³) | Cubic Feet (ft³) | × 35.3147 | 1 m³ = 35.31 ft³ |
| Cubic Metres (m³) | Cubic Inches (in³) | × 61,023.7 | 1 m³ = 61,024 in³ |
| Cubic Metres (m³) | US Gallons | × 264.172 | 1 m³ = 264.17 US gal |
| Cubic Metres (m³) | Imperial Gallons | × 219.969 | 1 m³ = 219.97 Imp gal |
| Cubic Metres (m³) | Cubic Centimetres (cm³) | × 1,000,000 | 0.001 m³ = 1,000 cm³ |
| Litres (L) | Cubic Metres (m³) | ÷ 1,000 | 5,000 L = 5 m³ |
| Cubic Feet (ft³) | Cubic Metres (m³) | × 0.028317 | 100 ft³ = 2.832 m³ |
| Cubic Inches (in³) | Cubic Metres (m³) | × 0.0000163871 | 1,000 in³ = 0.01639 m³ |
| US Gallons | Cubic Metres (m³) | × 0.003785 | 1,000 US gal = 3.785 m³ |
| Cubic Centimetres (cm³) | Litres | ÷ 1,000 | 500 cm³ = 0.5 L |
| Cubic Millimetres (mm³) | Cubic Metres (m³) | ÷ 1,000,000,000 | 1 billion mm³ = 1 m³ |
Cubic Metres in Construction, Shipping & Industry
Practical applications — how m³ is used in concrete, excavation, water, gas, and freight
The cubic metre is one of the most economically important units of measurement in any project involving bulk materials. Here is how it is used across the major industries where accurate volume matters most.
Concrete & Construction
Concrete is always ordered by the cubic metre (m³). Ready-mix trucks typically carry 6–8 m³. For M20 grade concrete, 1 m³ requires approximately 8 × 50 kg bags of cement, 0.42 m³ sand, 0.84 m³ aggregate, and 222 litres of water. Accurate volume calculation prevents over-ordering (waste) and under-ordering (cold joints).
Earthworks & Excavation
Soil and rock are measured in m³ for excavation, backfill, and disposal. A standard JCB excavator can move about 30–60 m³ per day. Note the "bulking factor": excavated soil occupies 20–30% more volume than in-situ. Always add the bulking factor when estimating truck loads.
Water & Liquid Storage
Tank and reservoir capacity is measured in m³ or litres (1 m³ = 1,000 L). A 1 m³ water tank weighs 1,000 kg when full. A standard overhead domestic tank in India is 500–1,000 litres (0.5–1 m³). Municipal overhead water tanks range from 500 m³ to several thousand m³.
Freight & Shipping
Cargo volume is measured in m³ or CBM (cubic metres). Freight charges use whichever is higher: actual weight or volumetric weight (m³ × 250 kg/m³ by air, × 333 kg/m³ by sea). A standard 20-ft container (TEU) holds ~33 m³. A 40-ft high-cube holds ~76 m³.
Natural Gas & LPG
Natural gas volumes are stated in cubic metres (Nm³ at normal conditions: 0°C, 1 atm). 1 Nm³ of natural gas ≈ 10.55 kWh of energy. LPG is measured in litres or kg. A 14.2 kg domestic LPG cylinder ≈ 25 litres of liquid, which expands to about 6.5 m³ of vapour at atmospheric pressure.
Landscaping & Agriculture
Topsoil, compost, and mulch are sold by the m³ or cubic yard (1 yd³ = 0.765 m³). A typical garden bed 4m × 1.5m × 0.3m deep = 1.8 m³ of soil. Irrigation reservoir capacity is measured in m³ or megalitres (1 ML = 1,000 m³). Grain silo capacity is typically 200–2,000 m³.
