user37639: 
On a percentage basis compared to the current theoretical limit how many more transactions per second will be possible after SegWit?
Will the answer to number 1 scale linearly with block size increases in the future?

Please exclude the impact of lightning or thunder networks for the purposes of my question.

user23123: Best estimates on effective blocksize with SegWit are 1.6-2.0 MB.
Current transactions/second possible are around 3 tx/s. Given that the effective increase is 1.6 - 2.0x, the transactions/second are also the same multiple giving us somewhere around 5-6 tx/s.
The second question is harder to answer. There's a reason I wrote "effective blocksize" since segwit transaction sizes are different. However a straight blocksize increase on top of segwit indeed would be linear.

37639: <ol>
<li>On a percentage basis compared to the current theoretical limit how many more transactions per second will be possible after SegWit?</li>
<li>Will the answer to number 1 scale linearly with block size increases in the future?</li>
</ol>

<p>Please exclude the impact of lightning or thunder networks for the purposes of my question.</p>
 23123: <p><a href="https://bitcoincore.org/en/2016/01/26/segwit-benefits/">Best estimates</a> on effective blocksize with SegWit are 1.6-2.0 MB.</p>

<p>Current transactions/second possible are around 3 tx/s. Given that the effective increase is 1.6 - 2.0x, the transactions/second are also the same multiple giving us somewhere around 5-6 tx/s.</p>

<p>The second question is harder to answer. There's a reason I wrote "effective blocksize" since segwit transaction sizes are different. However a straight blocksize increase on top of segwit indeed would be linear.</p>
