Calculate gravitational weight force from mass and local gravitational acceleration (W = mg), with planet presets for Earth, Moon, Mars, and more.
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Science — Physics
Weight force is the gravitational force acting on a mass: W = mg. Unlike mass, weight changes with the local gravitational field. This calculator solves for weight force, mass, or gravitational acceleration and makes the planet-by-planet difference visible enough to separate the idea of weight from the idea of mass.
Newton's second law gives force as F = ma. When the acceleration is gravitational (g), the resulting force is weight: W = mg. Standard Earth gravity is defined as exactly 9.80665 m/s² by international convention. Local gravity varies by latitude and altitude — near the equator at sea level it is about 9.78 m/s², and near the poles it reaches 9.83 m/s².
A 70 kg person under standard Earth gravity weighs about 686 N because 70 × 9.80665 ≈ 686.47. On the Moon, using about 1.62 m/s², the same 70 kg mass weighs roughly 113 N. The mass does not change; only the gravitational acceleration changes.
That comparison is a useful check because it shows why bathroom-scale language can be misleading in physics. Everyday speech often treats mass and weight as interchangeable, but the equation shows clearly that weight is a force and therefore depends on location.
Gravitational acceleration varies dramatically across the solar system: Moon (1.62 m/s²), Mars (3.72 m/s²), Venus (8.87 m/s²), Jupiter (24.79 m/s²), and the Sun's surface (274 m/s²). The calculator includes presets for each, making it easy to compare how the same mass feels in different gravitational environments.
Frequently asked questions
A newton (N) is the SI unit of force. One kilogram-force (kgf) is the force exerted by one kilogram of mass under standard Earth gravity, equal to 9.80665 N. Everyday scales often read in kgf, which is why a 1 kg mass "weighs" 1 kg on a spring scale at Earth's surface.
Earth is slightly oblate (wider at the equator), so the equator is farther from Earth's centre. Gravitational force decreases with distance, and centrifugal acceleration from Earth's rotation also reduces effective gravity at the equator. The combined effect is about 0.5% difference in weight between poles and equator.
The safest manual check is to follow the same formula or rule one step at a time and compare that working with the calculator output. That catches sign errors, bracket mistakes, and input-order mixups without requiring any extra method beyond the underlying maths itself.
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