die Steigung
slope
An uphill section of a path, road, or terrain.
Für Radfahrer ist diese Steigung eine echte Herausforderung.
For cyclists, this slope is a real challenge.

slope
Loading your saved state.
slope
An uphill section of a path, road, or terrain.
Für Radfahrer ist diese Steigung eine echte Herausforderung.
For cyclists, this slope is a real challenge.

The noun 'die Steigung' (slope / increase) comes from the verb 'steigen' (to rise / to climb). The ending '-ung' turns the verb into a feminine noun that describes the process or result of rising or climbing.
Die Temperaturen steigen heute auf über 30 Grad.
Temperatures are rising to over 30 degrees today.
You can recognize the meaning of 'Steigung' (slope / increase) from the context: with words like 'Straße' (road) or 'Berg' (mountain), it means an uphill path. In connection with 'Funktion' (function) or 'Kurve' (curve), it is about mathematics. With 'Preisen' (prices) or 'Temperaturen' (temperatures), it means an increase in values.
Die Straße hat hier eine gefährliche Steigung.
The road has a dangerous slope here.
When referring to a path or road, 'Steigung' (slope) is often described with the adjectives 'steil' (steep), 'stark' (strong), 'leicht' (slight), or 'sanft' (gentle).
Nach der langen Wanderung kommt eine letzte steile Steigung.
After the long hike, there is one final steep slope.
The steepness of a road or mountain is often expressed with the preposition 'von' (of) and a percentage.
Vorsicht, diese Straße hat eine Steigung von 15 Prozent!
Careful, this road has a slope of 15 percent!
In the meaning 'measure of the steepness of a curve', the word is a technical term from mathematics and is used mainly in this context.
Im Unterricht haben wir gelernt, wie man die Steigung einer linearen Funktion bestimmt.
In class, we learned how to determine the slope of a linear function.
ascent / rise
'der Aufstieg' and 'die Steigung' can be confused because both have to do with something going upward. 'Aufstieg' means the action or the path upward, for example when climbing a mountain or going up stairs. 'Steigung', by contrast, describes the uphill section of a path or how steep something is. So you say: 'Der Aufstieg war anstrengend' (the ascent was strenuous). But: 'Die Steigung war sehr steil' (the slope was very steep). With numbers, 'Steigung' can also mean an increase, while 'Aufstieg' is not usually used in this sense for individual values.

Auf dieser Straße ist die Steigung für viele Radfahrer zu stark.
On this road, the slope is too steep for many cyclists.
Der Aufstieg zur Hütte dauerte fast zwei Stunden.
The ascent to the hut took almost two hours.