What the normal force is
The normal force is the push a surface exerts on an object resting on it, directed perpendicular to the surface. It is what stops a book sinking into a table, and it adjusts itself to whatever is needed to keep the object from passing through. Its size depends on the weight, the angle of the surface and any extra push or pull, so it is often not equal to the weight.
This calculator takes the mass, the angle of the surface, an optional perpendicular force and a friction coefficient. It returns the normal force, the weight, the component of weight pulling along the slope and the maximum static friction, and it tells you whether the object would hold or slide.
The equations
- W = m g, the weight in newtons.
- N = m g cosθ + Fperp, with Fperp positive pushing into the surface. N cannot be negative; below zero the object has left the surface.
- Fparallel = m g sinθ, the component of weight along the slope.
- fmax = μs N, the largest static friction the surface can supply. The object slides when Fparallel exceeds fmax.
Worked example
A 10 kg box on a 30° ramp, no extra force, μs = 0.7, g = 9.81 m/s² (the defaults).
Weight W = 10 × 9.81 = 98.10 N. Normal force N = 98.10 × cos 30° = 98.10 × 0.8660 = 84.96 N. Downslope component = 98.10 × sin 30° = 49.05 N. Maximum friction = 0.7 × 84.96 = 59.47 N. Since 49.05 N is 82% of 59.47 N, the box holds but is close to slipping, which is the calculator's moderate rating. On a flat table (angle 0) the same box gives N = 98.10 N.
Common mistakes and how to read the result
- Assuming N = mg on a slope. The normal force shrinks as the slope steepens.
- Using kinetic friction. The hold-or-slide check needs the static coefficient, which is usually larger than the kinetic one.
- Angle in the wrong units. Enter degrees, not radians.
- Forgetting extra forces. A push down the slope or a rope pulling up it changes the parallel forces; this calculator only includes the weight component.