Normal Force on Incline
N = m × g × cos(θ). Component of weight perpendicular to incline surface.
Result
Normal force
424.785 N
Weight 490.50 N · parallel 245.25 N.
- Mass50 kg
- Incline angle30°
- Gravity9.81 m/s²
- Weight (mg)490.5000 N
- Normal force424.7855 N
- Parallel force245.2500 N
Step-by-step
- Weight = mg = 50 × 9.81 = 490.5000 N.
- Normal = mg cos θ = 490.5000 × 0.8660 = 424.7855 N.
- Parallel (along incline) = mg sin θ = 245.2500 N.
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 parallel exceeds max static friction: mg sin θ > μₛ × mg cos θ → tan θ > μₛ. Independent of mass!
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