There are no interrelations between these two settings. For example, if rate(http_requests_total{job="api-server"}[5m]) is your PromQL query, it yields a single value when you execute it at a specific point in time. If you have a Grafana dashboard with a 2h time range, then Grafana just repeatedly executes this query at a series of point in times during the past 2 hours, and displays you the result of each query as e.g. a graph.

For example, if the time range of your Grafana dashboard is 2h and the interval is set to 1 minute, then Grafana executes your query 120 times during the time span ranging the past 2 hours. The results of all these queries form a graph and that's what you see in your Grafana dashboard.

The interval with which Grafana executes the query is determined by the Max data points and Min interval settings in the Query options of your Grafana dashboard:

See the explanations about these settings in the Grafana documentation.

Note: Grafana uses the query_range endpoint of the Prometheus API to repeatedly execute the query over the given time range.

The following query will calculate the average decline rate in the last week, assuming your sample rate is 1 per minute.

avg_over_time(
  (
    deriv(level[60s:]) < 0
  )[1w:60s]
) / 60

Breakdown:

• deriv(level[60s:]): in each point in time, the current level minus the level one minute ago
• deriv(...) < 0: only the values where the value mentioned above is negative
• avg_over_time(...[1w:60s]): the average of all the recorded negative values in the last week
• ... / 60: since the values we calculated are equal to the level decline per sample (60 seconds), we divide the result by the sample duration in seconds to get the level decline per second

Note: the result might be slightly lower than the real decline rate, since some of the samples represent a time period in which the level both decreased and increased (the edges in the graph). The higher you sample rate is relatively to the level change rate, the more accurate your results will be. Your could also get rid of the edges in other ways but I'm guessing that in your case it will not be an issue.

For rate of change over time, Have a look at the perSecond function of Graphite.

For actual change (i.e the derivative) for your usecase id lookat the nonNegativeDerivative Function

https://graphite.readthedocs.io/en/latest/functions.html

I used this (as per the example) to calculate Network traffic