# Difference between revisions of "Mass units"

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I just wanted a reference for an accurate conversion - I could only find an approximation for the (crappy - not any exotic versions) of the lb ("pound")'s "mass" in kg. I also don't want to risk getting in that whole weight/mass thing. C'mon everyone knows what we mean. Alec (talk) 07:01, 10 March 2019 (UTC)

## SI Definition

Although it has a kilo-prefix the kilogram (Kg) is the SI Unit for mass. That is to say the gram is not the base unit, and the Kg simply [ilmath]1000[/ilmath] of them, the Kg is the base unit and the g is [ilmath]\frac{1}{1000}^\text{th} [/ilmath] of that (see SI prefixes also)

Currently it's defined by the weight of a "reference object" - that is some thing we[Note 1] made with careful choice of shape and materials which we simply call "1 kilogram" even if it changes (and it does) and irrespective of what the scale we "weigh" (cough) it on. However there are plans to define it by a number of atoms (cf: Avogadro's constant) and make a sphere with pretty close to that number I believe.

That's a whole topic of itself though.

### Historically

Historically the Kg was related to volume via "water"[Note 2] as exactly 1L of water (@ [ilmath]4^\circ\ [/ilmath]C - when water is its densest)

In turn the Litre is [ilmath]1000[/ilmath] cm3

A meter is of course [ilmath]1000[/ilmath] cm, so an m3 volume is [ilmath]100\times 100\times 100\eq 1,000,000[/ilmath] cm3

• Thus 1 cm3 = [ilmath]\frac{1}{1,000,000} [/ilmath] m3

So we see that 1L = 1000 cm3 = [ilmath]\frac{1}{1,000} [/ilmath] m3[Note 3]

So one way of defining the Kg is by having the meter defined, however I imagine getting reliably the same amount (volume) of water, accurately at a temperature is quite difficult. For example surface tension and what it forms on contact with the container's walls will be difficult. Hence the search for alternatives.

## Conversions to other units

Unit Multiplier
(to get Kgs)
Comment
Pound (lb) $4.535\ 923\ 7 \times 10^{-1}\ \left[\frac{\text{Kg} }{\text{lb} }\right]$
(or: [ilmath]0.453\ 592\ 37[/ilmath])
"Avoirdupois pound"[1] - not other forms (there are a lot of different pounds)

## Notes

1. Humans
2. Then water at a specific temperature, probably also had to be distilled I'd imagine as that'd cause changes too...
3. = [ilmath]1,000 \times \frac{1}{1,000,000} [/ilmath]

## References

1. https://www.nist.gov/pml/nist-guide-si-footnotes#f22 (as of 0653 (UK TIME) on the 10th of March 2019), from page https://www.nist.gov/pml/nist-guide-si-appendix-b9-factors-units-listed-kind-quantity-or-field-science. "avoirdupois pound"