user78195: I have seen similar questions without a clear answer. So, how does Segregated Witness make transactions smaller? I understand it removes data from the transaction hash and solves malleability ... But it adds a field called "witness", so, how does this save space? 
Also (this is related and helps understand the question), how is block size calculated? Does it include the witness?

user575: SegWit doesn't save space, per se.
What it does do is:

From the perspective of a non-upgraded node, it makes transactions seem smaller. The witness part is not recognized or considered by pre-fork nodes, so more of them can fit in a block.
From the perspective of an upgraded node, the block size is calculated differently. Less weight is assigned to witness data than to non-witness data. So for the purpose of the calculation, a SegWit transaction is considered lighter than a non-SegWit transaction. So more of them are allowed per block - but the physical data size of the block increases as a result.

SegWit was to be introduced anyway because it solves malleability etc. But it also offered an opportunity to increase the block size limit (to allow more transactions) without requiring a hard fork, and this opportunity was seized, resulting in the feature described above.

78195: <p>I have seen similar questions without a clear answer. So, how does Segregated Witness make transactions smaller? I understand it removes data from the transaction hash and solves malleability ... But it adds a field called "witness", so, how does this save space? </p>

<p>Also (this is related and helps understand the question), how is block size <a href="https://bitinfocharts.com/comparison/bitcoin-size.html" rel="nofollow noreferrer">calculated</a>? Does it include the witness?</p>
 575: <p>SegWit doesn't save space, per se.</p>

<p>What it does do is:</p>

<ol>
<li><p>From the perspective of a non-upgraded node, it makes transactions <em>seem</em> smaller. The witness part is not recognized or considered by pre-fork nodes, so more of them can fit in a block.</p></li>
<li><p>From the perspective of an upgraded node, the block size is calculated differently. Less weight is assigned to witness data than to non-witness data. So for the purpose of the calculation, a SegWit transaction is considered lighter than a non-SegWit transaction. So more of them are allowed per block - but the physical data size of the block increases as a result.</p></li>
</ol>

<p>SegWit was to be introduced anyway because it solves malleability etc. But it also offered an opportunity to increase the block size limit (to allow more transactions) without requiring a hard fork, and this opportunity was seized, resulting in the feature described above.</p>
