Normal Force
Estimate support force on flat or inclined surfaces. Free online calculator with formulas and step-by-step solutions.
Key formula
N = mg or N = mgcos(theta)
How do you calculate normal force?
On a horizontal surface with no other vertical forces, N = mg. On an incline with no extra perpendicular forces, N = mg cosθ. If something pushes down on a floor, N = mg + F_down; if something lifts, N = mg − F_up (and N cannot go below zero while contact lasts).
About this tool
Normal force is the support force a surface exerts perpendicular to itself. This page keeps N = mg on a flat floor and N = mg cosθ on a ramp visible so you can pick the right model instead of treating every surface as N = mg.
How to use this calculator
- Choose the variable you want to solve for and confirm which values are already known.
- Enter inputs in consistent units before calculating so the formula is applied correctly.
- Check whether the result is physically reasonable by comparing it with the size of the inputs.
- Use the step-by-step breakdown to see how the equation was rearranged and evaluated.
Worked examples
Example 1: 5.0 kg on a flat floor
With g = 9.8 m/s² and no extra vertical force, N = mg = (5.0)(9.8) = 49 N upward. The floor pushes up with 49 N; the block pushes down on the floor with 49 N.
Example 2: same mass on a 30° ramp
N = mg cosθ = (5.0)(9.8) cos(30°) = 49 × 0.866 ≈ 42.4 N. Check: at 0° this would be 49 N; at 60° it would be 24.5 N.
Example 3: 20 N downward push on a floor
A 2.0 kg box sits on a table while you push down with 20 N. N = mg + 20 = 19.6 + 20 = 39.6 N. A 20 N upward lift would give N = 19.6 − 20, which is not possible while contact remains — the box would leave the table.
Frequently asked questions
What is the formula for normal force?
The default school cases are N = mg on a horizontal surface and N = mg cosθ on an incline, with θ measured from the horizontal. Extra perpendicular forces add or subtract from that support.
Is normal force always equal to weight?
No. N equals weight only on a flat surface with no other vertical forces. On a ramp, in an elevator, or when you push down on a box, N is different from mg.
Why is it mg cosθ on an incline?
Weight still points straight down. The surface can only push perpendicular to itself, so the component of mg into the ramp is mg cosθ. The remaining mg sinθ is parallel to the ramp.
How does normal force relate to friction?
Kinetic or maximum static friction is Ff = μN. If you use mg instead of mg cosθ on a ramp, both N and friction will be wrong.
Can normal force be zero?
Yes, at the instant contact is lost — a jump off the floor, or an upward force larger than weight. While the object stays in contact, N ≥ 0.