The FARs define takeoff field length as the distance that allows takeoff at the MINIMUM of three possible weights:
1. (failed engine) For a Rejected Takeoff, the distance required to accelerate the a/c to a point where an engine failure occurs, accelerate to V1, and stop on the remaining runway.
2. (failed engine) If the engine fails AFTER V1, the distance required to accelerate to the engine failure speed and attain a height of 35' AGL
3. (no engine failure) 1.15 times the distance required to reach 35' AGL with all engines
Having defined that, the Balanced Field Condition is a condition in which the Accelerate-Stop Distance is equal to the Takeoff Distance, with:
Accelerate-Stop Distance being defined as the distance required for the a/c to accelerate with all engines operating, experience an engine failure, continue acceleration to V1, and come to a stop.
Takeoff Distance is the greater distance from the start of the takeoff run:
a) to which the a/c achieves a height of 35 AGL feet with one engine inop -or-
b) 1.15 times the total horizontal distance in which the a/c reaches 35 feet AGL with all engines operating.
(This is why takeoff data and speed cards are printed in tabular form!!!)