maximal
maximum
Expresses the highest possible, outermost, or permitted limit; at most.
Die maximale Teilnehmerzahl für diesen Kurs beträgt 15 Personen.
The maximum number of participants for this course is 15 people.

maximum
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maximum
Expresses the highest possible, outermost, or permitted limit; at most.
Die maximale Teilnehmerzahl für diesen Kurs beträgt 15 Personen.
The maximum number of participants for this course is 15 people.

'Maximal' (maximum / at most) can stand as an adjective before a noun or be used as an adverb to limit an amount or duration. As an adverb, it does not change its form.
Die maximale Ladezeit des Akkus beträgt zwei Stunden.
The maximum charging time of the battery is two hours.
'Maximal' (maximum) is the adjective related to the noun 'das Maximum' (the maximum). Both words refer to the highest point or upper limit of something.
Wir müssen das Maximum aus unseren Möglichkeiten herausholen.
We have to get the maximum out of our opportunities.
'Maximal' (maximum) is often combined with nouns that describe a limit or measurement. Typical examples are 'maximale Anzahl' (maximum number), 'maximale Geschwindigkeit' (maximum speed), 'maximale Höhe' (maximum height), or 'maximales Gewicht' (maximum weight).
Auf dieser Straße beträgt die maximale Geschwindigkeit 80 km/h.
On this road, the maximum speed is 80 km/h.
until / to
'bis zu' (up to) and 'maximal' can both express the highest permitted limit. 'bis zu' often comes directly before a number or amount and sounds very natural in information about prices, times, or numbers of people. 'maximal' also means 'not more than', but it can also be used as an adjective, for example 'die maximale Zahl' (the maximum number). They can be confused because both state an upper limit. The important point is: 'bis' alone has many other meanings; for this meaning, you usually need 'bis zu'.

Am Abend dürfen maximal sechs Personen an einem Tisch sitzen.
In the evening, a maximum of six people may sit at one table.
Für die Führung können sich bis zu 20 Nachbarn anmelden.
Up to 20 neighbors can sign up for the tour.