The latest versions of TLS hardly impact web application performance at all.
Because of the complex process of setting up a TLS connection, a web server must use some load time and computational power. The client and server must communicate back and forth several times before any data is transmitted. That eats up precious milliseconds of load times for web applications and some memory for both the client and the server.
However, there are technologies in place that help to mitigate potential latency created by the TLS handshake. TLS False Start lets the server and client start transmitting data before the TLS handshake is complete. Another technology to speed up TLS is TLS Session Resumption, which allows clients and servers previously communicated to use an abbreviated handshake.
These improvements have helped to make TLS a high-speed protocol that should not noticeably affect load times. As for the computational costs associated with TLS, they are mostly negligible by today’s standards.
TLS 1.3, released in 2018, has made TLS even faster. TLS handshakes in TLS 1.3 only require one round trip (or back-and-forth communication) instead of two, shortening the process by a few milliseconds. When the user has connected to a website before, the TLS handshake has zero round trips, speeding it up further.