Density Calculator | ρ = m/V, Mass & Volume
Calculate density, mass, or volume using ρ = m/V. Supports multi-unit inputs, 40+ material presets, specific gravity, buoyancy check, and full unit conversion table.
Solve for
What Is the Density Calculator | ρ = m/V, Mass & Volume?
Density (ρ, “rho”) is the amount of mass packed into a unit volume of a substance. It is one of the most fundamental physical properties: two objects of identical size but different materials will have different weights precisely because their densities differ. A steel ball is heavier than a foam ball of the same volume because steel (~7,874 kg/m³) is roughly 6,000 times denser than expanded foam (~1.3 kg/m³).
Specific gravity (SG) is the ratio of a material's density to the density of water (1,000 kg/m³ at 4°C). It is dimensionless and tells you whether a substance floats or sinks. SG < 1 means the material is less dense than water and will float; SG > 1 means it sinks. Ice has SG ≈ 0.917, it floats, keeping approximately 8% of its volume above the waterline (hence “tip of the iceberg”).
Density varies with temperature and pressure. Water is densest at 4°C (1,000 kg/m³) and less dense at both higher and lower temperatures, which is why ice floats. Gases are far more sensitive to pressure changes than liquids or solids; the density of air at sea level (1.225 kg/m³) drops to roughly 0.66 kg/m³ at 5,000 m altitude.
Formula
Density Formula, Solve for Any Variable
ρ = m / V (solve for density)
m = ρ × V (solve for mass)
V = m / ρ (solve for volume)
Specific gravity:
SG = ρ_material / ρ_water
ρ_water = 1,000 kg/m³ = 1 g/cm³ (at 4°C)
Floats on water if: ρ < 1,000 kg/m³ (SG < 1)
Sinks if: ρ > 1,000 kg/m³ (SG > 1)
| Symbol | Quantity | SI unit | Common alternatives |
|---|---|---|---|
| ρ (rho) | Density | kg/m³ | g/cm³, g/mL, lb/ft³ |
| m | Mass | kg | g, mg, lb, oz, t |
| V | Volume | m³ | cm³, L, mL, ft³, gal |
| SG | Specific gravity | dimensionless | Ratio vs water density |
How to Use
- 1Choose what to solve for: Click Density, Mass, or Volume at the top. The corresponding field is disabled, it will be calculated.
- 2Load a material (optional): Select from the material preset dropdown to automatically fill in a known density value.
- 3Enter the known values: Type the two known quantities and select the correct units from the dropdowns next to each field.
- 4Calculate: Click Calculate or press Enter. Results appear with the primary answer, specific gravity, buoyancy status, and full unit conversions.
- 5Check unit conversions: The results table shows the density, mass, and volume in multiple common units, no need to convert manually.
- 6Reset: Click Reset or press Esc to clear all fields and start a new calculation.
Example Calculation
Example 1, Identify an Unknown Metal
- ›You have a metal block with mass 1.58 kg and volume 200 cm³.
- ›ρ = m / V = 1.58 kg / (200 × 10⁻⁶ m³) = 7,900 kg/m³.
- ›Specific gravity: SG = 7,900 / 1,000 = 7.9.
- ›Comparing to the material table: iron/mild steel ≈ 7,874 kg/m³. This is likely steel.
- ›The material sinks in water (SG > 1) and in most liquids except mercury (SG 13.5).
Example 2, Find Mass from Density and Dimensions
- ›A concrete pillar is 0.3 m × 0.3 m × 2 m (volume = 0.18 m³). Concrete density ≈ 2,400 kg/m³.
- ›Select Mass as the solve-for. Enter ρ = 2,400 kg/m³ and V = 0.18 m³.
- ›m = ρ × V = 2,400 × 0.18 = 432 kg.
- ›At standard gravity: weight ≈ 432 × 9.81 = 4,238 N ≈ 4.24 kN.
- ›Useful for structural load calculations in construction.
Example 3, Gold Purity Check (Archimedes Method)
- ›A "gold" bar weighs 1 kg in air. Submerged, it displaces 60 cm³ of water.
- ›ρ = 1,000 g / 60 cm³ ≈ 16.67 g/cm³ = 16,670 kg/m³.
- ›Pure gold density = 19,300 kg/m³. The density is too low, the bar is not pure gold.
- ›16,670 kg/m³ is close to tungsten (19,250) alloyed with silver (10,490), common forgery material.
- ›This is Archimedes's original method (≈250 BC) for testing Hiero's crown.
Understanding Density | ρ = m/V, Mass & Volume
Material Density Reference Table
| Material | Density (kg/m³) | Density (g/cm³) | Specific gravity |
|---|---|---|---|
| Air (sea level, 20°C) | 1.204 | 0.0012 | 0.0012 |
| Ice (0°C) | 917 | 0.917 | 0.917 |
| Water (4°C) | 1,000 | 1.000 | 1.000 |
| Seawater | 1,025 | 1.025 | 1.025 |
| Gasoline | 740 | 0.740 | 0.740 |
| Ethanol | 789 | 0.789 | 0.789 |
| Aluminium | 2,700 | 2.700 | 2.700 |
| Concrete | 2,400 | 2.400 | 2.400 |
| Glass | 2,500 | 2.500 | 2.500 |
| Titanium | 4,507 | 4.507 | 4.507 |
| Iron / Mild steel | 7,874 | 7.874 | 7.874 |
| Copper | 8,960 | 8.960 | 8.960 |
| Lead | 11,340 | 11.340 | 11.340 |
| Mercury | 13,534 | 13.534 | 13.534 |
| Tungsten | 19,250 | 19.250 | 19.250 |
| Gold | 19,300 | 19.300 | 19.300 |
Density in Everyday Applications
- ›Hydrometer (brewing & wine-making): A floating instrument that reads specific gravity directly. Winemakers use it to track fermentation, as yeast converts sugar to alcohol (density 789 kg/m³), the SG drops from ~1.080 to ~1.000.
