The key metrics for measuring the usability of a GUI include:

1. Task completion rate: The percentage of users who complete a task successfully.

2. Task completion time: The time it takes for users to complete a task.

3. Error rate: The number of errors users make while completing a task.

4. User satisfaction: Measured through surveys, interviews, or questionnaires.

5. Net Promoter Score (NPS): Measures user loyalty and satisfaction.

6. Click-through rate (CTR): Measures the percentage of users who click on a specific element.

7. Bounce rate: Measures the percentage of users who leave the application or website.

8. Time on task: Measures the time spent on a specific task.

9. User engagement: Measures the level of user interaction with the GUI.

10. Accessibility metrics: Measures the GUI's compliance with accessibility standards.

11. Cognitive load: Measures the mental effort required to use the GUI.

12. Learnability: Measures how easy it is for users to learn the GUI.

13. Memorability: Measures how well users remember the GUI.

14. Error recovery: Measures how easily users can recover from errors.

15. User experience (UX) metrics: Measures the overall user experience, including emotional responses.

These metrics help identify areas for improvement, ensuring the GUI is intuitive, efficient, and user-friendly.