Do different types of paper with the same weight necessarily have the same thickness? For example, does 300g card stock have the same thickness as 300g photo paper, or do papers vary in thickness according to their type?
Short answer: no
The two different types of paper with the same mass would only have the same thickness if they had the same density.
Photo paper would have a much higher density than card stock, so 300gsm photo paper is actually quite a bit thinner than 300gsm card stock.
300gsm card is actually quite thick:
Whereas 300gsm photo paper (shown here: 300gsm luster paper) is actually quite thin:
Do different types of paper with the same weight necessarily have the same thickness?
BUT papers with the same "gsm" 'weight' rating do all have the same area for a given weight.
While, on reflection, that's an almost trivial statement, it's also more useful and (a little) profound than may at first be obvious. Read on ...
In the following text the following common conventions are used.
"m^2" = "square metres" and
" ... /m^2 = "per square metre
gsm = grams pr square metre
g = grams.
so g/m^2 = gsm.
Affect of density on thickness:
As others have noted, for a given number of grams per square meter a material's density will be inversely proportional to its thickness. ie for a given area
Double the density and halve the thickness to get the same grams.
Or halve the density and double the thickness to get the same grams.
A fluid example:
Consider this non-paper example to remove irrelevant aspects from consideration.
If you have a 1 m^2 (=one square metre) "pan" (with walls taller than maximum fluid depth used. containing water 10mm deep (1/100th of a metre) then the water will have a "weight" of 10 kg per square metre - so there will be 10 kg of water in the 1 m^2 pan.
If you now remove the water and pour in petrol ("gas") you will need to pour in more petrol than water to get the same mass per m^2. Petrol has a density of ABOUT 0.75 compared to 1.000r for water so you will need 1/0.75 = 1.33 x as thick a layer of lower density petrol to achieve the same weight per m^2 as water.
So, if water gave us 10 kg per m^2 with a 10mm layer of water, we will need about a 13.3mm layer of the lighter petrol to also give 10 kg/m^2.
If we instead used Mercury with a density of ABOUT 13.5 times as high as water, to get a weight er area of 10 kg per m^2 we'd need a mercury layer of 10mm/13.5 = ABOUT 0.75 mm of mercury to get 10 kg/m^2.
****Paper - The Axx sheet size system - the magic factor**.**
If we stick to gram / square metre paper weights, and "metric" (A0 A1 A2 A3 ...) paper sizes we discover some simple but useful magic which many people are unaware of.
As is well enough known:
If we fold a Sheet of A0 in half it gives an A1 sheet size
If we fold a Sheet of A1 in half it gives an A2 sheet size
If we fold a Sheet of A2 in half it gives an A3 sheet size
If we fold a Sheet of A3 in half it gives an A4 sheet size
If we fold a Sheet of A4 in half it gives an A5 sheet size
If we fold a Sheet of A5 in half it gives an A6 sheet size
Nothing too magic so far.
Each size change the sheet size halves.
We can get 2 x A1 from a sheet of A0
We can get 4 x A2 from a sheet of A0
We can get 8 x A3 from a sheet of A0
We can get 16 x A4 from a sheet of A0
We can get 32 x A5 from a sheet of A0
Still no magic.
Some enlightened souls decided on the following system:
As above, a sheet of A0 has been defined to have an area, by definition, of exactly one square metre.
So a sheet of A1 = 1/2 m^2
So a sheet of A2 = 1/4 m^2
So a sheet of A3 = 1/8 m^2
So a sheet of A4 = 1/16 m^2
So a sheet of A5 = 1/32 m^2
If we have say 320 gsm paper = 320 grams per square metre = 320 gsm.
As a sheet of A0 IS 1 m^2 then a sheet of 320 gsm A0 weighs 320 grams. So
A sheet of 320 gsm A1 weighs 320/2 = 160 grams
A sheet of 320 gsm A2 weighs 320/4 = 80 grams
A sheet of 320 gsm A3 weighs 320/8 = 40 grams
A sheet of 320 gsm A4 weighs 320/16 = 20 grams
A sheet of 320 gsm A5 weighs 320/32 = 10 grams
relative to a sheet of A0
and relative to 1 m^2
is 2 raised to the power of the sheet size.
k = 2^ N for AN sheet size.
For a sheet of A4 the divisor = 1/ (2^4) = 1/(2 x 2 x 2 x 2) = 1/16.
So a sheet of A4 has an area if 1/16th of a m^2.
And a sheet of XXX gsm A4 weighs xxx/16 grams.
Or for 320 gsm paper = 320/16 = 20 grams as above.
For AN paper
Divisor = 2^N . Call this "k"
Area = 1/(2^N) m^2 = 1/k m^2
Mass = gsm / k
Sheet in a square meter = k
Weight of X sheets = gsm/k x X
gsm = weight x k
So for eg A3, 70 gsm paper
Divisor = 2^N = 2^3 = 8 = k
Area = 1/k = 1/8 = 18th m^2
Mass = gsm / k = 70/8 = 8.75 grams
Sheet in a square meter = k = 8
Weight of say 5 sheets = gsm/k x X = 70/8 x 5 = 43.75 grams
gsm = weight x k = (working backwards) 8.75 x 8 = 70 gsm
The best example that I have found so far is this:
Canon Photo Paper Pro Platinum: 300 g/m^2, thickness 0.30 mm.
Hahnemühle Fine Art Paper: 350 g/m^2, thickness 0.57 mm.
Even if we take into account the slight difference in the grammage, the latter paper is more than 60 % thicker.
(Caveat: There are many different ways to measure the thickness of a paper. The above examples are from the same web site, so there might be at least some reason to believe they are comparable.)
300 Grams paper means: An A0 sheet of paper (1 m2) weights 300 grams. So essentially the thickness is not mentioned in here.
I think that the thickness of different types of paper of the same weight (matte, glossy, etc) do vary a bit, due to chemical treatments of the paper and/or different production methods/materials, but not very much.