das Gleichgewicht
balance
A stable physical state in which you do not fall over or sway.
Auf einem Bein zu stehen ist eine gute Übung für das Gleichgewicht.
Standing on one leg is a good exercise for balance.

balance / equilibrium
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balance
A stable physical state in which you do not fall over or sway.
Auf einem Bein zu stehen ist eine gute Übung für das Gleichgewicht.
Standing on one leg is a good exercise for balance.

The word is made up of 'gleich' (equal/same) and 'Gewicht' (weight). The literal meaning 'equal weight' is the basis for all meanings: physical balance, the balancing of forces, and inner calm.
Für das Rezept brauchen Sie gleiche Gewichte von Mehl und Zucker.
For the recipe, you need equal weights of flour and sugar.
In connection with the body, the most important verbs are 'das Gleichgewicht halten' (to keep one's balance), 'das Gleichgewicht verlieren' (to lose one's balance), and 'das Gleichgewicht wiederfinden' (to regain one's balance).
Auf dem glatten Eis habe ich fast mein Gleichgewicht verloren.
On the slippery ice, I almost lost my balance.
The expression 'jemanden/etwas aus dem Gleichgewicht bringen' (to throw someone/something off balance) is very common. The person or thing that is destabilized is in the accusative.
Diese unerwartete Nachricht hat sie völlig aus dem Gleichgewicht gebracht.
This unexpected news completely threw her off balance.
For abstract systems (e.g., nature, politics), the verbs 'stören' (to disturb), 'gefährden' (to endanger), or 'wiederherstellen' (to restore) are often used. The state is described with 'im Gleichgewicht sein' (to be in equilibrium/balance).
Der Bau der Fabrik könnte das ökologische Gleichgewicht des Flusses stören.
The construction of the factory could disturb the ecological balance of the river.
When referring to the psyche, 'Gleichgewicht' (balance/equilibrium) is often combined with adjectives like 'inneres' (inner) or 'seelisches' (emotional/psychological). You can 'finden' (find), 'verlieren' (lose), or 'suchen' (seek) it.
Durch Yoga hat er sein inneres Gleichgewicht wiedergefunden.
Through yoga, he regained his inner balance.
quiet / calm
'die Ruhe' and 'das Gleichgewicht' can both describe an inwardly stable state. 'Ruhe' emphasizes that you are relaxed and do not get upset. 'Gleichgewicht' emphasizes more that different feelings or areas of life fit together well and nothing becomes too strong. That is why people often say 'innere Ruhe' (inner calm) when someone is composed, and 'inneres Gleichgewicht' (inner balance) when someone is emotionally stable and balanced. 'Ruhe' sounds more direct in everyday language; 'Gleichgewicht' fits well when the focus is on balance and stability.

Durch feste Pausen hält Mehmet sein inneres Gleichgewicht.
By taking regular breaks, Mehmet maintains his inner balance.
Nach einem langen Spaziergang fand Lena endlich wieder etwas Ruhe.
After a long walk, Lena finally found a little calm again.