Normal Force Calculator
This normal force calculator finds the force with which a surface pushes perpendicular to a body. Example: 10 kg on a plane inclined at 30° gives N ≈ 84.93 N.
Example: Mass m 10 kg · Slope angle θ 30 ° · Gravitational acceleration g 9.8067 m/s² · Extra force perpendicular to the surface 0 N → Result: Normal force N = 84.9281 N (weight 98.0665 N). Source: NIST – Standard acceleration of gravity g_n = 9,80665 m/s² (exakt, CGPM 1901). Updated: .
How it is calculated
The normal force is the force with which a support pushes perpendicular to a body resting on it. It always acts at right angles (“normal”) to the contact surface and stops the body from sinking into it. It is not automatically equal to the weight.
Formula
On a plane inclined at the angle θ, N = m·g·cos θ. In addition, the component m·g·sin θ acts along the surface, down the slope. If another force presses or pulls perpendicular to the surface, it is added (a pull counts as negative). The maximum static friction is μ·N. The standard value g = 9.80665 m/s² is used for gravity.
Worked example
A 10 kg body rests on a plane inclined at 30°. Weight: 10 · 9.80665 = 98.0665 N. Normal force: 98.0665 · cos 30° ≈ 84.93 N. Force down the slope: 98.0665 · sin 30° ≈ 49.03 N. On a horizontal surface (0°) N = 98.0665 N, on a vertical wall (90°) it is 0.
- In an elevator or other accelerating frames the acceleration adds a term; the calculator treats bodies at rest.
- If the normal force is zero, the body lifts off the surface.
- For friction you need the coefficient μ from tables or measurement.
Frequently asked questions
How do you calculate the normal force?
On an inclined plane with N = m·g·cos θ. On a horizontal surface this is simply N = m·g.
Why is the normal force on a slope smaller than the weight?
Only the component of the weight perpendicular to the surface (cos θ) is carried by the surface; the rest (sin θ) acts along the surface as the force down the slope.
How is friction related to the normal force?
The maximum static friction is μ·N. The larger the normal force, the larger the possible friction force.
Sources and legal basis
- NIST – Standard acceleration of gravity g_n = 9,80665 m/s² (exakt, CGPM 1901)
- Halliday/Resnick/Walker, Fundamentals of Physics, Kap. „Force and motion“ (siehe Wikipedia – Normal force)
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