Mass Calculator
Calculate mass from density and volume with M = ρ × V. Enter any density and volume — get mass in kg and lbs for engineering, construction, and materials work.
Enter your values above to see the results.
Tips & Notes
- ✓Unit consistency is critical: if density is in kg/m³, volume must be in m³ to get mass in kg. If density is in g/cm³, volume in cm³ gives mass in grams (divide by 1,000 for kg). Common: water = 1.000 g/cm³ = 1,000 kg/m³; steel = 7.85 g/cm³ = 7,850 kg/m³.
- ✓Density of water as a reference: 1 g/cm³ = 1 kg/L = 1,000 kg/m³. A 1-cubic-meter volume of water weighs exactly 1,000 kg = 1 metric ton. Materials denser than water (ρ > 1 g/cm³) sink; materials less dense (ρ < 1 g/cm³) float.
- ✓Volume conversion before calculation: 1 m³ = 1,000,000 cm³ = 1,000 liters; 1 liter = 1,000 cm³; 1 cubic foot = 28,316.8 cm³ = 0.028317 m³. Convert volume to consistent units with your density value before multiplying.
- ✓For irregularly shaped objects, find volume by water displacement: submerge the object in a graduated container and measure the volume of water displaced. Multiply by density to get mass. Archimedes used this principle for the famous crown problem.
- ✓Buoyancy check: an object floats if its average density is less than the fluid. A hollow steel sphere with average density 0.5 g/cm³ floats in water (ρ_water = 1.0 g/cm³). Ships float because their overall density (steel hull + air inside) is less than seawater (1.025 g/cm³).
Common Mistakes
- ✗Mixing density units (g/cm³ with m³ volumes) — if density is 7.85 g/cm³ and volume is 0.5 m³: incorrect: 7.85 × 0.5 = 3.925 (wrong units). Correct: convert 0.5 m³ to cm³ (= 500,000 cm³) → mass = 7.85 × 500,000 = 3,925,000 g = 3,925 kg. Or convert density to kg/m³ first: 7.85 g/cm³ × 1,000 = 7,850 kg/m³ → 7,850 × 0.5 = 3,925 kg ✓.
- ✗Using bulk density instead of material density for porous materials — bulk density (e.g., sand = 1,600 kg/m³) includes air spaces between particles. Solid grain density of quartz sand = 2,650 kg/m³. Use bulk density for loose material; solid density for continuous material. A cubic meter of loose sand weighs 1,600 kg, not 2,650 kg.
- ✗Ignoring temperature effects on density — water density at 20°C = 0.9982 g/cm³; at 4°C = 1.0000 g/cm³; at 100°C = 0.9584 g/cm³. For most engineering, standard density at 20°C (or 25°C) is used. For precise thermodynamic or chemical calculations, use temperature-corrected densities.
- ✗Confusing mass and weight in gravity-variable contexts — M = ρ × V gives mass (kg), which is constant regardless of gravity. Weight = M × g (newtons). On the Moon (g = 1.62 m/s²), a 10 kg object weighs 16.2 N, not the 98.1 N it weighs on Earth. Mass is always mass; weight depends on gravitational acceleration.
- ✗Using wrong density for mixtures — the density of concrete (2,400 kg/m³) is an average of cement, sand, and aggregate. If you change the mix ratio, density changes. For alloys: brass density (8,500 kg/m³) differs from pure copper (8,960) and zinc (7,130). Use the specific alloy or mixture density, not a pure component value.
Mass Calculator Overview
The mass formula M = ρ × V is the fundamental link between geometry (volume), material properties (density), and the physical quantity that determines structural loads, shipping weights, and buoyancy. Understanding mass through density and volume is essential for engineers, construction professionals, chemists, and anyone specifying or ordering bulk materials.
