Slow version, fine if you have a reasonable number of files:
aws s3 ls --summarize --human-readable --recursive s3://YOUR-BUCKET-NAME/
Fast version, which uses CloudWatch stats:
aws cloudwatch get-metric-statistics \
--namespace AWS/S3 \
--start-time $(date) \
--end-time 2015-07-31T01:00:00 \
--period 86400 \
--statistics Average \
--region YOUR-REGION \
--metric-name BucketSizeBytes \
--dimensions Name=BucketName,Value=YOUR-BUCKET-NAME Name=StorageType,Value=StandardStorage
The CloudWatch stats are also visible in the AWS S3 console, on the Metrics tab under each bucket