Light Transport
Flight Crew Multiengine; Flight Crew Air Transport Pilot (ATP); Flight Crew Instrument
Troubleshooting; Fatigue
Aircraft Equipment Problem Less Severe; Deviation - Altitude Overshoot; Deviation / Discrepancy - Procedural Clearance; Deviation / Discrepancy - Procedural Published Material / Policy
Flight Crew Overcame Equipment Problem
Aircraft; Human Factors
During descent into ZZZ; we were assigned a crossing restriction of 10;000 feet at ZZZZZ intersection and given an altimeter setting of what we believed and read back as 30.27. We made the crossing restriction and about the same time we were handed off from center to approach. Approach immediately called and asked if we were on frequency. I said 'Aircraft X with you 10;000' He asked me to verify assigned altitude. I told him we were level at assigned altitude of 10;000 feet. He said we were showing 9;100 feet. I checked all 3 altimeters and they all showed 10;000 [feet]. He gave us a descent to 7;000 [feet]. I switched from transponder 1 to transponder 2. During the descent; he asked us to verify altitude. I don't recall where we were at but I told him and asked if it matched and he said we still showed 800 feet low and gave us the altimeter setting of 29.27. We set the correct altimeter setting and leveled at 7;000 feet (we were at 6;800 [feet] after correcting the altimeter and climbed back to 7;000 feet). I admitted that we had the incorrect altimeter setting and we corrected it. We now showed the correct altitude. There were no traffic conflicts during this time. We were prepared for landing at ZZZ in advance of this situation and had pre-selected the altimeter setting for ZZZ prior to our descent. Somehow; we even had that incorrect as it was showing 29.29 and we both had 30.29 in our preselect. So; when we were given the altimeter setting; I did not comprehend the difference from 30 to 29 as it made sense to me the numbers after the decimal were very close. In addition to this; I was very tired and becoming fatigued. I had been on afternoon starts for days and last night was a 10 hour turn to an XX:30 show time. That may not seem that early; but we had been prepared for a late night when our trip cancelled due to the lengthy delays caused by ZZZ1 weather. After that; they shut us right down with a 10 hour turn. I laid in bed for quite some time before sleeping. I felt ok at the beginning of the day and the flight to ZZZZ and back to ZZZ1 seemed fine. But after arriving ZZZZ; we found we now had a long ferry to ZZZ. That was followed by holding on the way into ZZZZ and delays leaving. At the time of leaving ZZZZ; I felt ok but about 2 hours into the flight I faded fast. I believe this fatigue was directly related to this error.
Corporate Captain reported using incorrect altimeter setting due to fatigue; resulting in erroneous altitude reporting.