Mass Calculator —
density, volume & Newton's second law.

Physics guide

Mass, density, and Newton's second law — explained.

Mass is one of the most fundamental quantities in physics. It describes how much matter an object contains, governs how it responds to forces, and determines its gravitational interaction with other objects. Understanding how mass relates to density, volume, force, and acceleration is essential in engineering, chemistry, and everyday science.

What is mass?

Mass is a scalar quantity that measures the amount of matter in an object. In SI units it is measured in kilograms (kg). Mass is an intrinsic property; it does not change based on location, gravity, or motion (at non-relativistic speeds). A 70 kg person has the same mass on Earth, on the Moon, and in deep space.

Mass is often confused with weight. Weight is the force exerted on an object by gravity: W = m × g, where g ≈ 9.81 m/s² on Earth. Weight is a force measured in newtons (N) or pounds-force (lbf); mass is measured in kilograms or pounds-mass (lbm). On the Moon (g ≈ 1.62 m/s²) you would weigh about one-sixth as much, but your mass would be identical.

Method 1: mass from density and volume

Density (ρ) describes how tightly matter is packed into a given space. It is defined as mass per unit volume:

Where m is mass in kg, ρ is density in kg/m³, and V is volume in m³. This formula is used constantly in engineering and material science — from calculating the mass of a steel beam to determining whether a ship will float.

You can also rearrange the formula to find density or volume:

• ρ = m / V: density from a known mass and volume (e.g., identifying an unknown material)
• V = m / ρ: volume from a known mass and density (e.g., sizing a tank to hold a specific mass of liquid)

Common material densities

Density values vary enormously across materials. Some useful reference points:

• Water: 1,000 kg/m³ (1 g/cm³). The reference density. A 1-litre bottle of water has a mass of exactly 1 kg.
• Aluminium: 2,700 kg/m³. Lightweight structural metal used in aircraft and packaging.
• Steel: 7,850 kg/m³. Dense and strong; a 1 m³ steel cube weighs nearly 8 tonnes.
• Gold: 19,300 kg/m³. One of the densest common metals. A gold bar (400 troy oz) is only about 21 × 9 × 4 cm yet weighs ~12.4 kg.
• Lead: 11,340 kg/m³. Dense and soft; used in radiation shielding and ballast.
• Air: 1.225 kg/m³ at sea level. Very low density; a room 5 m × 4 m × 3 m contains about 74 kg of air.
• Wood (oak): ~700 kg/m³. Less dense than water, so it floats.
• Concrete: ~2,400 kg/m³. A standard structural density used in civil engineering load calculations.

Method 2: mass from force and acceleration (Newton's second law)

Isaac Newton's second law of motion states that the net force acting on an object equals its mass times its acceleration:

Where F is force in newtons (N), m is mass in kilograms (kg), and a is acceleration in metres per second squared (m/s²). This relationship is the foundation of classical mechanics and is used in virtually every area of engineering and physics.

Rearranged forms are equally useful:

• F = m × a: force on an object of known mass undergoing known acceleration (e.g., rocket thrust calculations)
• a = F / m: acceleration produced by a known force on a known mass (e.g., how fast a car accelerates given engine force and vehicle mass)

Units of force

The SI unit of force is the newton (N), defined as the force that accelerates a 1 kg mass at 1 m/s²:

• 1 N = 1 kg·m/s²
• 1 kilonewton (kN) = 1,000 N — commonly used in structural engineering
• 1 pound-force (lbf) = 4.4482 N — used in US customary and imperial systems
• 1 dyne = 10⁻⁵ N — CGS unit, used in older physics texts and some chemistry

Weight in everyday life is often expressed in "kilograms" colloquially, but this is technically kilogram-force (kgf) — the gravitational force on 1 kg at Earth's surface. Strictly, 1 kgf = 9.80665 N.

Units of acceleration

The standard unit is metres per second squared (m/s²). Earth's standard gravitational acceleration is:

In aviation and vehicle dynamics, acceleration is often expressed as multiples of g ("g-force"): a car braking at 1g decelerates at 9.81 m/s², a jet fighter pulling 9g experiences 9 × 9.81 ≈ 88 m/s² centripetal acceleration.

Mass vs. weight, a practical summary

• Mass: kg, g, lb — measures amount of matter. Invariant across locations.
• Weight: N, kN, lbf — the gravitational force on that mass. Depends on local gravity.
• On Earth: W (N) = m (kg) × 9.81. A 70 kg person weighs ≈ 686 N.
• On the Moon: W (N) = m (kg) × 1.62. The same 70 kg person weighs ≈ 113 N.

Mass unit conversions

• 1 kg = 1,000 g = 0.001 t (metric tonne)
• 1 kg = 2.20462 lb (pounds-mass)
• 1 lb = 16 oz (ounces) = 453.592 g
• 1 metric tonne (t) = 1,000 kg ≈ 2,204.62 lb
• 1 short ton (US) = 2,000 lb = 907.185 kg
• 1 long ton (UK) = 2,240 lb = 1,016.05 kg
• 1 stone = 14 lb = 6.35029 kg
• 1 slug = 14.5939 kg (used in US engineering)