Why is this mass equation giving me mass = weight when clearly it isn't?

Convert the weight measured in pounds to the equivalent in Newtons. In the formula for determining mass based on weight, mass is measured in Newtons. Weight is measured in Kilograms, and the acceleration of gravity on Earth is measured as 9.8 meters per second squared. These are metric system unit measurements. To find the equivalent in U.S. units, you perform conversions. One pound is equal to 4.44822162 Newtons. Therefore, to convert pounds to Newtons, multiply the weight in pounds by 4.44822162. For example, to convert 150 lbs to Newtons, calculate as follows: 150 x 4.44822162 = 667 Newtons.

Divide the weight in Newtons by the acceleration of gravity to determine the mass of an object measured in Kilograms. On Earth, gravity accelerates at 9.8 miles per second squared (9.8 m/s2). For example, to determine the mass of an object weighing 667 Newtons, calculate as follows: 667 Newtons / 9.8 m/s2 = 68 kilograms.

Convert the mass measured in kilograms to the mass in pounds. One kilogram is equal to 2.20462262 pounds. Therefore, to convert kilograms to pounds, multiply the kilogram value by 2.20462262. For example: 68 kilograms x 2.20462262 = 150 pounds.

This obviously is not right because 2 things that weigh the same can have a different mass. What is wrong with this conversion?

• 'mass is measured in Newton. Weight is measured in Kilograms' - no, it's the other way around, mass is in kg, weight is in Newton. Your weight changes when you go to the moon (smaller g), your mass doesn't – Michiel Mar 5 '14 at 17:41
• Are you sure you don't start with mass in kg and weight in N, instead of the other way around? – The Photon Mar 5 '14 at 17:42
• It is weight in pounds converted to newtons, divided by the force of gravity to get kilograms, and then kilograms to pounds and it starts with 150 and ends with 150 – Caters Mar 5 '14 at 17:55
• ^That makes no sense at all. @caters, you're getting weight, mass, density and volume confused. Weight is the force gravity exerts on mass. For a given object, its mass is constant. The weight changes depending on the acceleration due to gravity. – tangrs Mar 6 '14 at 2:00
• A pound of butter and a pint of water have the same mass if you've measured their weight at the same point on the surface of the earth. They do have different densities, and therefore will occupy different volumes, but their mass is the same. – d_b May 6 '14 at 14:56

There's a thing called a "slug". " It is a mass that accelerates by 1 ft/s2 when a force of one pound-force (lbF) is exerted on it." (wikipedia).

Sometimes you'll see reference to a "pound-mass" to indicate a mass which weighs one pound at sea level (on Earth, thank you! :-) ).

The problem is that pounds and kilograms have been used colloquially since forever to describe the weight of objects. Scientific usage differs from informal usage such as "shipping weight".

• Don't forget poundals ... – DJohnM Mar 5 '14 at 19:40
• There is also a dyne. – LDC3 Apr 5 '14 at 4:56

Your error is that one pound-force is not a pound. A pound-force is a force while a pound is a mass.

A pound-force has Imperial units of $$1\,{\rm lbf}=1\,{\rm slug\cdot\,\frac{ft}{s^2}}$$ where slug is the Imperial unit of mass.

One pound is equal to 0.45359237 kilograms, thus 150 lbs = 68 kg as you expect when doing the conversions.

• we use pounds, tons, ounces all the time when we talk about weight and we are referring to actual weight and not mass. – Caters Mar 5 '14 at 18:56
• @caters: Not really – Kyle Kanos Mar 5 '14 at 18:59
• when we weigh a truck with its load to know if it is oversized load, we don't factor out the gravity, we just look at what the scale says and the scale doesn't factor out gravity either. – Caters Mar 5 '14 at 19:28
• The distinction between pounds-force and pounds-mass has no basis in deep history and had to be applied as physics developed and it's usage has not been consistent. In particular the idea that mass is the default and force has to be specified is not fully uniform; there are those who do it the other way 'round. Safest to always say which one you mean. – dmckee --- ex-moderator kitten Mar 5 '14 at 20:26
• Kyle, what scales are sensitive to and what they are calibrated in are distinct ideas. Spring scales and strain-gauge transducers devices are sensitive to force. Balance style scales (two-pan and beam-types) are (assuming locally constant gravity, but independent of what that gravity is) sensitive to mass. Either type can be scaled in the other unit by assuming a gravity. – dmckee --- ex-moderator kitten Mar 5 '14 at 22:02