Although Latin is considered a 'dead' language, it continues to hold significance for many, spanning from scholars to devout Roman Catholics to those seeking to craft their own motto. Whether you're translating the English term peace into Latin for academic, religious, or personal reasons, fear not! While Latin may seem intimidating, a straightforward translation of peace is pax. However, read on to discover how you can utilize it appropriately to impress your acquaintances and loved ones! Pax vobiscum (peace be with you)!
Steps
Clarify Your Concept of 'Peace.' Latin, as the language that dominated European thought and culture for centuries, boasts a rich vocabulary. Although the default translation is usually 'pax,' if you're aiming to convey notions of serenity, tranquility, or composure, opting for tranquillitas (the noun for quietness, stillness, or calm) might be more appropriate. In political or religious contexts, pax is the preferred term.

Determine the Part of Speech You Require! Similar to certain English words like 'who' and 'whom,' the form a Latin word takes indicates its function in a sentence. Unlike English, Latin words can assume numerous forms to convey nuances of meaning that English lacks. While English typically differentiates between singular and plural forms, Latin employs various forms to convey information, irrespective of word order. While the following explanations are simplified, they should suffice for basic understanding, given that this isn't a Latin grammar lesson.

For a SINGULAR SUBJECT in a sentence... 'Peace is pleasant.' --> PAX.

For a SINGULAR POSSESSIVE or describing a PART or PIECE... 'Peace's role in the world,' or 'We all desire a portion of peace.' --> PACIS.

For when you would use the word 'TO' WITH A SINGULAR NOUN (i.e., AN INDIRECT OBJECT) (not with a verb!) in English... 'I dedicate my life to peace.' --> PACI.

For the SINGULAR DIRECT OBJECT of a sentence (i.e., something directly affected, recognized in English as the word usually following the verb)... 'He cherishes peace.' --> PACEM.

For when a SINGULAR noun is TAKING ACTION... 'We championed the cause with peace.' --> PACE. Note that when we use the word 'with' in English to mean 'alongside' or 'accompanied by,' the form PACE is also appropriate--but you'll also need to include the word cum to denote that sense. This is why we observe the -cum ending in the vobiscum of 'pax vobiscum.' Latin, unlike English, isn't as concerned with word order! The same sentence could be written: 'Pax cum vobis.'

When referring to the PLURAL SUBJECT of a sentence... 'Various peaces are delightful.' --> PACES. Honestly, it's rare to encounter such usage in English, as the concept of 'peace' is typically singular. However, if you ever find yourself needing to express multiple instances of peace as the subject, PACES would be appropriate.

When describing a PLURAL POSSESSIVE or a PART or PIECE of a group... 'The roles of various peaces in the world,' or 'We all desire involvement with the peaces.' --> PACUM. Once again, the practical application of this form in real-world contexts is uncertain, but it's provided here for completeness.

When indicating the recipient of an action with a PLURAL NOUN (i.e., PLURAL INDIRECT OBJECTS) (not with a verb!) in English... 'I dedicate my life to the peaces.' --> PACIBUS.

For PLURAL DIRECT OBJECTS in a sentence... 'He cherishes various peaces.' --> PACES. While not commonly used with 'peace,' this form parallels the distinction between 'He loves the dog' and 'He loves the dogs.'

When a PLURAL noun is INVOLVED IN AN ACTION... 'We promoted harmony with various forms of peace' (suggesting the use of different types of peace to achieve harmony). --> PACIBUS. The same guidance regarding the use of cum applies here as well.
PointersYou might have observed that some forms appear identical! This can pose a challenge when translating Latin into English but shouldn't be problematic in the reverse direction.
If you're interested in the formal designations for the various forms mentioned above (e.g., if you wish to explore more detailed grammar information), they are: NOMINATIVE, GENITIVE, DATIVE, ACCUSATIVE, and ABLATIVE--and the same sequence repeats for plural forms.
CautionsThese forms are specific to the word pax, which is a 'feminine third declension' noun in Latin. Latin features three genders and five declensions for nouns! While it's possible that the same endings may apply to other nouns, there's also a chance they won't.
The term cum is just one example of a word that influences the form of the subsequent word. Others include ad, in, and ex. If a preposition precedes the word 'peace' in your sentence, consulting a dictionary or online resource to ascertain the required form is advisable.