Mass from density and volume:
M = ρ × V | ρ = M / V | V = M / ρ | SI: kg = (kg/m³) × m³
EX: Steel column 0.25 m × 0.25 m × 3 m tall = 0.1875 m³ × 7,850 kg/m³ = 1,472 kg = 3,245 lbs. Concrete slab 10 m × 5 m × 0.15 m = 7.5 m³ × 2,400 kg/m³ = 18,000 kg = 18 metric tons = 39,683 lbsUnit conversion for density calculations:
1 g/cm³ = 1,000 kg/m³ | 1 kg/L = 1 g/cm³ | 1 m³ = 1,000 L = 1,000,000 cm³
EX: Honey at 1.4 g/cm³: 5-liter jar → volume = 5,000 cm³ → M = 1.4 × 5,000 = 7,000 g = 7 kg = 15.43 lbs. Or: 1.4 g/cm³ = 1.4 kg/L → M = 1.4 × 5 L = 7 kg ✓Material density reference (kg/m³ and g/cm³):
| Material | Density (kg/m³) | Density (g/cm³) | Mass of 1 m³ in lbs |
|---|---|---|---|
| Air (20°C, 1 atm) | 1.204 | 0.001204 | 2.65 lbs |
| Pine wood (dry) | 500-600 | 0.50-0.60 | 1,102-1,323 lbs |
| Water (4°C) | 1,000 | 1.000 | 2,205 lbs |
| Concrete | 2,300-2,400 | 2.30-2.40 | 5,071-5,291 lbs |
| Aluminum | 2,700 | 2.70 | 5,952 lbs |
| Iron / Steel | 7,750-7,900 | 7.75-7.90 | 17,085-17,416 lbs |
| Copper | 8,960 | 8.96 | 19,754 lbs |
| Lead | 11,340 | 11.34 | 25,000 lbs |
| Gold | 19,300 | 19.30 | 42,549 lbs |
| Application | Volume | Density | Mass (kg) | Mass (lbs) |
|---|---|---|---|---|
| Bathtub of water | 300 L | 1.0 kg/L | 300 kg | 661 lbs |
| Car fuel tank (full) | 60 L gasoline | 0.74 kg/L | 44.4 kg | 97.9 lbs |
| Office desk (oak) | 0.1 m³ | 800 kg/m³ | 80 kg | 176 lbs |
| Concrete slab (1m×1m×0.15m) | 0.15 m³ | 2,400 kg/m³ | 360 kg | 794 lbs |
| Steel I-beam (10m, W12×96) | variable | 7,850 kg/m³ | ~1,430 kg | ~3,152 lbs |
Frequently Asked Questions
Mass = Density × Volume. Ensure units are consistent. Examples using kg/m³ and m³: steel block 0.1 m³, density 7,850 kg/m³ → Mass = 7,850 × 0.1 = 785 kg = 1,730.6 lbs. Water 2 m³, density 1,000 kg/m³ → Mass = 1,000 × 2 = 2,000 kg = 4,409.2 lbs. Using g/cm³ and cm³: aluminum cube 500 cm³, density 2.70 g/cm³ → Mass = 2.70 × 500 = 1,350 g = 1.35 kg = 2.976 lbs.
Material densities (kg/m³): concrete 2,300-2,400; granite 2,600-2,700; brick (fired) 1,800-2,000; dry wood (pine) 500-600; dry wood (oak) 700-900; glass 2,400-2,800; aluminum alloy 2,700; iron/steel 7,700-7,900; copper 8,960; lead 11,340; gold 19,300. Example: a concrete slab 5 m × 4 m × 0.15 m = 3.0 m³ → mass = 3.0 × 2,350 = 7,050 kg = 15,543 lbs ≈ 7.05 metric tons.
Same formula: M = ρ × V. For liquids: water 1.000 kg/L (at 4°C); whole milk 1.030 kg/L; honey 1.36-1.45 kg/L; ethanol 0.789 kg/L; crude oil 0.78-0.97 kg/L. Example: 200 liters of diesel (density 0.845 kg/L) → mass = 0.845 × 200 = 169 kg = 372.6 lbs. For gases: must specify temperature and pressure. Air at 20°C, 1 atm: density = 1.204 kg/m³. A room 5 m × 4 m × 3 m = 60 m³ of air → mass = 1.204 × 60 = 72.24 kg = 159.3 lbs.
Structural engineers calculate mass to determine loads. A steel I-beam W12×96 (96 lbs/ft = 143.3 kg/m) spanning 10 m: mass = 143.3 × 10 = 1,433 kg = 3,159 lbs. Concrete floor slab: area 100 m² × 0.20 m thick × 2,400 kg/m³ = 48,000 kg = 48 metric tons — this is the dead load on the supporting structure. Water tank 50,000 liters of water: 50,000 kg = 50 metric tons = 110,231 lbs — this is the structural load when full. Foundation sizing, beam selection, and column design all depend on accurate mass calculations from density and volume.
Specific gravity (SG) is the ratio of a material density to water density (1,000 kg/m³ or 1 g/cm³). SG is dimensionless and equals density in g/cm³ numerically. SG > 1: sinks in water. SG < 1: floats. Examples: aluminum SG = 2.70 (same as 2.70 g/cm³ = 2,700 kg/m³); wood (oak) SG = 0.7-0.9 (floats); gold SG = 19.3 (sinks rapidly); ice SG = 0.917 (floats — why icebergs float); seawater SG = 1.025. Mass calculation using SG: M = SG × 1,000 (kg/m³) × V (m³). A 0.5 m³ piece of oak (SG = 0.8): M = 0.8 × 1,000 × 0.5 = 400 kg = 881.8 lbs.
Buoyancy (Archimedes principle): buoyant force = weight of fluid displaced = ρ_fluid × g × V_submerged. An object floats when buoyant force equals gravity force. Condition: ρ_object < ρ_fluid. Steel ship example: steel density 7,850 kg/m³ is far greater than seawater (1,025 kg/m³). But the ship hull creates a large enclosed volume — the average density of (steel hull + enclosed air) is less than 1,025 kg/m³. A 50,000-ton ship displaces 50,000 m³ of seawater (≈50,000 metric tons displaced). Net buoyancy calculation: if average ship density including all cargo is 0.95 g/cm³, it floats in seawater (1.025 g/cm³). Adding cargo increases average density — overloading causes sinking.