# If you are on Earth, are your mass and weight the same?

I was wondering how mass and weight are different so I Googled it. I found that mass is constant no matter where you are because it is the amount of matter in an object and weight changes because it's the pull of gravity on an object.

This lead me to another question. If you are on Earth are your mass and weight the same?

• Depends where on Earth you're standing. If you happen to be standing in a location where the force of gravity is 1G then your mass and weight will be identical (ignoring centrifugal force). The gravity at the top of Mt. Everest is about 0.434% less than 1G. (I can't find an exact number, but the effect of centrifugal force at the Equator is about 1%.) – Hot Licks Jan 28 '15 at 1:57
• Possible duplicates: physics.stackexchange.com/q/43195/2451 , physics.stackexchange.com/q/147439/2451 and links therein. – Qmechanic Feb 23 '15 at 21:33

From a unit analysis point of view mass and weight are different kinds of things: mass is a quantity of material substance and weight is a force. Things of a different kind can never be the same.

That said, historically the distinction was not always recognized and traditional systems of weight-and-measure (including the original metric system, but not SI) use the same unit for both.

In those systems of measurement, there have the same numeric value on Earth by construction.

• Depends on where you are on the Earth. g changes with location, altitude, local masses, etc. Therefore a spring scale will give different values for the weight of a mass and a balance will not --> equivalence experiments. Launch locations for ICBMs that use inertial guidance (not GPS) required detailed local gravity maps. – C. Towne Springer Jan 27 '15 at 6:52
• @C.TowneSpringer Well, yes. But those traditional systems of units that lump mass and weight together don't acknowledge or account for that issue (which usually appear in the 3rd or 4th digit). – dmckee Jan 27 '15 at 14:42
• @dmckee, "Things of a different kind can never be the same", can you define different and same objectively, eg Spin (SAM) and Orbital Angular Momentum (OAM) are distinguishable yet both measured in angular momentum units afaik. – alancalvitti Jan 28 '15 at 1:11
• @alancalvitti They are both angular momentum. They have distinct sources but they are the same kind of thing. We know this because they obey the same rules for combining with one another and for interacting. As for an objective definition, I'd go with something like "quantities which can be combined in addition are the same", which is not rigorous but encapsulates one of the major rules of unit analysis. – dmckee Jan 28 '15 at 1:33
• @dmckee Re unit analysis, since distinct units can be multiplied, their logarithms can be added. Re "same rules"? "spin is an intrinsic property of a particle, unrelated to any sort of motion in space and fundamentally different from orbital angular momentum" > en.wikipedia.org/wiki/Angular_momentum. So even if OAM and SAM share the same units (multiple of hbar, with SAM limited to +/-hbar, while OAM can take unbounded integer multiples of hbar), they are differen types of motion. – alancalvitti Jan 29 '15 at 4:08

I believe weight is defined using the basic equation

$$F=ma$$

where $m$ is mass and $a$ is acceleration. When you weigh yourself on a scale, you aren't measuring mass but force. It's how hard is the earth pulling you towards it. This isn't the same thing as mass. A simple way to think about it, anytime you want to know your weight, you need two things: $m$ and $a$. You plug them into that equation above, and boom out pops the weight.

Newton's gravity and mass versus weight

Newtonian gravity is a model of gravity. It's usually this one where people first learn the difference between weight and mass. It's a good model because it describes many gravitational phenomena. But it isn't the best. Einstein's theory is better, but for many people that's too complicated and Newton's ideas are enough. Newton's gravity follows the equation

$$F_{g} = \frac{Gm_1 m_2}{r^2}$$ where $F_g$ represents the amount of force, $G$ is a constant, $m_1,m_2$ are masses, and $r$ is the distance between them.

Now let's suppose one of these masses is HUGE, like the earth. Let $m_1$ be this mass. Then for much smaller masses, it really won't make much difference how much they differ. So while a car and a coffee mug seem very different in terms of how much they weigh, they actually have the same acceleration because the earth is SOO much bigger than either of them.

For many simple physics examples, people treat $\frac{Gm_1}{r^2}$ as a constant called "little g", usually given a value around $g = 9.81$. People like this because it makes it easy to use the first equation. $g$ is just the acceleration $a$. This is a very crude model but yields surprisingly good results for doing experiments like dropping a ball from a roof top or stair way and seeing how hard and fast it hits the ground.

So if you find Newton's equation confusing, just use the following equation

$$F_g = mg$$

Gravity isn't a quantity. It's a thing

The phrase "your gravity" isn't the right way to speak about gravity. Gravity isn't a quantity or a measurement. It's a fundamental force in nature, a way particles, objects, etc interact with each other. You can quantify how strong the gravitational force is. But you don't say "how much gravity". It just isn't the way the word is used, at least in my experience.

• I meant to say weight just edited. – michaelpri Jan 27 '15 at 4:23

Your weight is the product of your mass and the acceleration. Hence, on earth your weight is:$$W=M*g$$

Hence, as weight and mass have different units, they cannot be "the same". In SI units, if your mass is in kg, then your weight is in Newtons (see the wiki page on Weight), the same units used for a force. As dmckee pointed out, in older systems the same units may be used for both mass and weight/force. For example, in the US a pound can be either a force of a mass.

There is a slight complication to your question. The earth's gravity varies from place to place. The difference is not enough that you'd notice, but you weigh more on the poles than on the equator (as the earth is a flattened sphere, the poles are closer to the centre of the earth). Mountains and other geological structures can also change the value of $g$. Measuring $g$ is one of the techniques used to find petroleum for instance.

Hence, while your mass is constant anywhere on earth (and space), your weight varies from place to place, even on the earth.

Actually when we measure our weight in a weighing machine, it is a big confusion that it is our mass or weight, because it measures in kg, which is unit of mass. But weighing machine measures our weight and its unit is in kgf (kilogram force) not kg, its a metric unit of weight, and as we know that N (Newton) is a SI unit of weight and 1Kgf = 9.807N

So as from Newton’s second law F= ma,

                      Weight  (W)= mg


if a body have a mass of 1kg and g=9.807 m/s^2
W= 1*9.807 kg-m/s^2 = 9.807 N

And as we know 9.807N= 1kgf,

Then weight of body of mass 1kg on earth,

                         W= 9.807N= 1kgf


So a weighing machine measure a weight in kgf (metric system). In metric system our weight is 1kgf and our mass is 1kg, so its reason why we become little bit confuse that on earth our weight and mass are same. But in actuality it is not...

As stated in the other answers (and your own question), mass and weight (downward force due to gravity) are two distinctly different units, but related via acceleration. So, in the presence of a gravity field such as we experience on the surface of the Earth, it can be convenient and more-or-less reliable to measure the weight of a thing to determine its mass. Since weight was the first (and to this day) easiest way to measure the mass of an object, a pound (mass) will exert a pound (force) at Earth standard gravity (approx 32ft/sec/sec or just under 10m/sec/sec). The units share the same name (pound), and values for weight and mass coincide at the Earth's surface, but only because of the origins of the units. In the metric system, units of mass (gram) and force (Newton) are clearly different. We only say that a thing weighs so many grams because it's convenient to measure the quantity of something by measuring its weight (downward force due to gravity). We could make scales which display weight in Newtons; it would be more formally correct to do so, but less meaningful for the usual purpose of a scale - to measure the quantity of something.