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Mass and Weight: There's a Difference


Everyone is familiar with mass and weight, but the two are not the same, and they aren’t really directly related.

Starting with how each is defined, mass is an inherent or absolute property of physical matter, but weight is not. The mass will never change for a rock, for example, but it’s weight will depend on gravity, and is in fact a product of the mass times the acceleration of gravity:

The two are related by a factor of g, which means the two should never get confused.  In the metric system, g is approximately equal to 9.8 meters/sec/sec (or m/s2), which is a factor of about 10X.  The two should never really be confused !

Now, how about units.  In the metric system, mass is typically given in kilograms (kg) and the weight in Newtons (N).  One unit should never be used in place of the other where again it is possible to cause an error by a factor of 10.

In English units, weight is typically given in pounds (lbs) and the mass in slugs.  These are the units that scientists and engineers often use.  It is all based on the simple straight-forward formula W = mg.  So far, so good. Almost.

As it turned out, in human history, somebody didn't like the word “slugs” for the English unit of mass, and they resorted to calling it by another name such as “pounds-mass” (lbm).  Another English unit is “avoirdupois” and is about half-a-kilogram.  The gravitational constant in English units is about 32.2 ft/s2 which is another reason mass and weight should never get mixed up.  (It can introduce an error over 30X !).

Something that was seemingly so straight-forward, is now, perhaps not.   And it may all be due to an issue over what to call something.  The best advice is to always refer to the metric system.  This is where W = mg should always show consistent (Newtons for force, Kilograms for mass).   The direct parallel in English units is then pounds for force and slugs for mass.  In this way, the gravitational constant will always be a length per time-squared (the normal unit for acceleration).1, 2

But alas, it did not go this way, and for some reason during everyday usage you may come across such units as pounds-mass (lbm) or pounds-force (lbf) possibly mixed with kilograms or Newtons.  It is assumed that you know what all these units are, and that if you need to perform a calculation, you will convert everything to one system (metric or English).  But you better make certain you know the difference between lbf and lbm, and if your co-workers are using English or Metric, and know that “converting” mass to weight is not a direct unit conversion. Centimeters to inches is a direct unit conversion (involving length only) and so is liters to gallons (involving volume only).  But mass to weight is not a direct unit conversion.  The two are related by a formula (W = mg) where each is a different entity.

An example is pitching a baseball.  Whether you throw a baseball to homeplate at Wrigley Field or in a space station free of gravity, the baseball will pop the catcher’s mitt the same way.  It will impact the catcher’s mitt with the same force.  If the catcher were to miss catching the ball in the space station, it will most likely do substantial damage.  Now, in the space station, you simply hold the baseball in front of you and release it, and it will float.  Although throwing a baseball caused as hard an impact in the space station as it did on Earth, it will simply float if dropped on the space station (it has no weight).

The area of practice which most likely caused an issue over what to name units are shipping customs.

The area of practice which most likely caused an issue over what to name units are shipping customs.  Most everyone is involved in, or has experienced, shipping and transportation.  With the number of people, and types of people, involved in shipping it's no wonder we could not adhere to just one system of units.  Although scientists and engineers may strictly use ‘slugs’ for mass, the general layperson doesn’t always understand this.  And if the force unit of a Newton is named after a person, they don’t always understand this either.  Because of this, you will see shipping cartons marked in lbs (which is weight) and others marked in Kg (which is mass).  Pounds and kilograms are not the same type of unit, and weight scales only measure weight.  Therefore all shipping customs should be using weight units (pounds or Newtons).  To overcome this, some have resorted to a unit called a “kilogram-force” (kgf)  - but this introduces yet another unit to keep track of.  Ridiculous ?  Possibly.

What is the best advice to follow ?  Stay organized with your co-workers.  Hold meetings within your organization regarding this topic.  If there appears to be any confusion within the organization, call another meeting-to-order. It would be good to include principles, such as those outlined in this article, in employee training programs.  (It could make a better world).

Above is an aircraft placard displaying a correct usage of weight units.  

Something that was seemingly so straight-forward, is now, perhaps not...
The best advice is to always refer to the metric system



1.  The unit for acceleration, length per time-squared (m/s2  or  ft/s2), by itself does not carry physical meaning (i.e., What on earth is sec2 ?).  This is sometimes complained about, but the thing to remember is that units for acceleration are only a mathematical consequence (consequence of a formula).  Acceleration is the change of velocity, and velocity already has time in its denominator.  (Thus, sec2).  There exists other physical relationships in science with non-meaning units.


2.  The units for acceleration are normally length/time2 (m/s2  or  ft/s2) and are derived from the kinematics of Physics, considered the genuine origin of acceleration.  This is in contrast when attempting to use pounds-mass (lbm) and the units for acceleration of gravity become 32.2 lbm-ft/lbf-s2.  This is a man-made constructed unit, and is considered not to have a genuine origin


 3.  See also Mass is Not Measured But Calculated (8/15/23)