Normal Force Calculator
Calculate the perpendicular force exerted by surfaces on objects
Normal Force Calculator
Add an external force acting on the object (push, pull, etc.)
Mass of the object in kilograms
Standard Earth gravity: 9.807 m/s²
Normal Force Results
Formula used: F_N = mg
Surface type: Horizontal
Example Calculation
Book on an Inclined Desk
Given: A 2 kg book on a desk tilted at 30°
Find: Normal force exerted by the desk on the book
Solution
Using the inclined surface formula: F_N = mg cos(α)
F_N = 2 kg × 9.807 m/s² × cos(30°)
F_N = 19.614 N × 0.866
F_N = 17.0 N
Result: The desk exerts 17.0 N of normal force on the book
Types of Forces
Normal Force
Perpendicular contact force from surfaces
Always acts perpendicular to surface
Weight
Gravitational force pulling objects down
W = mg
Friction
Parallel resistance force
Opposes motion along surface
External Force
Applied forces (push, pull, etc.)
Can affect normal force magnitude
Common Incline Angles
Understanding Normal Force
What is Normal Force?
Normal force is the perpendicular contact force that a surface exerts on an object. It prevents objects from passing through solid surfaces and is always directed perpendicular (normal) to the contact surface. This force is a direct result of Newton's third law - for every action, there is an equal and opposite reaction.
Key Characteristics
- •Always perpendicular to the contact surface
- •Magnitude varies with surface angle and external forces
- •Can never be negative (surfaces can only push, not pull)
- •Equal to weight only on flat surfaces with no external forces
Normal Force Formulas
Flat Surface:
F_N = mg
Normal force equals the object's weight
Inclined Surface:
F_N = mg cos(α)
α is the angle of inclination from horizontal
With External Force:
F_N = mg ± F sin(θ)
θ is the angle between external force and surface
Normal Force vs. Weight
A common misconception is that normal force always equals an object's weight. This is only true for:
When F_N = Weight:
- • Object on a flat, horizontal surface
- • No external forces acting vertically
- • Object at rest or moving at constant velocity
- • No acceleration in the vertical direction
When F_N ≠ Weight:
- • Object on an inclined surface
- • External forces with vertical components
- • Elevator accelerating up or down
- • Object being pushed or pulled at an angle