# Normal Force Calculator

Find the force exerted by a surface on an object by just providing a few required inputs to the normal force calculator.

Try this normal force calculator to determine the amount of force a surface applies on an object to prevent it from falling.

## What Is Normal Force?

The normal force is exerted on an object by a surface. For instance, you have a glass and you put it on a table, and the gravitational force pulls the glass downward. To stop the glass from going down the table exerts a force on it.  This force that is exerted by the table is known as the normal force. It is denoted by $$F_N$$ or N and the unit that is used for the normal force is Newton. This normal force follows the principle of Newton's Third Law of Motion.

## How To Calculate Normal Force On Incline & Flat Surfaces?

Normal force acts perpendicular to the surface and it changes on whether the object is on an incline or a flat surface.

## Normal Force Formula:

The formula that is used for knowing the normal force on a thing that is placed on a horizontal surface is as follows: $$Normal\ Force\ =\ F_N = m.g$$ Where
• m is representative of the mass of an object
• g is the gravitational acceleration
If the object is placed on an inclined surface then the normal force on an incline is: $$Normal\ Force\ =\ F_N = m.g.cos(a)$$ Where
• a is the surface inclination angle
When the object is placed on a horizontal surface and an external force acts on it in an upward direction then the normal force equation is as follows: $$Normal\ Force\ =\ F_N = m.g - F.sin(x)$$ Where
• F is the external force that acts on the object
• x is the angle between the outward force and the surface
If the object is present on a horizontal surface and an external force acts on it in the downward direction then the formula of normal force is: $$Normal\ Force\ =\ F_N = m.g + F.sin(x)$$

## Normal Force Examples:

1. Let's suppose an object is placed on a table if the mass of the object is 1 kg. The Angle of inclination is 45°, so how to find normal force?
Solution: Mass = m = 1 Kg Angle = θ = 45° $$F_N = m * g * cos(α)$$ Substituting the values in the normal force formula $$\text{Normal Force} = F_{N}$$ = 1 * 9.8 * cos (45°) = 6.92N
1. Suppose An object of mass of 10 kg is sliding down with a force of 200 N from a slant surface at an angle of 30°. Calculate the normal force being exerted on it.
Solution: Given that: F = 200 N m = 20 kg g = 9.8 ms^-2 θ = 30° Using the formula we get, $$Normal\ Force\ =\ F_N = mg + Fsin θ$$ $$Normal\ Force\ =\ F_N = 20 (9.8) + 200* sin (30°)$$ $$F_N = 196 + 200 (1/2)$$ $$F_N = 196 + 100$$ $$F_N = 296 N$$