How this calculator works
Normal force is the compressive contact force perpendicular to a surface. In perpendicular equilibrium it balances the perpendicular components of weight and external load. If a pull would require negative normal force, an unbonded surface cannot supply it, so the result is zero and the equilibrium assumption fails. This model excludes perpendicular acceleration and adhesive contact.
Formula
N = max(0, mg cos(theta) + s F sin(phi)), where s = +1 for pressing and -1 for pulling; phi is measured from the surface.
Worked example
A 10 kg mass at g = 10 m/s² on a horizontal surface with a 20 N perpendicular push has N = 120 N. Without that push on a 60 degree incline, N = 50 N.
Advertisement
Frequently asked questions
Is normal force always equal to weight?
Only on a horizontal surface with no other perpendicular force and no vertical acceleration.
What does zero normal force mean?
The surface is no longer supplying a compressive support force; the body can lose contact.
Can I model an accelerating lift?
Use a free-body diagram with the vertical acceleration. This page assumes perpendicular equilibrium.