EMB-505 Captain reported misreading the clearance and climbing to the wrong altitude.
Synopsis
EMB-505 Captain reported misreading the clearance and climbing to the wrong altitude.
Narrative
Captain received clearance from ATC for initial altitude of 5000' and then misread his own writing (due to hurrying to write down clearance as received) and read his '5' in 5000 as a '3'.Departure chart showed initial altitude as 'As Assigned by ATC'; so I had no reason to doubt what was entered in the altitude selector for takeoff.To compound the issue the departure controller was distracted with dealing with another aircraft; so he did not catch the error of our level off at 3000 until he received a low altitude alert. He then directed us to climb immediately to 6000' which we did without further incident.It was still day VMC and we were able to see clearly. We were not in imminent danger of conflicting with terrain during this deviation; but our altitude was apparently below the MVA for the area due to surrounding terrain.ATC departure controller asked if we had leveled off which we confirmed was the case. He then announced a low altitude alert and directed us to climb immediately to 6000'.Cause: Captain misread his writing of the initial assigned altitude.We climbed to 6000' as directed without further incident.Suggestion: Take time to write clearances clearly when given; even if we have to have to ask Clearance to repeat something. However; I'm not sure that would actually apply here since the clearance was read back and the controller acknowledges read back was correct. Again; just seems to be an issue of writing clearly. Fatigue may have been an issue also since this was the beginning of leg 4 of 5 for the day?
Second reporter narrative
On departure from runway XX in ZZZ; ZZZZZ departure we leveled off at 3;000 feet; when the clearance assigned was 5;000 feet.Once handed over to departure I checked in with them at the same time as another aircraft (inbound for ZZZ) was checking in and my radio transmission of 2;100 (ish) climbing 3;000 was stepped on. The controller took the inbound aircraft's radio call first and we leveled off at 3;000. ATC then asked for us to check in again and I transmitted level 3;000; he then asked again if we were level at 3; to which I responded affirmative. He then instructed us to climb to 6;000 and informed us the MVA for the area was 3;400.Cause: When verbally receiving clearance; I did not hear the name of the departure we were given; which caused me to be slightly behind on writing down the rest of my clearance. I wrote down everything correctly but wrote fast. The 5 I wrote down for initial altitude looked slightly like a 3. When I went to set up the AFCS (Automatic Flight Control System) Panel I read it as a 3; and set it accordingly. The departure altitude is assigned by ATC; so when I went to check my work with the departure the error did not stand out to me.We immediately set 6;000 feet in the altitude window and climbed to 6;000 feet as instructed.Suggestions: Suggestions for myself would be don't scribble down clearances trying to catch back up when I miss a portion; I should have simply started over.
Source: NASA Aviation Safety Reporting System (public domain). Reports are voluntary submissions and are not verified by NASA.