Weight on Other Planets, Explained

After reading this you will be able to convert your Earth mass into the weight you would feel on any body in the solar system, using nothing more than each body's surface gravity and a single multiplication.

What this tool does and one quick example

Your bathroom scale reads a force, not an amount of matter. That force is your weight: the gravitational pull of a planet on your body. The amount of matter in you is your mass, and it does not change when you travel. This tool takes your Earth mass (or your Earth weight) and reports the weight you would register standing on the Moon, on Mars, on Jupiter's cloud tops, and on other bodies, each of which pulls with its own strength.

Here is the hook. A person with a mass of 70 kg weighs about 686 N on Earth. Stand that same person on the Moon and the reading drops to about 114 N, roughly one sixth. Put them at Jupiter's visible surface and the reading climbs to about 1735 N, about 2.5 times their Earth weight. Same body, same 70 kg of matter, three very different scale readings.

When this calculation applies, and when it does not

The model works cleanly for standing on a solid surface where you are essentially at rest. It gives the static force a scale would read. It assumes you are at the body's nominal surface radius and that the body is a uniform sphere, so a single number called surface gravity describes the pull everywhere on the surface.

Several bodies stretch this idea. Jupiter, Saturn, Uranus and Neptune have no solid surface, so the "surface gravity" is quoted at the pressure level of the visible cloud tops. The Sun has surface gravity too, but you could never stand there. The number is still physically meaningful as the acceleration a test mass would feel at that radius.

The formula and why it is just multiplication

Weight is force, and Newton's second law says force equals mass times acceleration. For an object resting on a surface, the relevant acceleration is the body's surface gravity, written g. So weight is

Here W is weight in newtons (N), m is mass in kilograms (kg), and g is surface gravity in meters per second squared. On Earth g \approx 9.81 m/s², so a 70 kg mass weighs 70 \times 9.81 = 686.7 N.

Where does g itself come from? Newton's law of gravitation gives the pull between two masses. Set one mass to the planet's mass M and the other to a test mass m at the surface radius R, then divide out the test mass to get the acceleration:

In this expression G = 6.674 \times 10^{-11} N·m²/kg² is the gravitational constant, M is the body's mass in kilograms, and R is its radius in meters. The inverse square on R is why small dense bodies can pull surprisingly hard and large fluffy ones surprisingly weakly.

To compare your weight on two bodies you rarely need G at all. Since mass is constant, the ratio of your weights equals the ratio of the gravities:

A worked example with the demo data

Reading and interpreting the results

The output is a list of weights, and the useful signal is usually the ratio, not the absolute newton value. A ratio of 0.165 for the Moon means everything you lift feels one sixth as heavy, which is why the Apollo astronauts could hop in bulky suits. Mars at 0.378 is closer to a third, still a marked difference you would notice in every step.

Notice that gravity does not track size in a simple way. Uranus has a much larger radius than Earth but a surface gravity of only about 8.87 m/s², slightly less than Earth's, because its mass is spread through a large, low density volume. The g = G M / R^2 formula explains this: growing R in the denominator can offset a larger M in the numerator.

Common mistakes

The most frequent error is treating kilograms as a unit of weight. A kilogram is mass. When a scale reads "70 kg," it is really measuring your weight of about 686 N and dividing by Earth's g to display an implied mass. Take that same scale to the Moon and it would read about 11.6 kg, because it still divides by 9.81 internally, which is now wrong for the Moon.

A second mistake is using the wrong g for Earth. Values from 9.78 at the equator to 9.83 at the poles are all correct locally. This tool uses 9.81 m/s² as the standard. The spread is about 0.5 percent, small enough to ignore for a weight comparison but real.

A third pitfall is expecting the gas giant numbers to describe a walkable surface. There is no floor at Jupiter's cloud tops. The quoted 24.79 m/s² is the acceleration at that reference radius, useful for physics but not a place you could stand.

Related tools

The surface gravity used here comes straight from Newton's law of gravitation. To compute the force between any two masses at any separation, use the Newton's Law of Gravitation Calculator. If you want to know how fast you must move to orbit or escape a body rather than how heavy you feel on it, the Escape & Orbital Velocity Calculator uses the same M and R. For the distances between these bodies rather than their gravity, see the Astronomical Distance Converter. And if you plan to observe them through glass, the Telescope Calculator covers magnification and resolution.

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