Load factor at the bottom and at the top
Along a curved path of radius R at true airspeed V, the centripetal acceleration is V²/R, or V²/(gR) in g units. In a pull-up that starts from level flight, lift must also support the weight, so the load factor — lift over weight — at the bottom is
nbottom = 1 + V² / (g R)
A 100 kt pull-up with a 1,000 ft radius is about 1.89 g at the bottom. A push-over from level flight has the opposite sign, n = 1 − V²/(gR). At the top of a loop the airplane is inverted and weight helps the turn:
ntop = V² / (g R) − 1
That top load factor is only physical when V²/(gR) is greater than 1; otherwise the speed and radius cannot sustain an inverted top. This page reports all three numbers from the same V and R, and will invert any two of {V, R, nbottom} for the third: R = V² / (g(n − 1)) and V = √[g R (n − 1)].
Accelerated stall and a level-turn contrast
Stall speed rises with the square root of load factor, Vs,n = Vs √n, the same rule as the stall-speed vs weight and bank calculator. A 60 kt wings-level stall becomes 90 kt at 2.25 g. That is independent of whether the load factor comes from a pull-up or from a level banked turn (where n = 1 / cos φ). For radius and rate in a level turn, use the turn-radius calculator. For the airspeed that protects the limit load factor in turbulence, see maneuvering speed vs weight.
Sources
FAA Pilot's Handbook of Aeronautical Knowledge (load factor, accelerated stall); FAA Airplane Flying Handbook; NASA Glenn Beginner's Guide (lift and load factor); Anderson, Introduction to Flight (pull-up and loop). g = 9.80665 m/s² (32.174 ft/s²).
Frequently asked questions
What is the load factor at the bottom of a 100-knot, 1,000-foot pull-up?
About 1.89 g. n = 1 + V²/(gR), with V converted to feet per second and g = 32.174 ft/s².
When is the top of a loop possible?
When V²/(gR) is greater than 1, so n_top = V²/(gR) − 1 is positive. At 100 kt and 1,000 ft, V²/(gR) is only about 0.89, so that combination cannot sustain an inverted top.
Is this the same as load factor in a level turn?
No. A level coordinated turn has n = 1 / cos φ, with the load factor in the vertical used to provide the centripetal force in the horizontal plane. A pull-up is a vertical-plane maneuver: n = 1 + V²/(gR) at the bottom. Both raise stall speed by √n.