| Object | Approximate Volume | In Litres | Notes |
|---|---|---|---|
| Teaspoon | 0.000005 m³ | 5 mL | 5 millilitres |
| 1 litre bottle | 0.001 m³ | 1 L | Standard water bottle |
| Bathtub (full) | 0.2–0.3 m³ | 200–300 L | Standard residential tub |
| Domestic water tank | 0.5–1 m³ | 500–1,000 L | Typical overhead plastic tank |
| Cement mixer drum | 0.12–0.35 m³ | 120–350 L | Typical site mixer |
| Ready-mix concrete truck | 6–8 m³ | 6,000–8,000 L | Standard transit mixer |
| Standard room (3.5×4×2.7m) | 37.8 m³ | 37,800 L | Air volume for HVAC |
| Swimming pool (25m standard) | ~375–500 m³ | 375,000–500,000 L | 25m × 12m × 1.25–1.7m |
| 20-ft shipping container | ~33 m³ | 33,000 L | Inner volume approx. |
| Olympic swimming pool | 2,500 m³ | 2,500,000 L | 50m × 25m × 2m |
Volume Formula Reference — All 3D Shapes
Complete formula sheet with worked examples for every shape in this calculator
| Shape | Formula | Variables | Worked Example (result in m³) |
|---|---|---|---|
| Box / Cuboid | L × W × H | L=length, W=width, H=height | 5×4×3 = 60 m³ |
| Cylinder (vertical) | π × r² × h | r=radius, h=height | π×0.5²×2 = 1.571 m³ = 1,571 L |
| Cone (full) | ⅓ × π × r² × h | r=base radius, h=height | ⅓×π×1²×2 = 2.094 m³ |
| Frustum (truncated cone) | ⅓πh(R² + Rr + r²) | R=bottom r, r=top r, h=height | ⅓π×2×(1.5²+1.5×0.5+0.5²) = 5.76 m³ |
| Sphere | 4/3 × π × r³ | r=radius | 4/3×π×1³ = 4.189 m³ |
| Hemisphere | 2/3 × π × r³ | r=radius | 2/3×π×1³ = 2.094 m³ |
| Triangular Prism | ½ × b × h_t × L | b=tri base, h_t=tri height, L=length | ½×4×3×10 = 60 m³ |
| Trapezoidal Prism | ½×(a+b)×h×L | a,b=parallel widths, h=depth, L=length | ½×(4+6)×2×10 = 100 m³ |
| Square Pyramid | ⅓ × L × W × H | L=base length, W=base width, H=height | ⅓×4×4×3 = 16 m³ |
| Horizontal Cylinder (full) | π × r² × L | r=radius, L=length (horizontal) | π×0.8²×3 = 6.032 m³ |
| L-Shaped Prism | (A×B − C×D) × H | A,B=outer; C,D=cut-out; H=height | (8×6−3×2)×1.5 = 63 m³ |
How to Measure & Calculate Cubic Metres — Practical Guide
Step-by-step measuring instructions for construction, shipping, concrete, pools, and soil
Accurate volume calculation starts with accurate measurement. The most common mistake is using mixed units — measuring some dimensions in metres and others in centimetres without converting first. All inputs must be in the same unit before multiplying.
Swimming Pool Volume
Measure length, width, and average depth (not maximum depth). For a pool with variable depth: average depth = (shallow end + deep end) ÷ 2. Multiply all three. A 10×5m pool averaging 1.4m deep = 70 m³ = 70,000 litres. Add 10% for evaporation top-up planning.
Concrete Slab Volume
Measure length × width in metres, thickness in metres (e.g., 150mm = 0.15m). Multiply all three for m³. Add 5–10% for wastage and over-pour. Example: 8m×6m×0.15m = 7.2 m³ + 10% = 7.92 m³, so order 8 m³. At M20 grade, that's about 64 × 50kg bags of cement.
Shipping & Freight CBM
Measure each box: L×W×H in metres = CBM per box. Sum all boxes. Round up to nearest 0.01 m³. For sea freight, the minimum charge is typically 1 CBM. Example: 10 boxes each 60×40×30cm = 0.6×0.4×0.3 = 0.072 m³ each × 10 = 0.72 CBM.
Water Tank & Reservoir
For rectangular tanks: L×W×H(depth). For cylindrical tanks: π×r²×h. Always work in metres. Note: 1 m³ = 1,000 litres = 1 metric tonne of water. A 5,000 L tank = 5 m³. Deduct 15–20cm from height for freeboard (safety margin at the top).
Soil & Earthwork
Excavation volume = length × width × depth (all in metres). Remember the bulking factor: excavated soil expands by 20–30%, so 10 m³ in-situ becomes 12–13 m³ in a truck. For backfill calculation, use the original in-situ volume (soil compacts back down).
Grain Silo & Stockpile
Cylindrical silos: π×r²×h. Cone-topped silos: add (1/3)×π×r²×h_cone. For pyramid-shaped stockpiles: V = (1/3)×L×W×H. For conical stockpiles: V = (1/3)×π×r²×h. Bulk density of grain ≈ 750–850 kg/m³, sand ≈ 1,600 kg/m³, gravel ≈ 1,500–1,800 kg/m³.
Frequently Asked Questions — Cubic Metres & Volume
Expert answers to the most searched questions about cubic metre calculations