Normal Force Calculator

The normal force is the contact force a surface exerts on an object, always directed perpendicular (normal) to the surface. The word normal here means perpendicular in the geometric sense, not normal in the ordinary sense. The normal force arises as a reaction to the force pressing the object into the surface, per Newton's third law: if you press a table with your hand, the table pushes your hand back with an equal and opposite force — that is the normal force.

On a flat plane with no other vertical forces, the formula is N = m × g. Example: a 10 kg mass on a flat floor with g = 9.80665 m/s² gives N = 10 × 9.80665 = 98.07 N. In this case the normal force exactly equals the object's weight. If there are additional forces (e.g. you press the object downward), add them to the computation — use the Applied Force mode on the calculator above.

On an inclined plane at angle θ, the formula is N = m × g × cos θ. Example: a 10 kg mass on a 30° incline gives N = 10 × 9.80665 × cos 30° = 84.93 N. The steeper the plane, the smaller the normal force; at θ = 90° (vertical wall) the normal force becomes zero. The weight component parallel to the plane — which makes the object slide — is m × g × sin θ = 49.03 N for this example, and is shown in the Inclined Plane mode.

This is a very common mistake. The weight component parallel to the inclined plane (what makes the object slide) indeed uses sin θ, but the normal force points perpendicular to the plane so it uses cos θ. Quick check: at θ = 0° (flat plane), cos 0° = 1 so N = m × g — correct. If you used sin, θ = 0° would give N = 0 — clearly wrong since an object on a flat floor still presses on the floor.

The two compute different things. This calculator computes one specific force: the contact force perpendicular to the surface. The net force calculator sums all forces acting on the object as vectors to get the resultant (F_net = ΣF), complete with direction. Use the normal force calculator to find N, then use the net force calculator if you want to combine N with other forces like friction, rope tension, or push forces.

If a force F acts at angle φ to the horizontal on an incline of angle θ, the formula becomes N = m × g × cos θ − F × sin(φ − θ). Pulling upward away from the surface (φ greater than θ) reduces the normal force, while pushing toward the surface increases it. If the computed N is negative, the lifting force already exceeds the pressure on the surface — the object lifts off and loses contact. The calculator shows a special warning for this condition.

Inside a vertically accelerating elevator, the normal force on the elevator floor is N = m × (g + a), with a positive for upward acceleration. Example: a 70 kg person in an elevator accelerating upward at 2 m/s² feels N = 70 × 11.80665 = 826.47 N — feeling heavier than usual. Conversely when the elevator accelerates downward, N shrinks; at a = −g (free fall) N = 0 and you experience weightlessness.

No. The normal force only equals weight on a flat plane with no other vertical forces. On an inclined plane, N = m × g × cos θ so it is always smaller than weight. Pushing the object downward makes N larger than weight, pulling it upward makes N smaller. In an accelerating elevator, N can be larger or smaller than weight depending on the acceleration direction.

This calculator supports mass units kg, g, and lb, and force units N, kN, and lbf. Conversions used: 1 lbf = 4.44822 N; 1 lb (mass) = 0.45359237 kg; 1 kN = 1000 N. The default gravity g is 9.80665 m/s² and can be changed — e.g. enter 1.62 to compute normal force on the Moon or 24.79 for Jupiter.

This calculator assumes a rigid surface that does not bend under load, the object as a rigid block, and normal force always N ≥ 0 — normal force cannot pull the object (pulling toward the surface is adhesion or rope tension, not normal force). Friction is not computed here; only the force components shown on the diagram. For a complete motion analysis involving friction, combine the N result from this calculator with the net force calculator.