What is the normal force?

The normal force is the perpendicular support force a surface provides to prevent an object from passing through it. On a flat surface it equals the object's weight; on an incline it is the component of weight perpendicular to the surface.

Why does the formula use cosine?

Weight (mg) acts straight down. On an inclined surface at angle θ, the component perpendicular to the surface is mg·cos(θ). The parallel component mg·sin(θ) acts along the surface and causes sliding.

What happens at 0° and 90°?

At 0° (flat surface) cos(0°) = 1, so N = mg — the full weight. At 90° (vertical wall) cos(90°) = 0, so N = 0 — the surface provides no perpendicular support.

Does this account for external forces pushing the object into the surface?

No. This calculator assumes gravity is the only force. If an additional perpendicular force is applied, add it to mg·cos(θ) manually.

How do I use this to find friction force?

Multiply the calculated normal force by the coefficient of friction (μ): Friction = μ × N. Kinetic friction uses μk; static friction uses μs.

Normal Force Calculator

Enter an object's mass and the surface angle to instantly calculate the normal force using N = mg·cos(θ).

Inputs

Mass

Surface Incline Angle (degrees)

0° (flat) 45° 89° (vertical)

Using standard gravity g = 9.80665 m/s²

Incline Diagram

Results

Normal Force

—

Newtons (N)

Pounds-force

—

lbf

Weight (mg)

—

Parallel Force

—

N (mg·sin θ)

Angle Used

—

degrees

Formula Applied

N = m × g × cos(θ)

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Summary

The normal force is the perpendicular contact force a surface exerts on an object resting against it. On a flat surface the normal force equals the object's weight (mg), but on an inclined plane it is reduced by the cosine of the incline angle: N = mg·cos(θ). This calculator lets you input mass in kilograms, grams, or pounds and an angle from 0° to 89°, then instantly shows the normal force in Newtons and pounds-force.

How it works

Enter the object's mass and choose its unit (kg, g, or lb).
Set the surface incline angle in degrees (0° = flat, 89° = nearly vertical).
The calculator converts mass to kilograms and applies N = mg·cos(θ).
Results are shown in both Newtons (N) and pounds-force (lbf).
A visual diagram updates to reflect the chosen incline angle.

Use cases

Physics homework — quickly verify normal-force calculations on inclined planes.
Engineering checks — estimate contact forces on ramps, chutes, or slides.
Friction analysis — normal force is needed to compute friction (f = μN).
Weight distribution — understand how incline reduces perpendicular load.
Teaching aid — demonstrate how N drops to zero as the angle approaches 90°.
Sports science — assess ski-slope or cycling-ramp forces on equipment.

Frequently Asked Questions

Last updated: 2026-05-28 · Reviewed by Nham Vu