# How precise can current technologies measure the mass of an object?

Masses of various objects are listed on this wikipedia page: Orders of magnitude (mass). For example, mass of an HIV-1 virus is on the order of 1 femtogram.

• Are these data actually measured (which I really doubt), or calculated?

• What is the most precise measurement technique we have to measure the mass of an object?

• The most precise mass measurement are probably the latest electron mass measurement and then atomic mass measurements made in Penning traps. A virus is not a well defined and isolated object, it usually lives in an environment with air and water, i.e. one can't really assign a precise molecular mass to it (nor does it matter). – CuriousOne Apr 28 '16 at 5:16
• Do you really mean precise, or do you mean sensitive? When you are asking about the measurement of very tiny masses, it seems you are more interested in sensitivity than precision. Can you please clarify? – Floris Apr 28 '16 at 5:19
• @Floris I do mean precision as I do want to know the tiny mass of an object. A measurement apparatus can be extremely sensitive, but not precise. An example could be smoke detector. An ideal smoke is infinitely sensitive and even an infinitesimally small surge of smoke would trigger it, but it does not tell one how much smoke there is. So, yes, I think I'm more interested in precision rather than sensitivity. – user3336365 Apr 28 '16 at 5:24

The most precise measurement of the mass of an electron was reported by Sturm et al in Nature 506, 467–470 (27 February 2014), quoting a relative precision of $3\times 10^{-11}$, meaning they determined the mass to better than $3\times 10^{-41}~\rm{kg}$.

If that is not the best, at least it gives you an upper bound...

Note that if you could weigh such a small mass directly with scales on earth, the force would be equivalent to the gravitational pull of a mosquito (mass 2.5 mg) on a grain of sand (0.7 mg) at a distance of about 6 million kilometers - about 17 times the distance to the moon...

Astonishing.

Acknowledgement: CuriousOne's comment got me thinking about the measurement of the mass of the electron, and led me to the above analysis.

• I vote the mosquito-sandgrain-gigameter be adopted as a new standard unit of force. so we can just say the force is 0.6 Floris ;-) – RedGrittyBrick Apr 28 '16 at 9:51
• How can you measure a mass to a precision which is far greater than the precision achieved when comparing the mass of the international prototype kilogramme with the masses of the replica standard kilogrammes housed in various standards laboratories around the world? – Farcher Apr 28 '16 at 12:53
• @Farcher Well, you don't get a long lever and put a reference kg on one end and the thing you are trying to measure on the other. – Yakk Apr 28 '16 at 13:37
• @Yakk But if you know the mass of electon in $\text{kg}$s with a relative precision of $3 \times 10^{-11}$, then you know the mass of the international prototype in $m_\text{e}$s with a relative precision of $3 \times 10^{-11}$. How can you know that but apparently not the same for the replicas? – JiK Apr 28 '16 at 15:55
• @JiK easy: you don't measure relative to the kg. You make up some ad-hoc standard that you can precicely measure against. They you calculate a ratio. Then, people talk about it as kg, because while your paper talked about (say) the ratio between electron mass energy and the energy of a 1 gHz photon, or the Planck mass, or some other reference mass, people think about mass as kg. – Yakk Apr 28 '16 at 16:01

Many of them are calculated. All the ones that have $u$ or $Da$ as the unit are in atomic mass units, referenced above in the table. They just count up the atoms and add. For bacteria, yeast, and the like it will vary from one specimen to another. Not much precision is quoted and it is likely they use the volume (easy to measure with a photograph) and assume a density like water.