1/ The iodine method:
I found the answer on this video (from Cody's lab YouTube channel). Cody's show how to make activated carbon/charcoal and how to test its efficiency.
It's quite easy. The test below measures the absorption's efficiency of your charcoal filter (activated or not).
Quick facts:
- Cody use iodine but it seems to work with any dye (it works with methylene blue and even red Fanta.
- Non activated carbon (normal charcoal) does filter, but it's much less efficient.
- To check if the carbon is activated or not just put it in some water, activated carbon is bubbling.
Tuto:
- Take 1 gram of active charcoal (from your filter)
- Put it in a test tube
- Add 2ml hydrochloric acid (to make sure the charcoal is acidified, because otherwise, the alkaline ash in the charcoal will react with the iodine).
- warms it a little to help the reaction.
- Add 25ml of iodine (iodine with alcohol). Cody uses ≈ 4mg/ml.
- Wait 24h, then look at the color of your solution: the lighter the color the more effective is the charcoal (the lighter, the more it has absorbed iodine which is dark). You could compare it with some active carbon you bought, or normal charcoal

To measure more precisely the efficiency of your charcoal:
The titration method:
- Take 10ml of the solution you made above.
- Add some thiosulfate to it (drop after drop) until your solution becomes clear.
- Measure the quantity of thiosulfate that was needed.

See Cody's video for more details.
Someone in a comment says:
"When titrating iodine, it pays to use starch as an indicator. The change from dark blue to colorless makes the endpoint much clearer than the slow fading out of yellow you were dealing with. This would also be much clearer on camera."
2/ The Formaldehyde (or VOIC) method (requires a Formaldehyde Meter):
If you want to know if your activated carbon filter works, you can also test it using Thomas Talhelm method (he is the most famous air pollution DIY expert). But this technique requires a solution of formaldehyde, and a device to mesure the quantity of formaldehyde in the air.
- Buy a formaldehyde solution.
- warm it (e.g., using a rice cooker) in a closed room.
- measure the level of formaldehyde
- turn ON your activated carbon filters, and keep measuring.
If your filter is working you should see that:

With a fan only (red line), formaldehyde levels stayed high. But with
a carbon filter on the fan (blue line), formaldehyde levels went down.