Calculate mass from volume and density, or volume from mass and density using m = ρ × V. Free online physics calculator for material properties, chemistry, and engineering calculations.
Calculate mass from volume and density, or volume from mass and density
Formula:
m = ρ × V
Where: m = Mass, ρ (rho) = Density, V = Volume
Examples: Water = 1000 kg/m³, Iron = 7850 kg/m³, Air = 1.225 kg/m³
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Converting between volume and mass is a fundamental calculation in physics, chemistry, engineering, and materials science. The relationship between these quantities is defined by density, which represents how much mass is contained in a given volume. Our Volume to Mass Calculator simplifies these conversions using the formula: m = ρ × V, where m is mass, ρ (rho) is density, and V is volume.
Whether you're working with materials, calculating shipping weights, analyzing chemical substances, or solving physics problems, understanding how to convert between volume and mass is essential. Our calculator helps you determine mass from volume, volume from mass, or density from both, making complex calculations simple and accurate.
Our Volume to Mass Calculator offers three calculation modes:
Select your calculation mode, enter the known values with appropriate units, and click Calculate to get instant results with detailed step-by-step solutions.
The relationship between mass, volume, and density is fundamental to physics:
Mass = Density × Volume
Where:
Density is a material property that describes how much mass is packed into a unit volume. It's a characteristic property of substances, meaning different materials have different densities:
Volume to mass conversions are essential in numerous practical applications:
Knowing common material densities helps with quick conversions:
| Material | Density (kg/m³) | Density (g/cm³) |
|---|---|---|
| Air (at sea level) | 1.225 | 0.001225 |
| Water (at 4°C) | 1000 | 1.0 |
| Ice | 917 | 0.917 |
| Aluminum | 2700 | 2.7 |
| Steel | 7850 | 7.85 |
| Iron | 7870 | 7.87 |
| Copper | 8960 | 8.96 |
| Gold | 19320 | 19.32 |
| Lead | 11340 | 11.34 |
| Wood (Oak) | 600-900 | 0.6-0.9 |
| Concrete | 2400 | 2.4 |
Note: Densities can vary with temperature, pressure, and composition. Values shown are approximate at standard conditions (20°C, 1 atm).
A container holds 2.5 m³ of water. What is the mass of the water? (Water density = 1000 kg/m³)
m = ρ × V
m = 1000 kg/m³ × 2.5 m³
m = 2500 kg = 2.5 metric tons
The container holds 2500 kg (2.5 metric tons) of water.
A block of aluminum has a mass of 5400 kg. What is its volume? (Aluminum density = 2700 kg/m³)
V = m / ρ
V = 5400 kg / 2700 kg/m³
V = 2 m³
The aluminum block has a volume of 2 cubic meters.
A metal object has a mass of 7850 kg and occupies 1 m³. What is its density?
ρ = m / V
ρ = 7850 kg / 1 m³
ρ = 7850 kg/m³
The metal has a density of 7850 kg/m³, which matches the density of steel.
Our Volume to Mass Calculator supports multiple units for each parameter:
Unit Conversion Tip: The calculator automatically converts between different units, ensuring accurate calculations regardless of the unit system you use. All internal calculations are performed in base SI units (kg, m³, kg/m³).
Common Relationships:
To convert volume to mass, multiply the volume by the density: m = ρ × V. For example, if you have 1 m³ of water (density = 1000 kg/m³), the mass is 1 m³ × 1000 kg/m³ = 1000 kg. The density must be known or measured to perform this conversion.
To convert mass to volume, divide the mass by the density: V = m / ρ. For example, if you have 2000 kg of aluminum (density = 2700 kg/m³), the volume is 2000 kg ÷ 2700 kg/m³ = 0.741 m³. You need to know the material's density to perform this conversion.
The formula is: Mass = Density × Volume, or m = ρ × V. This formula shows that mass is directly proportional to both density and volume. If you double either the density or volume, the mass doubles.
Density depends on how tightly packed the atoms or molecules are in a material. Materials with heavier atoms (like lead or gold) or more tightly packed structures tend to have higher densities. Density is also affected by temperature and pressure - most materials expand when heated, decreasing density.
No, you cannot convert volume to mass without knowing the density. Density is the essential link between volume and mass. Each material has a characteristic density (which can vary with temperature and pressure), and this density value is required for the conversion m = ρ × V.
Temperature affects density because most materials expand when heated, increasing volume while mass stays constant. This means density decreases with increasing temperature (ρ = m/V, so if V increases, ρ decreases). For accurate conversions, use density values at the same temperature as your measurements. Water is a notable exception - its density is highest at 4°C.
The density of pure water at 4°C is 1000 kg/m³ (or 1 g/cm³, or 1 g/mL). This is often used as a reference. At room temperature (20°C), water density is approximately 998 kg/m³. The density of water decreases as temperature increases (except between 0-4°C where it increases).
No, the conversion factor (density) is different for each material. A given volume of lead (density ≈ 11,340 kg/m³) will have much more mass than the same volume of water (density = 1000 kg/m³). You must use the correct density value for the specific material you're working with.
Understanding how to convert between volume and mass using density is a fundamental skill in physics, chemistry, engineering, and many practical applications. Our Volume to Mass Calculator simplifies these conversions, making it easy to determine mass, volume, or density for any material.
Whether you're calculating shipping weights, analyzing materials, solving physics problems, or working on engineering projects, this calculator provides accurate results with step-by-step solutions. Ready to explore more physics concepts? Check out our other calculators like the Density Mass Volume Calculator for related calculations, or use our Buoyancy Calculator which also uses density in its calculations.
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