grob
rude
Impolite, inconsiderate, or insulting in behavior or expression.
Sei nicht so grob zu deiner kleinen Schwester!
Don't be so rude to your little sister!

rude / rough / approximate
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rude
Impolite, inconsiderate, or insulting in behavior or expression.
Sei nicht so grob zu deiner kleinen Schwester!
Don't be so rude to your little sister!

The meaning of 'grob' depends strongly on the noun it describes. If it refers to a person, it means 'unhöflich' (rude). With an idea or estimate, it means 'ungefähr' (approximate). If it describes a material, it means 'rau' (rough), and with a mistake, it means 'schwerwiegend' (serious).
Sein grober Tonfall hat alle überrascht.
His rude tone surprised everyone.
In the meaning of 'ungefähr' (approximate), 'grob' is often used for plans and estimates. Typical combinations are 'eine grobe Schätzung' (a rough estimate), 'ein grober Plan' (a rough plan), or 'ein grober Überblick' (a rough overview).
Der Architekt zeichnete einen groben Entwurf des Hauses.
The architect drew a rough draft of the house.
When it comes to mistakes or negative behavior, 'grob' intensifies the negative meaning. Common expressions are 'ein grober Fehler' (a serious mistake), 'grobe Fahrlässigkeit' (gross negligence), or 'grober Unfug' (serious nonsense/mischief).
Der Fahrer beging einen groben Verstoß gegen die Verkehrsregeln.
The driver committed a serious violation of traffic rules.
When 'grob' describes rude behavior, it is often used with the preposition 'zu' and the dative to name the person affected.
Er war am Telefon sehr grob zu mir.
He was very rude to me on the phone.
'Grob' can also be used as an adverb to modify a verb. It then means 'not finely' or 'not in detail'.
Schneiden Sie das Gemüse für die Suppe nur grob.
Cut the vegetables for the soup only roughly.
approximately
'ungefähr' and 'grob' can both express that something is not exact, but only estimated. 'ungefähr' is very general and works with numbers, times, quantities, and distances. 'grob' is often used with words like 'geschätzt' (estimated), 'gerechnet' (calculated), or 'geplant' (planned). It emphasizes that only the basic idea or a simple estimate is meant. In many everyday sentences, 'ungefähr' sounds more natural. 'grob' fits especially well when you want to show: this is not exact yet or not in detail.

Nach dem Gespräch plant das Team grob die Kosten für das Projekt.
After the discussion, the team roughly estimates the costs for the project.
Die Fahrt dauert ungefähr zwei Stunden.
The trip takes about two hours.