How do I know how many partitions a DynamoDB table is spread over?
It says, "When storing data, Amazon DynamoDB divides a table's items into multiple partitions, and distributes the data primarily based on the hash key element."
What you really want to know is the throughput of a single partition. It seems like you can test that by hammering a single key.
See this page: http://docs.aws.amazon.com/amazondynamodb/latest/developerguide/GuidelinesForTables.html#GuidelinesForTables.Partitions
Which has some simple calculations you can carry out based on the amount of read and write capacity you provision. Note that this is only for initial capacity. As your usage of dynamodb continues, these calculations will have less and less relevance.
A single partition can hold approximately 10 GB of data, and can support a maximum of 3,000 read capacity units or 1,000 write capacity units.