# How many Newtons are in a kg exactly?

I understand that it is supposed to equal the gravity coefficient, which is defined as exactly 9.80665. But when i search google i saw one result saying 9.80665002864, and at first i thought it may have just been a precision error, but when i ran a google search for the number 9.80665002864 then i get plenty of results, all having to do with Newton conversion but none at all had anything to do with gravity. Is it just 9.80665 and all these websites made the same precision error? Or is a kg/newton not the same as exact gravity?

• Please share a reference for your "exact" value for a "gravity coefficient." I don't know what "exact gravity" means. Jul 8, 2017 at 1:31
• Newton is a unit of force, not mass, so the title is confusing. Moreover, the value of $g$, the gravitational acceleration near the surface of the Earth, is not uniform on the surface of the Earth. There are local variations due to height and geological features below the surface where $g$ is measured. Jul 8, 2017 at 1:31
• Welcome to Physics SE! Please do have a tour of this site. As it stands, your question is rather unclear, since newtons are a unit of force, and kgs are a unit of mass. Edit your post, and hopefully it will have better reception. Good luck, and hope you get what you're looking for! Jul 8, 2017 at 4:49

There are a couple of misunderstandings in your questions, but I think I can see what is ultimately being asked. If you don't mind, I need to tidy up your question just a bit:

How many Newtons are in a kilogram, exactly. I thought that it was 9.80665 by definition. However, I found numerous sources on the web that seem to give the exact same answer for g, the acceleration due to gravity. Most all of them seem to give 9.80665002864 meters/sec^2. What gives?

First off, the others posting answers to this question are ultimately correct - there really is no direct conversion between kilograms and Newtons. Kilograms is a unit of mass (how much matter is in an object) while Newtons is a measure of the force that the Earth's gravity exerts on the object. These two may seem like they are exactly the same thing, but they are just different enough to be completely different things.

Now, if we limit our question to "how many Newtons would a 1kg object weigh at the Earth's surface", then yes I suppose there is a conversion between the two, and yes that conversion is about 9.81 m/s^2.

Now, on to the part you asked about the number of decimal places, accuracy, and g being "defined" as 9.80665. The fact is that g has never had any defined value to speak of (unlike the speed of light, but that's another story). Most of the best measurements at the Earth's surface put the g number at about 9.81, but this may vary around a bit because the Earth isn't exactly a sphere, and so fourth.

All of these web pages that seem to be giving you the same value of 9.80665002864 must be getting their information from the same source. Besides, I'm not sure what leads anyone to think that g can be calculated to this many decimal places - moving around from continent to continent will result in different g values that differ by roughly 1%.

Hope this helps.

• For perspective on how unrealistically precise that number is, using Newton's law of Universal Gravitation, we can determine that a 1kg mass a full meter away from your test apparatus would be enough to substantially alter that last digit. The pull of gravitation of the building around you would certainly have a noticeable effect at that precision. Not only would it differ if you went to another continent, it'd differ if you went to another room (or even a different corner of the room!) Jul 9, 2017 at 18:46

g0 = 9.80665 m/s2 was the standard gravity value, adopted in 1901. It is the exact value by definition, it does not have more decimals. It is the theoretical value for g at sea level and 45° of latitude. Precision barometers used at sea were calibrated for this value of g. An elaborate correction formula could be applied for other latitudes and heights. g0 was also used in the definition of the kilogramforce, an obsolete unit of force.

Standart kilogram is a unit of mass, the Newton is a unit of force. Those are fundamentally different units as other people have noted. You can talk about a force acting on one kilogram $F=mg$ that will change depending on where you are.

However there's a non-SI unit of force called kilogram-force (kgf). It's defined as gravitational force acting on one kilogram in a standard gravity field i.e. $g=9.80665 m/s^2$. It may not be equal to the actual gravitational force acting on a kilogram in this specific place.

A Newton is a unit of force. A kilogram is a unit of mass. There is no conversion between these two units.

Regarding gravity, at the surface of the earth, there is a downward force of 9.81 Newtons (I deliberately reported only 3 significant digits) on a 1 kg mass. This means that the acceleration due to gravity is 9.81 N/kg, which, if you do proper dimensional analysis, is also 9.81 $m/s^2$.

As you continue learning physics, it is VITALLY important to learn what units are associated with each type of measurement, and it is VITALLY important to learn what dimensional consistency is. Physics is NOT math, and attempts to ignore units and just multiply a bunch of numbers together are guaranteed to lead to a LOT of confusion.

• The downward force (commonly called "weight") varies sufficiently with location on Earth that three significant figures are too many... Jul 8, 2017 at 1:39
• Yes, Floris ... I'm aware of that. Jul 8, 2017 at 3:52