Normal Force on Incline
N = m × g × cos(θ). Component of weight perpendicular to incline surface.
Result
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How to use this calculator
- Enter mass, incline angle, gravity.
- Read normal + parallel.
About this calculator
On an incline at angle θ, weight (mg) splits into two components: normal (perpendicular to surface) = mg cos θ, and parallel (along surface, pulling object down the slope) = mg sin θ. Normal force is what gives friction grip; parallel is what tries to slide the object. Combined with friction (f = μN), you can compute when an object slides: tan θ = μ at the angle of repose.
Frequently asked
When does object slide?+
When parallel exceeds max static friction: mg sin θ > μₛ × mg cos θ → tan θ > μₛ. Independent of mass!
Why cos and sin?+
Decomposing weight into parallel/perpendicular components. Geometry of incline.
Flat surface (θ=0)?+
Normal = mg (full weight); parallel = 0. Standard horizontal case.
Vertical wall (θ=90°)?+
Normal = 0; parallel = mg. Object falls freely. Wall must apply force perpendicular to gravity.
Real-world?+
Roof pitch design, vehicle hill climb, ski slope friction, conveyor incline.
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