What is the noun for degree?

There isn't one single noun that perfectly encompasses all the meanings of "degree". It depends on the context:

For academic degrees:

* Qualification: This is a general term for any achievement that shows you have specific skills or knowledge.

* Award: This emphasizes the formal recognition given by an institution.

* Certification: This is often used for specific skills or training.

For levels of intensity, amount, or extent:

* Extent: This refers to the range or scope of something.

* Level: This signifies a specific point or stage within a range.

* Amount: This is used for measurable quantities.

* Intensity: This refers to the strength or force of something.

For angles and measurement:

* Angle: This is the specific geometric concept.

* Measurement: This is the general term for any numerical value assigned to something.

The best noun will depend on the specific situation you are describing.