How do you calculate takeoff distance and what factors affect it?

Takeoff distance is calculated by integrating the equation of motion from rest to liftoff speed, accounting for: Ground roll (thrust minus drag minus friction until rotation), Rotation (transition to climb attitude), and Climb to screen height (35 ft for FAR 25). Key factors: Thrust/weight ratio (higher reduces distance), Wing loading (lower reduces liftoff speed), CLmax (flaps increase, reducing liftoff speed), Density altitude (high altitude increases ground speed and distance), Runway gradient (upslope increases distance), Wind (headwind reduces ground roll), and Temperature (hot decreases thrust). Balanced field length ensures safe abort or continue if engine fails at decision speed V1.