Digikey has one of the best search tools of any electrical distributor and the mobile app is pretty useful too! Not only does their app have access to their search tools and catalog, it's also packed with a handful of useful calculators. Packed into this free app is a resistor color code calculator, pressure conversion, battery life calculator, ohms law calculator, LED series resistor, and conversion calculators. All of which don’t require internet access!
Electronics Engineer Toolkit
The Electronics Engineer Toolkit is a paid app that is packed with a ton of useful tools and is reviewed highly. This app is packed with a lot of tools such as an LED series resistor calculator, an ohms law calculator, a resistor color code calculator, SMD device codes, Cut off frequency calculator, op-amp example circuits, series/parallel resistor finder, linear regulator adj resistance calculator, an audio function generator and plenty more. At the price of $4.99, there is plenty of functionality in the app.
Wolfram Alpha is a “computational knowledge engine”, in other words, it's a pretty powerful calculator and knowledge engine. Queries such as "op amp" lead to op amp calculators and "Ohm's Law" leads to another calculator and related equations. In additional Wolfram Alpha can also do all sorts of conversions, plotting, calculus and other math. The list of what it can do is quite impressive. While the $2.99 app isn't needed, and can provide an easier way to use the tool. One thing to keep in mind is that all the calculations are done on Wolfram's servers, meaning a data connection is needed.
Ever want an app to do simple circuit analysis on your phone or tablet? With iCircuit you can. While it's not nearly as powerful as some of the desktop circuit analysis tools it can be a valuable tool for seeing how a circuit will function. The application features components such as current sources, voltage sources, switches, diodes, transistors, LEDs, motors and much more. At $9.99 this isn't a cheap app, but it certainly can be useful.
Tesla Bot is a really cool app that lets you detect magnetic fields with your phone. This app uses the compass in the device to determine the magnetic field strength.