⚖️ Normal Force Calculator
Calculate normal force
0° for horizontal surface
How to Use This Calculator
Enter the Mass
Input the mass of the object in kilograms (kg). For example, if an object weighs 10 kg, enter 10. Make sure to use positive values only.
Enter the Incline Angle
Input the angle of the inclined surface in degrees (°). For a horizontal surface, enter 0. For an inclined plane, enter the angle between 0° and 90°. For example, a 30° ramp would be entered as 30.
Click Calculate
Press the "Calculate Normal Force" button to compute the normal force. The calculator will use the standard gravity of 9.81 m/s² unless you specify otherwise.
Review Results
The results will show the normal force in Newtons (N), which is the perpendicular force exerted by the surface on the object. The calculator also displays the object's weight for reference.
Formula
N = mg cos(θ)
For horizontal surface: N = mg (when θ = 0°)
Formula Explanation
- N: Normal force (in Newtons, N)
- m: Mass of the object (in kilograms, kg)
- g: Acceleration due to gravity (9.81 m/s² on Earth)
- θ: Angle of incline (in degrees)
- cos(θ): Cosine of the incline angle
Understanding Normal Force
The normal force is the perpendicular force exerted by a surface on an object in contact with it. It prevents the object from falling through the surface and is always perpendicular to the surface.
On a horizontal surface (θ = 0°), the normal force equals the weight (mg). On an inclined plane, the normal force is reduced by the cosine of the angle because only the component of weight perpendicular to the surface contributes to the normal force.
Worked Examples
Example 1: Object on Horizontal Surface
A 10 kg object rests on a horizontal table (θ = 0°):
N = mg cos(0°) = (10 kg)(9.81 m/s²)(1) = 98.1 N
On a horizontal surface, normal force equals weight.
Example 2: Object on 30° Inclined Plane
A 5 kg object on a 30° ramp:
N = mg cos(30°) = (5 kg)(9.81 m/s²)(0.866) = 42.5 N
cos(30°) ≈ 0.866, so the normal force is reduced compared to horizontal.
Example 3: Object on 45° Inclined Plane
A 20 kg object on a 45° incline:
N = mg cos(45°) = (20 kg)(9.81 m/s²)(0.707) = 138.7 N
cos(45°) = 0.707, so normal force is about 70.7% of the weight.
Frequently Asked Questions
What is normal force?
Normal force is the perpendicular force that a surface exerts on an object resting on it. It's called "normal" because it acts perpendicular (normal) to the surface. It prevents objects from falling through surfaces and is a reaction force to the component of weight pressing against the surface.
Why does normal force decrease on an incline?
On an inclined plane, only the component of weight perpendicular to the surface contributes to the normal force. As the angle increases, more of the weight acts parallel to the surface (causing sliding), while less acts perpendicular. This is why the normal force decreases with increasing angle.
Is normal force always equal to weight?
No, normal force equals weight only on a horizontal surface with no other forces. On an inclined plane, normal force is less than weight. If there are additional forces (like someone pushing down or pulling up), the normal force can be different from the weight.
Can normal force be greater than weight?
Yes, if additional forces are applied downward on the object (like someone pressing down), the normal force can exceed the weight. However, in the basic case with just weight and no other forces, normal force is always less than or equal to weight.
What happens at 90° (vertical surface)?
At 90°, cos(90°) = 0, so the normal force would be zero. However, in reality, an object can't simply rest on a vertical surface without additional forces (like friction or a support). This illustrates why objects slide down steeper inclines.
What units should I use?
Use kilograms (kg) for mass and degrees (°) for the angle. The calculator uses standard gravity (9.81 m/s²) and returns normal force in Newtons (N). 1 Newton = 1 kg·m/s².
About Normal Force Calculator
The Normal Force Calculator is an essential tool for understanding and calculating the perpendicular force that surfaces exert on objects. This force is fundamental in physics, especially when analyzing objects on inclined planes, friction problems, and statics scenarios.
When to Use This Calculator
- Calculating normal force on horizontal and inclined surfaces
- Solving friction problems (friction depends on normal force)
- Analyzing forces on ramps and inclined planes
- Understanding statics and equilibrium problems
- Designing ramps and slopes in engineering applications
Why Use Our Calculator
- Quick calculation of normal force for any mass and angle
- Handles both horizontal and inclined surfaces
- Clear display of weight and normal force relationship
- Educational tool with formula explanations and examples
- Free to use with no registration required
- Mobile-friendly for calculations anywhere
Common Applications
- Physics Education: Understanding forces on inclined planes and friction
- Engineering: Designing ramps, loading docks, and conveyor systems
- Architecture: Calculating loads on sloped surfaces and roofs
- Transportation: Analyzing vehicle forces on hills and ramps
Tips for Using This Calculator
- Remember that normal force is always perpendicular to the surface
- On horizontal surfaces (0°), normal force equals weight (mg)
- As the angle increases, normal force decreases due to the cosine factor
- Normal force is crucial for calculating friction (f = μN)
- This calculator assumes no additional forces beyond gravity