B737 FLC DETERMINE; AFTER TKOF; THAT INCORRECT WTS WERE CALCULATED FOR RWY USED.

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DISPATCH PLANNED TKOF ON RWY 27. I REVIEWED NOTAMS ON DISPATCH RELEASE. DID NOT MAKE A MENTAL NOTE THAT THE LAST 4600 FT OF RWY 15L WERE CLOSED DUE TO CONSTRUCTION. FO FILLED OUT TKOF DATA CARD USING RWY 15L DATA. HE DID NOT WRITE DOWN THAT THE LAST 4600 FT OF RWY 15L WERE CLOSED WHEN HE COPIED THE ATIS ON THE CARD. HE ALSO USED THE FULL LENGTH DATA FOR RWY 15L FROM THE TKOF DATA RPT. WE WEIGHTED 117000 LBS. HIS DATA SHOWED A FLAPS 1 DEG TKOF WITH REDUCED THRUST FOR 45 DEGS C WOULD LIFT THE WT. AS WE PUSHED BACK; WE WERE TOLD TO EXPECT RWY 26. AFTER CONTACT WITH GND CTL; THEY ASKED US IF WE WANTED RWY 15L. THE WIND WAS 360 DEGS AT 8 KTS. WE ACCEPTED RWY 15L KNOWING THAT THE TAILWIND WOULD DECREASE OUR TKOF WT BY A FEW THOUSAND LBS. WE WOULD STILL BE TAKING OFF AT A WT BELOW THE WT ALLOWED BY A REDUCED THRUST. AT NO TIME DID THE GND OR TWR CTLR RPT THAT THE S 4600 FT WERE CLOSED. WE SET TKOF PWR. APPROX 3000 FT INTO OUR TKOF ROLL; I NOTICED CONSTRUCTION EQUIP ON THE RWY -- WE WERE APCHING IT QUICKLY. I MENTALLY COMPUTED THAT WE WOULD BE ABLE TO CONTINUE THE TKOF SAFELY. WE WERE AIRBORNE ABOUT 1500 FT BEFORE THE CLOSED SECTION. AFTER REVIEW; WE FOUND THE TKOF DATA FOR THE SHORTENED RWY. IT REQUIRED FLAPS 5 DEGS AND FULL THRUST. WE TOOK OFF 5000 LBS OVERWT. RECOMMENDATIONS: 1) BOTH PLTS LISTEN TO ATIS. 2) BOTH PLTS REVIEW TKOF DATA. 3) CTLRS BE REQUIRED TO TELL PLTS THAT RWY IS SHORTENED. 4) A SIGN IS PLACED AT THE END OF RWY STATING THAT THERE IS CONSTRUCTION AND THE NEW RWY TKOF LENGTH AVAILABILITY. 5) DISPATCH NOTIFY PLTS IN REMARKS SECTION OF ANY SHORTENED RWYS.