Normal Force Calculator

The normal force is the contact force a surface exerts on an object, directed perpendicular to the surface. It is not always equal to the object’s weight — it depends on the surface angle and any additional forces applied perpendicular to the surface.

On a flat surface (θ = 0°): N = mg

The normal force exactly equals the weight.

On an inclined plane at angle θ: N = mg × cos(θ)

As the slope steepens, the normal force decreases. At θ = 90° (a vertical wall), cos(90°) = 0 and the normal force is zero — the surface is not supporting any weight. At θ = 45°, the normal force is mg × cos(45°) ≈ 0.707mg.

With an additional perpendicular force F_extra: N = mg × cos(θ) + F_extra

Positive F_extra pushes the object into the surface (like a person pressing down on a block); negative F_extra pulls it away (like a suction cup or upward applied force component). Leave F_extra at zero if none applies.

The normal force determines friction: f_max = μ × N, where μ is the coefficient of friction. Reducing the normal force (say, by pushing up at an angle) directly reduces the maximum static friction — which is how people move heavy furniture by tilting it.

The θ = 0 case gives you the weight in newtons at Earth’s gravity. The chart of normal force vs incline angle would show a cosine curve from mg down to 0.