RMAN Info

Job Status

SELECT input_bytes_display, 
       output_bytes_display, 
       status, 
       time_taken_display, 
       det.* 
  FROM V$RMAN_BACKUP_JOB_DETAILS det 
 WHERE TRUNC(SYSDATE)=TRUNC(START_TIME)
 ORDER BY START_TIME DESC;

Viewing RMAN Job Status and Output
Job Throughput
How to measure the throughput of RMAN
RMAN Backup Async IO Rate

SELECT 'DUPLICATE/RESTORE THROUGHPUT',
  round(SUM(v.value/1024/1024),1) mbytes_sofar,
  round(SUM(v.value     /1024/1024)/nvl((SELECT MIN(elapsed_seconds)
  FROM v$session_longops
  WHERE OPNAME LIKE 'RMAN: aggregate input'
  AND SOFAR            != TOTALWORK
  AND elapsed_seconds IS NOT NULL
  ),SUM(v.value     /1024/1024)),2) mbytes_per_sec,
  n.name
  FROM gv$sesstat v,
  v$statname n,
  gv$session s 
  WHERE v.statistic#=n.statistic# 
  AND n.name = 'physical write total bytes' 
  AND v.sid = s.sid 
  AND v.inst_id=s.inst_id 
  AND s.program like 'rman@%' 
  GROUP BY 'DUPLICATE/RESTORE THROUGHPUT',n.name;

How to measure throughput of RMAN
Articles
Cataloging and Uncataloging with RMAN

Archivelog Status

spool to log '/tmp/log.txt';
list backup of archivelog all;
list archivelog all;
spool log off;

RMAN Backup Size Query

set linesize200
set pagesize200
select name,open_mode from v$database;
select sum(bytes)/1024/1024/1024 from dba_segments;
SELECT completion_time  , type, round(sum(bytes)/1048576) MB, round(sum(elapsed_seconds)/60) min
FROM   (  SELECT
  CASE
    WHEN s.backup_type='L' THEN 'ARCHIVELOG'
    WHEN s.controlfile_included='YES' THEN 'CONTROLFILE'
    WHEN s.backup_type='D' AND s.incremental_level=0 THEN 'LEVEL0'
    WHEN s.backup_type='I' AND s.incremental_level=1 THEN 'LEVEL1'
  END type,
  TRUNC(s.completion_time) completion_time,
  p.bytes,
  s.elapsed_seconds
FROM v$backup_piece p, v$backup_set s
WHERE p.status='A'
and s.backup_type in ('D','I')
AND p.recid=s.recid
UNION ALL
SELECT 'DATAFILECOPY' type, TRUNC(completion_time), output_bytes, 0 elapsed_seconds FROM v$backup_copy_details
)
where completion_time > sysdate -15
group by completion_time, type
order by 1 asc,2,3;