Computational science is applied to systems in many different disciplines, from the natural sciences and the environmental sciences over cognitive science to social science and economics. Some sample applications are:

• Computational fluid dynamics is regularly used now in the aerospace and automobile industry. Aerodynamical properties of aircraft and cars can today be reliably predicted by computers. This saves tremendous amounts of experiments in expensive wind channels and allows to optimize them to a much farther degree.

• Computational mechanics and finite-element methods are used in mechanical engineering to model machines and tools and predict their behavior and performance. Some advanced machines require sophisticated computational control to function.

• Computational chemistry, molecular modeling and computational materials science can reliably predict the properties of chemical bonds and materials and improve commercial synthesis processes as well as help to find novel materials.

• Bioinformatics in pharmaceutical research, jump-started by the sequencing of the genome, marks the beginning of large-scale computer applications in biology. Even more recent is the field of computational systems biology that deals with modeling of the complete network of chemical and physical processes in living organisms.

• Computational finance has played an important role in the banking industry over the last decade, and many complex derivatives and transactions would be impossible without computational models. Computational economics is used to model economies on a national and international scale.

• Computer-based imaging in medical technology, such as ultrasound, x-ray and magnetic-resonance tomography, is impossible without the real-time solution of mathematical equations.

• Computational architecture and computational structural engineering help to design and verify buildings without the need to build expensive scale models.

• Weather forecasting, based on numerical models of the atmosphere developed over several decades, is one of the oldest and most advanced computational science applications. It finds an extension in computational environmental science and computational geophysics.

• Cryptography and compression algorithms are special examples of computational mathematics.

• Computational linguistics and cognitive science are example of non-numerical computational science