I have noticed most of the books about stochastic calculus are targeted fo finance and derivatives. Are there any other areas outside finance where stochastic calculus is applicable?
Stochastic calculus is a huge area in physics, engineering, and pure math.
What is a really huge topic in research right now are SPDEs. Stochastic partial differential equations. Take your favorite PDE and add some noise to it. Now you have a SPDE. These equations have numerous mathematical challenges, such as issues of roughness and defining solutions, but also have great applications in fluid mechanics, thermodynamics, quantum dynamics, whatever PDE you're interested in!
Additionally, another thing that is only SDEs and stochastic calculus is Wright Fischer diffusion. There is an SDE that explains the distribution of alleles in a population. This is a connection to biology.
Really, anything with "noise" in it, might require some stochastic calculus!