Date: 201601
Local time of day: 1801-2400
Location: ZZZ.Airport, US
Aircraft: B737-800
Operator: Air Carrier
Operating under: Part 121
Flight plan: IFR
Mission: Passenger
Flight phase: Parked
Reporter organization: Air Carrier
Reporter function: Pilot Flying; Captain
Reporter qualification: Flight Crew Air Transport Pilot (ATP)
Human factors: Workload; Time Pressure
Second reporter function: Pilot Not Flying; First Officer
Anomaly: Deviation / Discrepancy - Procedural Published Material / Policy; Deviation / Discrepancy - Procedural Weight And Balance; Inflight Event / Encounter Fuel Issue
Detector: Person Flight Crew
When detected: In-flight
Result: General None Reported / Taken
Contributing factors: Human Factors
Primary problem: Human Factors

Narrative: Flight was third and last scheduled of day and last day of four day sequence. Arrival of retained aircraft was 19 minutes late due to required de-ice procedure at departure airport. Captain was met with multiple redundant requests as flight planning occurred at gate departure desk for return flight. Five gate agents were providing input as printer issues ensued. Each required flight planning document had to be requested separately from Captain's iPhone. The base manager called me on land line emphasizing an on time departure; while concurrently the flight had an EDCT of XA:37 which would have put flight crew beyond duty limit without relief or extension. First Officer stated he would not extend; putting our duty time limit at XA:13. After getting all flight planning documents I then worked with Dispatch and Clearance to get EDCT reduced and made them aware of flight duty limits. I instructed the First Officer that we would respect non-extended duty limits; push as soon as we were able; and if crew duty limits were exceeded; we would return to the gate and inform the company. The flight pre-departure checklist was read and when fuel check was prompted. Due to fatigue and saturated with previous multiple non-essential tasks; I responded with fuel total as release fuel amount and balanced. I did NOT notice or it did not register that all tanks had roughly the same amount of fuel; which had the wing tanks less than full (all at 6500 lbs. = 19.4 total) and that this was a limitation violation. I did not have my glasses on at the time and the 6 may have looked like an 8 in the low light of the flight deck; so did not grab my attention or the First Officer's either.Flight was out at XA:30 local (15 minutes after original schedule) and we continued to work the EDCT which had been moved up to XA:07 at OUT time. Coordination with tower improved our EDCT such that OFF time was at XA:49 and within standard duty day limits for flight crew. After climbing through 10;000 feet; I noticed the fuel load and recognized the error in fuel loading. I took a photo with for documentation. My fuel load showed the following: Right Tank 6.50; Center 4.82; Left Tank 6.51.; Total 17.8. There was no fuel system malfunction either. I then realized this was not correct with standard fuel loading. Flight continued; maintenance was informed of the issue. This concludes the event. Summary is that crew failed to notice in a timely manner an improper fuel load for departure; and took off with this improper fuel load.


Second narrative: [Report narrative contained no additional information.]


Synopsis: The B737 crew reported their flight took off with improper fuel loading.