- ›Ship ballast: Ships use water ballast tanks to adjust buoyancy and stability. As cargo is loaded, ballast water is pumped out to maintain the correct waterline.
- ›Geotechnical engineering: Soil bulk density (typically 1,400–1,800 kg/m³) affects load-bearing capacity, drainage, and compaction requirements for foundations.
- ›Medical imaging: Bone density (measured via DEXA scan) is used to diagnose osteoporosis. Normal bone mineral density: ~1,850 kg/m³; osteoporotic bone can drop below 1,600 kg/m³.
Frequently Asked Questions
What is the density of water?
- ›Pure water at 4°C: exactly 1,000 kg/m³ = 1 g/cm³ = 1 g/mL. This is the reference point for specific gravity.
- ›At 20°C (room temperature): 998.2 kg/m³, slightly less dense than at 4°C.
- ›At 100°C (boiling): 958.4 kg/m³. Steam at 100°C: only 0.597 kg/m³.
- ›Seawater: 1,020–1,030 kg/m³ due to dissolved salts (~3.5% by mass).
- ›Ice at 0°C: 917 kg/m³, less dense than liquid water, which is why ice floats.
Why does ice float on water?
- ›Water is unusual, its solid form (ice) is less dense than its liquid form.
- ›Ice at 0°C: ~917 kg/m³. Liquid water at 0°C: ~999.8 kg/m³.
- ›Specific gravity of ice: 917/1000 = 0.917, so ~91.7% of an iceberg is submerged.
- ›The molecular cause: when water freezes, hydrogen bonds force molecules into a hexagonal lattice that takes up more space than the disordered liquid arrangement.
- ›This property is critical for aquatic life, lakes freeze from the top down, keeping liquid water beneath where life survives.
What is specific gravity and how is it different from density?
- ›Specific gravity (SG) = ρ_material / ρ_water. It is a dimensionless ratio.
- ›Density has units (kg/m³, g/cm³, etc.); specific gravity has no units.
- ›For liquids and solids, SG numerically equals the density in g/cm³.
- ›Example: Aluminium has density 2.7 g/cm³ and SG = 2.7.
- ›SG > 1: sinks in water. SG < 1: floats. SG = 1: neutrally buoyant.
- ›Specific gravity is used in brewing (to measure sugar content), gemology, and soil science.
How does temperature affect density?
- ›For most substances, density decreases as temperature increases, thermal expansion reduces density.
- ›Water is the major exception: it is densest at 4°C and less dense both above and below that temperature.
- ›For gases: density is strongly temperature-dependent. Hot air is less dense, which is why hot air balloons rise.
- ›Metals expand very slightly with temperature. Steel: ~12 × 10⁻⁶ per °C coefficient of thermal expansion.
- ›For engineering applications, always specify the temperature when reporting a material's density.
What are the units of density and how do I convert between them?
- ›1 g/cm³ = 1 g/mL = 1,000 kg/m³ = 1 kg/L.
- ›1 lb/ft³ ≈ 16.018 kg/m³.
- ›1 lb/gal (US) ≈ 119.83 kg/m³.
- ›For g/cm³ to lb/ft³: multiply by 62.428.
- ›Water: 1 g/cm³ = 1,000 kg/m³ = 62.43 lb/ft³ = 8.34 lb/gal.
- ›This calculator converts between all common density units automatically.
How do engineers use density in practice?
- ›Structural engineering: calculating weight loads from material volume (concrete pours, steel beams, soil fill).
- ›Aerospace: material selection prioritises low density, titanium (4,507 kg/m³) vs steel (7,874 kg/m³) at similar strength.
- ›Fluid mechanics: buoyancy, pipe flow, and mixing calculations all depend on fluid densities.
- ›Chemical engineering: density determines whether phases separate (oil/water), and is used to convert between mass and volume in reactor design.
- ›Shipping and logistics: cargo weight limits are often applied as mass per volume (density), with "dimensional weight" pricing common in air freight.
Why is gold so much denser than aluminium?
- ›Gold (19,300 kg/m³) is about 7× denser than aluminium (2,700 kg/m³) due to two factors.
- ›Atomic mass: gold atoms are much heavier (197 amu) than aluminium atoms (27 amu).
- ›Crystal structure: gold has a face-centred cubic (FCC) structure with relatively close-packed atoms.
- ›The "lanthanide contraction" also plays a role, relativistic effects in heavy elements cause electron orbitals to contract, pulling atoms closer together in the metallic lattice.
- ›Tungsten (19,250 kg/m³) is nearly as dense as gold, which is why it is sometimes used in counterfeiting.
How do I measure the volume of an irregular object?
- ›Displacement method: submerge the object in a measuring cylinder of water. Volume = rise in water level.
- ›This is Archimedes's method, the volume of water displaced equals the volume of the object.
- ›For porous materials: coat the surface with wax or use a non-absorbed liquid.
- ›For very small objects: use a graduated pipette or pycnometer (specific gravity bottle).
- ›For regular shapes: use geometric formulas (sphere: 4/3πr³, cylinder: πr²h, rectangular prism: l×w×h).
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