
der Rand
edge / margin
The outer edge, boundary, or end of a surface or object.
Bitte schreibe nicht über den Rand des Blattes.
Please don't write beyond the margin of the page.
edge / margin
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edge / margin
The outer edge, boundary, or end of a surface or object.
Bitte schreibe nicht über den Rand des Blattes.
Please don't write beyond the margin of the page.

margins
The periphery of a society or group; a position outside the center of social life.
Er engagiert sich für Menschen, die am Rand der Gesellschaft leben.
He is committed to helping people who live on the margins of society.

in passing
As a casual remark or side note; not as the main topic.
Er erwähnte nur am Rande, dass er bald umziehen wird.
He only mentioned in passing that he will be moving soon.

to be out of control
To get completely out of control; to behave wildly and without restraint.
Nach dem Sieg waren die Fans im Stadion völlig außer Rand und Band.
After the victory, the fans in the stadium were completely out of control.
'Rand' (edge / margin) is a common component of compound words. It always refers to the outer zone of something, for example in 'Stadtrand' (outskirts of town), 'Waldrand' (edge of the forest), or 'Randnotiz' (side note / marginal note).
Wir wohnen in einem ruhigen Haus am Stadtrand.
We live in a quiet house on the outskirts of town.
Pay attention to the case after the preposition: 'am Rand' (at/on the edge, dative) describes a position, while 'an den Rand' (to the edge, accusative) expresses movement toward it.
Das Glas steht gefährlich nah am Rand des Tisches.
The glass is standing dangerously close to the edge of the table.
The figurative meaning 'Peripherie' (periphery) is used almost exclusively in the fixed expression 'am Rand der Gesellschaft' (on the margins of society). It describes people in an outsider position.
Soziale Projekte helfen Menschen am Rand der Gesellschaft.
Social projects help people on the margins of society.
The expression 'am Rande' (in passing / as a side note) functions like an adverb and means 'nebenbei' (by the way) or 'nicht als Hauptpunkt' (not as the main point). It often stands in the middle of the sentence.
Ich möchte nur am Rande bemerken, dass wir im Zeitplan zurückliegen.
I would just like to note in passing that we are behind schedule.
The idiom 'außer Rand und Band sein' (to be completely out of control) is a fixed unit. It describes wild, unrestrained, and often loud behavior, usually by a group.
Die Kinder waren auf dem Fest völlig außer Rand und Band.
The children were completely out of control at the festival.
border / limit
“Grenze” and “Rand” can both refer to the end of an area. A “Grenze” is a line that separates two areas from each other. The “Rand” is the outer edge or outer part of a surface; it does not necessarily separate two areas.

Am Rand des Parks stehen mehrere alte Bäume.
Several old trees stand at the edge of the park.
Der Fluss bildet die Grenze zwischen dem Park und dem Wohngebiet.
The river forms the border between the park and the residential area.