Conditions and alternatives (pod warunkiem, że; w razie; w przeciwnym razie)

Provided that

provided that, on condition that

pod warunkiem, żeprovided that, on condition that — states a condition more firmly than jeśli. The comma goes before że.

I agree, on condition that you pay.
Zgadzam się, pod warunkiem, że zapłacisz.

In case of

in case of (+ Genitive)

w razie + Genitive — in case of: w razie deszczu, w razie problemów. in the case of, in the event of (+ Genitive; formal)
w przypadku
+ Genitive — in the case of — the same idea in formal, written Polish (notices, instructions).

In case of rain we will stay at home.
W razie deszczu zostaniemy w domu.
In the event of a breakdown, please turn off the valve.
W przypadku awarii proszę zakręcić zawór.

Otherwise

otherwise (if not)

w przeciwnym razieotherwise — spells out what happens if the condition is not met. otherwise; differently, in another way
inaczej
does the same job in one word, and also means differently, in another way.

Pay today, otherwise you will lose the discount.
Zapłać dzisiaj, w przeciwnym razie stracisz zniżkę.
It can be done differently.
Można to zrobić inaczej.

Just in case — and under no circumstances

just in case

na wszelki wypadekjust in case.

under no circumstances, no way

w żadnym wypadkuunder no circumstances, no way — as an answer or before a negated verb (w żadnym wypadku nie otwieraj).

Take an umbrella just in case.
Weź parasol na wszelki wypadek.

Contributors