Inclined Plane Calculator
Enter mass, angle and (optional) friction to compute the parallel and normal force components on an incline.
Input Data
Results
At a glance:An inclined plane redirects an object's weight into components relative to the slope. The component parallel to the surface is mg·sinθ (driving motion down the incline) and the component perpendicular is mg·cosθ, which equals the normal force N when no other vertical force acts. If friction is present with coefficient μ, the friction force is f = μ·N opposing motion, and the net force is mg·sinθ − f (down-slope positive). Mechanical advantage of an ideal frictionless ramp is the length/height ratio = 1/sinθ. This tool resolves the forces for a given mass, angle, gravity and optional μ.
Formula
Parallel: F_parallel = mg·sinθ
Normal: N = mg·cosθ
Friction: f = μ·N
Net: F_net = mg·sinθ − f
$$F_{\parallel} = mg\sin\theta, \quad N = mg\cos\theta, \quad f = \mu N, \quad F_{\text{net}} = mg(\sin\theta - \mu\cos\theta)$$How to Use
- Enter mass m, angle θ (°), and gravity g.
- Optionally enter a friction coefficient μ.
- The calculator returns parallel, normal, friction (if μ given) and net force.
Case Studies
Pushing up a ramp
m = 50 kg, θ = 20°, g = 9.81, no friction.
Parallel = 50×9.81×sin20 ≈ 167.7 N, N = 50×9.81×cos20 ≈ 461.4 N.
You push ~168 N instead of the full 490 N weight.
FAQ
What is the mechanical advantage of a ramp?
An ideal frictionless incline lets you lift a load with force mg·sinθ instead of mg, gaining advantage 1/sinθ (the run/rise ratio) at the cost of a longer push distance.
Why is the normal force less than weight?
Only the perpendicular component of weight presses the plane: N = mg·cosθ < mg (except at θ=0). At steep angles N shrinks and the parallel component grows.
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References
Content review: Calculatorism Science Team. Results are for reference only; please refer to the relevant authorities for the official figures.