By Zencalcy Editorial TeamLast reviewed About us
A scale measures the normal force it exerts, not gravity directly. When a lift accelerates upward the floor must push harder than the person's weight; when it accelerates downward it pushes less. This calculator solves N = m(g + a) with acceleration positive upward.
Find the scale reading when a lift accelerates up or down.
| Positive when speeding up upward; negative when speeding up downward. | |
N = m (g + a)
a is positive upward. A lift speeding up downward has negative a, so the scale reading falls. If a is more negative than −g the object loses contact and the reading is zero.
| Symbol | Meaning |
|---|---|
| N | Apparent weight (normal force), in newtons. |
| m | Mass, in kilograms. |
| g | Standard gravity, 9.80665 m/s². |
| a | Vertical acceleration, positive upward, in m/s². |
With a = +2 m/s² the scale reads 70 × (9.80665 + 2) = 826.5 N, about 1.20 times the person's normal weight. Accelerating down at 2 m/s² instead would give 546.5 N.
Continue with the Banked Turn Calculator, Centripetal Force Calculator, or the Coefficient of Restitution Calculator — or browse more dynamics tools and all physics calculators.
Starting upward means accelerating upward. The floor must supply both the force to support the person's weight and the extra force to accelerate them, so the normal force rises.
Results are computed from the standard equations of classical mechanics. Unit conversions use the SI definitions published by NIST. Air resistance is ignored unless the calculator names a drag model.
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Last reviewed: September 2026. See how we build and check every tool on the about page.
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Content updated: September 2026