Normal Force Calculator

Calculate the normal force on a surface, including inclines and applied loads.

About Normal Force Calculator

The normal force is the surface’s reaction perpendicular to itself, so on a slope it is only the cosine component of the vertical load. That is why friction and traction both fall as a slope steepens. Normal force determines available friction, so a vehicle on a steep slope has less grip available exactly when it needs more.

Formula

Normal Force

N = (m g + applied load) cos θ

N: Force perpendicular to the surface
θ: Slope angle from horizontal

Worked example

With the default values below, Normal Force Calculator returns Normal Force of 553.103. Change any input above and every figure here is recalculated in your browser.

Inputs used

Massminimum 0 kg: 60 kg
Surface angle from horizontalaccepts 0–89 degrees: 20 degrees
Additional vertical loadminimum 0 N: 0 N
Gravitational accelerationminimum 0.01 m/s2: 9.81 m/s2

Results

Normal Force: 553.103 N
Weight: 588.600 N
Component Along the Slope: 201.313 N
Normal Force as Share of Weight: 93.97%
Pressure Over One Square Metre: 553.103 Pa

Step by step

1Values used
2Normal Force
3Normal Force= 553.103 N
4Weight= 588.600 N
5Component Along the Slope= 201.313 N
6Normal Force as Share of Weight= 93.97
7Pressure Over One Square Metre= 553.103 Pa

Assumptions and limits

The result is derived only from the 4 inputs listed above. Anything not among them is not part of the calculation.
In particular, this calculator does not take inflation, tax or compounding frequency into account.
Figures are rounded for display to 3 decimal places, so totals built from several rounded parts can differ slightly from the unrounded arithmetic.

How these calculators are built and tested is described on the Methodology page. If a figure looks wrong, please report it.

Frequently Asked Questions

How is Normal Force calculated?

N = (m g + applied load) cos θ The normal force is the surface’s reaction perpendicular to itself, so on a slope it is only the cosine component of the vertical load. That is why friction and traction both fall as a slope steepens.

Why does Normal Force matter?

Normal force determines available friction, so a vehicle on a steep slope has less grip available exactly when it needs more.

What values do I need to enter?

This calculator takes 4 inputs: Mass, Surface angle from horizontal, Additional vertical load, Gravitational acceleration. The pre-filled defaults are a realistic starting point — replace them with figures from your own environment for a result you can act on.