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Normal Force Calculator

Find the force exerted by a surface on an object by entering a few required inputs into the normal force calculator.

External Force:

Outside Force:

kg ▾

Angle:

deg ▾

inclined

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Use this normal force calculator to determine the force a surface exerts on an object to prevent it from falling.

What Is Normal Force?

The normal force is the upward force exerted by a surface on an object resting on it. For example, if you place a glass on a table, gravity pulls the glass downward, and the table exerts an upward force to counteract it. This upward force is called the normal force.

It is denoted by \(F_N\) or N, and its SI unit is the Newton (N). Normal force follows Newton’s Third Law of Motion.

How to Calculate Normal Force on Flat & Inclined Surfaces

Normal force acts perpendicular to the surface. Its magnitude depends on whether the object is on a flat (horizontal) surface or an inclined plane.

Normal Force Formula

1. Horizontal Surface:

\(F_N = m \cdot g\)

Horizontal Surface

m = mass of the object
g = gravitational acceleration (\(\approx 9.8 \text{ m/s²}\))

2. Inclined Surface:

\(F_N = m \cdot g \cdot \cos(\alpha)\)

Inclined Surface

\(\alpha\) = angle of incline

3. Horizontal Surface with External Force Upward:

\(F_N = m \cdot g - F \cdot \sin(x)\)

Horizontal Surface Upward Force

F = external force acting on the object
x = angle between the force and the surface

4. Horizontal Surface with External Force Downward:

\(F_N = m \cdot g + F \cdot \sin(x)\)

Horizontal Surface Downward Force

Normal Force Examples

Example 1: Object on an Inclined Table

Problem: An object of mass 1 kg is on a table inclined at 45°. Find the normal force.

Solution:

Mass: \(m = 1 \text{ kg}\)
Angle: \(\theta = 45^\circ\)
Formula: \(F_N = m \cdot g \cdot \cos(\theta)\)

Calculation:

\(F_N = 1 \cdot 9.8 \cdot \cos(45^\circ) \approx 6.92\ \text{N}\)

Example 2: Object on a Horizontal Surface with Downward Force

Problem: An object of mass 20 kg is on a horizontal surface with an external downward force of 200 N at 30°. Find the normal force.

Solution:

Mass: \(m = 20 \text{ kg}\)
Gravity: \(g = 9.8\ \text{m/s²}\)
External Force: \(F = 200\ \text{N}\)
Angle: \(\theta = 30^\circ\)

Formula: \(F_N = m \cdot g + F \cdot \sin(\theta)\)

Calculation:

\(F_N = 20 \cdot 9.8 + 200 \cdot \sin(30^\circ) = 196 + 100 = 296\ \text{N}\)

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