Physics overview
What is normal force?
Normal force is the contact force exerted by a surface on an object. It acts perpendicular to the surface and prevents the object from passing through it.
Normal force is not automatically equal to weight. Inclines and external forces can change its magnitude.
Horizontal surface
Normal-force formula on a level surface
Horizontal surfaceN = mg + Fdown − Fup
- N is normal force in newtons.
- m is mass in kilograms.
- g is gravitational acceleration.
- Fdown is any additional downward force.
- Fup is any additional upward force.
Inclined surface
Normal-force formula on an incline
Inclined surfaceN = mg cos(θ) + Fdown − Fup
Only the component of weight perpendicular to the incline contributes directly to the normal force. That perpendicular component is mg cos(θ).
Worked example
A 10 kg object on a horizontal surface
- Use the formula: N = mg.
- Substitute the values: N = 10 × 9.81.
- Calculate the result: N = 98.1 N.
Incline example
A 10 kg object on a 30° incline
- Write the formula: N = mg cos(θ).
- Substitute the values: N = 10 × 9.81 × cos(30°).
- Calculate the result: N ≈ 84.96 N.
External forces
How pushes and pulls affect normal force
Downward force
Increases normal force
Pressing an object into the surface increases the supporting force.
Upward force
Reduces normal force
Pulling an object away from the surface reduces the supporting force.
Weight comparison
Normal force and weight are different
Weight is the gravitational force acting on an object. Normal force is the support force supplied by a surface.
They have equal magnitudes only in specific conditions, such as an object at rest on a horizontal surface with no additional vertical forces.
Loss of contact
Normal force cannot be negative
A surface can push an object but cannot pull it toward itself. If an upward force becomes large enough to lift the object, contact is lost and the normal force becomes zero.
Friction connection
Why normal force matters in friction
Many friction calculations use the normal force. The maximum static friction and kinetic friction are commonly modeled using a coefficient multiplied by normal force.
Friction relationshipFf = μN
Units
Use consistent SI units
- Mass should be entered in kilograms.
- Forces should be entered in newtons.
- Gravity should be entered in meters per second squared.
- Angles should be entered in degrees.
Assumptions
What the calculation assumes
- External forces act perpendicular to the surface.
- The incline angle is at least 0° and less than 90°.
- The object remains in contact with the surface.
- Gravity is treated as constant.
- The calculator does not include vertical acceleration of the surface.
Related tools
Continue your force calculations
Use the Weight Calculator to calculate gravitational force from mass and gravity.
Use the Force Calculator to solve general force, mass, or acceleration problems.
Use the Acceleration Due to Gravity Calculator to estimate gravity for a planet or celestial body.
Questions and answers
Normal force calculator FAQ
What is normal force?
Normal force is the support force exerted by a surface on an object in contact with it. It acts perpendicular to the surface.
What formula is used on a horizontal surface?
For a horizontal surface, the calculator uses N = mg + Fdown − Fup, where downward forces increase normal force and upward forces reduce it.
What formula is used on an inclined surface?
For an incline, the calculator uses N = mg cos(θ) + Fdown − Fup.
Is normal force always equal to weight?
No. Normal force equals weight only on a horizontal surface when there are no additional vertical forces and no vertical acceleration.
What happens if the upward force is greater than the supported weight?
The object loses contact with the surface, so the normal force becomes zero rather than negative.