Geometry, Mass, and Force

Volume is capacity only after you name the unit

CAD mass properties often report volume in a model’s document units. Before treating that number as a tank capacity or a material quantity, state the volume unit and convert it to the form the drawing or specification requires.

Static solved reservoir example

A SolidWorks model gives a hydraulic reservoir internal volume of 2.5 ft³. Its capacity is 2.5 ft3 × 7.48051948 U.S. gal/ft3 = 18.7013 U.S. gal, or 18.7 U.S. gal. This assumes the reported CAD volume is the usable internal volume and no design headspace has yet been subtracted.

Density connects volume to mass

Density is mass per volume, and its symbol is ρ (rho): ρ = m/V. Turned around, when material density and CAD volume use compatible units, m = ρV produces mass.

(kg/m3) × (m3) = kg

For example, a volume of 0.13824 m³ made of material with a density of 2,700 kg/m³ has mass m = 2,700 kg/m3 × 0.13824 m3 = 373.248 kg.

Static solved steel example

A steel I-beam has a volume of 0.2 m³ and a density of 7,850 kg/m³. Its mass is m = 7,850 kg/m3 × 0.2 m3 = 1,570 kg. That is the same mass the weight example below starts from — a CAD volume and a material card are usually where a weight calculation actually begins.

Check the CAD assumptions before trusting mass properties

Confirm the assigned material, density, document unit, bodies included, and whether the model represents solid material or an internal void. A precise calculation based on the wrong material card is still wrong.

Force and weight are separate quantities

Force is a push or pull. For constant mass, Newton’s second law is Fnet = ma. Weight is one particular force: the force due to gravity, written W = mg.

F_net

Net force, in newtons (N) or pound force (lbf). It is the combined force that produces acceleration.

W

Weight, a gravitational force. Near Earth’s standard gravity, g0 = 9.80665 m/s2; local gravity can differ slightly.

m

Mass, in kilograms, pound mass, or slugs. It is not measured in newtons or pound force.

In coherent SI, 1 N = 1 kg · m/s2. In the coherent foot–slug–second system, 1 lbf = 1 slug · ft/s2. Do not silently replace lbm with lbf.

Static solved weight example

For a 1,570 kg mass at standard gravity, W = mg = 1,570 kg × 9.80665 m/s2 = 15,396.44 N, or 15.4 kN. This is a weight calculation at standard gravity, not a claim that the mass is 15.4 kN.

CAD scale, mass, and weight lab

This model begins with an area and volume in SI units, scales them, then uses density and gravitational acceleration to show the separate mass and weight results.