# How can I roughly measure a fraction of a gram?

My son got a crystal making kit (from a relative) and it lists seed crystal weights of 0.5g for a small crystal solution and 0.75 g for a large crystal solution. The trouble is I (his father) don't have a scale that can measure a fraction of gram, so I guessed how much.

Can I roughly get the weight that a fraction of a gram without buying a scale just for this crystal making kit?

• I notice that you are in Japan, so it may help to know that the mass of a 1 yen coin is 1 gram. As already suggested, you can make an equal-arm pan balance. For small mass measurements it is important to keep the balance mass small. Use a 20 cm long balsa stick for the beam and sheet balsa squares for the pans. Hang everything with fine silk sewing thread. For small weights, buy a box of tiny washers (M2 or similar) and count the number needed to balance the coin. For even smaller increments, use lengths of fine copper wire. Jan 4 at 14:25
• I might be mistaken, but isn't a 0.5 g seed crystal rather large? Do you have such big crystals already? Or do you add many small crystals that accumulate to 0.5 g? And do you have a scale with an accuracy of, let's say, 1 g? Jan 4 at 17:05
• What is the material to crystallize? Is it copper sulfate, or alum? Jan 4 at 18:06
• The seeds are various minerals and the core solution is Alum I think. Jan 4 at 23:15
• While there are some great and creative answers here, reasonable mg scales are really cheap these days. I can see $35 being a big expense for some just the same, but if it's not then it's actually a really handy thing to have around. You might find you end up using it more than you expected once you have one. – J... Jan 5 at 19:24 ## 5 Answers You ask: Can I roughly get the weight that a fraction of a gram without buying a scale just for this crystal making kit? Absolutely. You're in Japan. You have access to Japanese coins which conveniently are just what you need for this project. Because they are currency, you can also be assured that they weigh exactly as advertised. • You need one each of 5-yen, 10-yen, and 50-yen coins • For the scale, make something like this balance, and note that you might want to scale it down given the small amounts you're working with • To get 0.5 g, add enough crystal to the cup with a 50-yen coin in it such that it's balanced with the one with a 10-yen coin in it • To get 0.75 g, add enough crystal to the cup with a 5-yen coin in it such that it's balanced with the one with a 10-yen coin in it I suggest you tape the coins to the weighing cups so you don't have to get the powder all over them. You might tape the coins on the underside of the cups and be sure to use a similar size section of tape so the weight of it is more or less equal. • Our 3 lightest coins (1, 2, 5 Czech crowns) have$\pu{3.6 \pm 0.15 g}$,$\ce{3.7 \pm 0.15 g}$,$\pu{4.8 \pm 0.15 g}$. I guess coin mass differences may have generally rather high relative SD. Jan 4 at 14:35 • Repeated measurements will take care of minimizing the sum total SD of weights. The Japanese Mint doesn't indicate differences, so I'm assuming they are minimal. Jan 4 at 14:42 • Hm, scientists usually consider data with explicit uncertainty or tolerance as more reliable. Jan 5 at 7:08 • Given the project in question, "rough" estimate asked for by the OP, and my general lack of knowledge of coinage and minting processes in Japan and other countries, I'm willing to let this one slide ;) Jan 5 at 14:08 • A scaled-down version of that balance could be made from Lego, mainly Technic, and fishing line. Lego tolerances are impressively tight (though some bricks have changed mould over the years - use the same age bricks) so zeroing the empty scale may not even be needed. Cross-axle parts can be used to provide a continuously-variable adjustment if necessary. Jan 5 at 14:18 I think the mass of the seed is not critical. But you can create your own scale - or even better, involve the son in its creation. You can create a 2-shoulder scale, with 2 stuff holders hanging at equal distances from the central holding. Or, you can create a 1-shoulder scale, with the stuff holder hanging on some elastic string or wire. For a scale weight for the former, or as the calibration of the latter, you can use the fact the typical water drop has volume $$\pu{0.03 mL}$$, i.e. $$\pu{30 mg}$$. You can check the actual value by counting drops filling a known small volume. You can find a web tips or precedures to make homemade scales like in this Kid science article. • Complementary: a grain of barley$\approx \pu{65 mg}$, grain of wheat$\approx \pu{50 mg}\$ (Wikipedia). At least, the grain is «the only unit that is equal throughout the troy, avoirdupois, and apothecaries' systems of mass.» (same source). Though greater in mass (which may be compensated by the lengths of the arms of a balance), the mass of coins in your pocket are a standardized alternative, too. Jan 4 at 13:43

If you know the density of the crystal (usually a salt), you can estimate the mass of a crystal based on its volume, i.e. by measuring the lengths of its sides.

For example, table salt (sodium chloride) has a density of $$\rho=2.16\ \mathrm{g\ cm^{-3}}$$.
Thus a cube of $$10\ \mathrm{mm}\times10\ \mathrm{mm}\times10\ \mathrm{mm}$$ has a mass of about $$2.2\ \mathrm g$$.
And a cube of $$5\ \mathrm{mm}\times5\ \mathrm{mm}\times5\ \mathrm{mm}$$ has a mass of about $$0.3\ \mathrm g$$.

The precision of this estimate should be enough to select a suitable seed crystal.

• The main problem with this solution is its a powder (beside knowing the substance) so it will trap a lot of air and I need to make a press to make it work. Jan 6 at 11:03

Very roughly, you could take a hint from the old British Imperial measurements. The smallest unit of weight is the grain, which before standardisation was the weight of a single grain of wheat, which was then standardized as something which translates roughly to 64mg. (Although with plant breeding since then, I would not be surprised if modern wheat grains are much heavier! )

I suspect rice grains are lighter than wheat grains.

You could weigh some grains of a raw cereal (or peppercorns, mustard seeds ...) against a coin of known weight, count them, and divide, to get a somewhat more accurate idea of the weight of each.

Use a balance with uneven arms like in a factor of 1:10. Test it with known weights to see if the factor is correct or recalculate to the exact factor and use it to measure with the lowest weight on the longest arm.