Mass

Prof. Dr. Thorsten Jungmann (last updated 2025-09-04)

Mass (German: Masse) is a fundamental physical quantity and one of the seven base quantities. In electrical engineering, it is relevant to the mechanical properties of components, the inertia of moving systems and the calculation of forces in electromechanical applications.

1 Quantity symbol and unit

The quantity symbol of mass is $m$.
Its unit is the kilogram, one of the seven SI base units, with the unit symbol $\mathrm{kg}$.

$$[m]=\mathrm{kg}$$

2 Practical and worked examples

2.1 Weight-force of a transformer

The weight-force $F_g$ of a transformer is calculated from its mass and the gravitational acceleration:

$$F_g=m\cdot g$$

Example: transformer with $m=250\mathrm{kg}$, $g=9.81m/{\mathrm{s}}^2$

$$F_g=250\mathrm{kg}\cdot 9.81m/{\mathrm{s}}^2=\underline{2453\mathrm{N}}$$

For the dimensioning of the base plate, $F_g$ plays a role as an area load.

2.2 Mass of a copper conductor

You can calculate the mass from the density $\delta$ and the volume $V$, or from the cross-section $A$ and the length $l$:

$$m=\delta \cdot V=\delta \cdot A\cdot l$$

Example: copper conductor with $A=2.5\mathrm{m}{\mathrm{m}}^2$, $l=100\mathrm{m}$, ${\delta }_{Cu}=8.96g/c{\mathrm{m}}^3$

$$V=2.5\cdot 10^{-6}{\mathrm{m}}^2\cdot 100\mathrm{m}=2.5\cdot 10^{-4}{\mathrm{m}}^3$$ $$m=8960kg/{\mathrm{m}}^3\cdot 2.5\cdot 10^{-4}{\mathrm{m}}^3=\underline{2.24\mathrm{kg}}$$

3 Typical orders of magnitude

• Semiconductor chips: $10^{-6}$ to $10^{-3}\mathrm{kg}$ (micrograms to milligrams)
• Electronic components: $10^{-3}$ to $10^{-1}\mathrm{kg}$ (milligrams to decigrams)
• Printed circuit boards: $10^{-2}$ to $1\mathrm{kg}$ (grams to kilograms)
• Household appliances: $1$ to $50\mathrm{kg}$
• Control cabinets: $50$ to $500\mathrm{kg}$
• Transformers: $100\mathrm{kg}$ to $100\mathrm{t}$ (tonnes)

4 Example phrasings

• ‘The control cabinet has a mass of $120\mathrm{kg}$ and requires appropriate mounting.’
• ‘The printed circuit board weighs $45\mathrm{g}$ and is therefore light enough for mobile applications.’
• ‘With a mass of $2.5\mathrm{t}$, the transformer has to be transported by crane.’
• ‘The relay has an armature mass of $5\mathrm{g}$ and therefore achieves short switching times.’

5 Related quantities

• The weight-force is calculated from mass and gravitational acceleration:

$$F_g=m\cdot g$$

• The kinetic energy of moving masses:

$$E_{kin}=\frac{1}{2}\cdot m\cdot v^2$$

• The moment of inertia of rotating bodies:

$$J=\int r^2\mathrm{d}m$$

• Density as mass per volume:

$$\delta =\frac{m}{V}$$

6 Related components

• Relay and contactor: armature mass determines switching speed and mechanical stress
• Electric motor: rotor mass influences starting behaviour and moment of inertia
• Transformer: core mass determines transport and foundation