Date: 201706
Local time of day: 0001-0600
Location: ZZZ.Airport, US
Light: Daylight
Aircraft: B737 Next Generation Undifferentiated
Operator: Air Carrier
Operating under: Part 121
Flight plan: IFR
Flight phase: Taxi; Takeoff / Launch
Airspace: Class D ZZZ
ATC / advisory: Tower ZZZ
Reporter organization: Air Carrier
Reporter function: Captain; Pilot Not Flying
Reporter qualification: Flight Crew Air Transport Pilot (ATP)
Human factors: Other / Unknown
Second reporter function: Pilot Flying; First Officer
Anomaly: Deviation / Discrepancy - Procedural Published Material / Policy; Deviation / Discrepancy - Procedural FAR; Deviation / Discrepancy - Procedural Weight And Balance
Detector: Person Flight Crew
When detected: In-flight
Result: General None Reported / Taken
Contributing factors: Procedure; Human Factors
Primary problem: Human Factors

Narrative: While approaching Runway XY (shortened on Taxiway C) I asked the First Officer if that was the point at which the takeoff calculation was made. He said yes. It looked about right; especially since the displaced threshold was in front of us from that intersection. I asked the question because there was a little bit of runway that looked usable to our left. (The runway construction was on the approach end of the runway to our left.)Takeoff was uneventful; however; it did seem that we rotated and lifted off a bit closer to the end than I would have expected. That and a query to Tower about usable runway by the aircraft behind us made us recheck our work when we got to cruise. It turns out there was no C intersection option available in the computer. We should have queried ATC and back-taxied to the correct position for takeoff.I should have been more vigilant in determining the correct takeoff point on the runway. Although it was a bit deceiving due to the displaced threshold being to our right (towards departure end of runway) I should have called ATC to verify. There should be a Dispatch note on the Release to advise Crews to back-taxi from C on that runway. It's an easy mistake to make but one with potentially grave consequences. We were lucky that we were not heavier.


Second narrative: We had loaded [takeoff data] for takeoff Runway XY with NOTAM for [runway] XY short 2100 feet. Weight and balance listed flaps 1 with reduced takeoff power and 734 feet stopping margin. ATC instructed us to taxi XY; shortened at C upon reaching; we were cleared for takeoff XY shortened at C. Captain lined the aircraft on center line and transferred controls to me; I recall seeing a 6000 feet marker ahead of aircraft as we accelerated and lifted off with approximately 1500 feet remaining; with normal rotation. During climb out we heard an RJ query ATC if they needed to back-taxi on XY to get the runway length of 7900 feet; and ATC said they needed to. Both the Captain and I realized at that point we departed with less than the 7900 feet available. The computer doesn't list Runway XY at C as an option. ATC normally; as I recall; will instruct an aircraft to back-taxi when they are cleared for takeoff on a runway that is shortened at brake release. When ATC cleared us for takeoff; I incorrectly assumed the intersection C and 2100 feet shortened distance were the same. I briefed the Captain about the shorted runway and that it was inputted into the WB; but we didn't discuss where that point was in relation to C.


Synopsis: B737NG flight crew reported mistakenly departing from a taxiway intersection even though the takeoff calculations were for using the entire runway.