Weight
Total gravitational force W = mg, vertically downward.
Physics · Mechanics · Motion & Energy
Inclined plane forces — weight components and normal reaction
Resolve an object's weight into components parallel and perpendicular to an inclined plane. The normal reaction shown here assumes no other force or acceleration perpendicular to the plane.
Created v1.0
By Thibaut Grzelak, Mechanical Analysis Engineer
02
Results
Parallel weight component
Down-slope component W∥ = mg sin θ.
Normal reaction
N = mg cos θ only when no other perpendicular force or acceleration acts.
Relation and numerical substitution
W = m × g—
Rigid plane and point-mass force balance perpendicular to the plane; no other perpendicular force and no perpendicular acceleration. Friction is not included.
01Formulas and symbols
Formulas used
W
W = m × gWeight magnitude from mass and gravitational acceleration.W∥
W∥ = W × sin(θ)Component of weight parallel to the plane.N
N = W × cos(θ)Normal reaction balancing the perpendicular weight component under the stated assumptions.02Assumptions and limits
Scope of validity
- Rigid plane and point-mass force balance perpendicular to the plane; no other perpendicular force and no perpendicular acceleration. Friction is not included.
03Validation example
Reference numerical case
- For m = 10 kg, θ = 30° and g = 10 m/s²: W = 100 N.
- The components are W∥ = 100 sin 30° = 50 N and N = 100 cos 30° = 86.602540… N.
04References
Technical references
FAQ
Is N always equal to mg cos θ?
No. That equality requires no other force or acceleration perpendicular to the plane. A push, pull or constrained acceleration can change N.
Does this calculator include friction?
No. First determine N here, then use the related friction-force calculator with the appropriate friction coefficient.
What happens at 0° and 90°?
At 0°, W∥ = 0 and N = W. At 90°, W∥ = W and N = 0 under this idealized model.
05Resolve weight along plane axes
Choose one axis parallel to the plane and one perpendicular to it. Projecting the vertical weight vector W = mg gives W∥ = W sin θ down the slope and W⊥ = W cos θ into the plane. With no other perpendicular force or acceleration, the plane reaction has magnitude N = W⊥.
06Limits of the force balance
This calculator does not solve friction, applied forces, cable tension or acceleration along the slope. The normal-reaction result is invalid if another perpendicular load acts or if the object accelerates away from or into the plane.
07Angle and normal-force checks
Measure θ from the horizontal, not from the vertical. Do not replace mass in kilograms with weight in newtons. At θ = 0°, the parallel component must vanish; at θ = 90°, the ideal normal reaction must vanish.