how to calculate distance while walking in android?

There are different ways to do this:

1. GPS: Keep adding GPS distance between 2 points every X seconds (say 10 sec). Check Android Location.distanceTo or distanceBetween. Check My Tracks app, it is open source. GPS is not available indoors and would have error if user is changing direction very frequently (read every 1-2 second)
2. Accelerometer: Look for code/library for step detection using accelerometer. Distance comes from double integration of acceleration, errors can add up very quickly here.
3. Step detector: Built-in in Nexus 5. Google must have taken care of accelerometer errors to extent possible. This is hardware-based computation, consumes less battery but not available in most of handsets as of date.

You can also check Pedestrian dead reckoning

One way to go about it is using the accelerometer data. Your app should continuously record the accelerometer data after the user presses the Start button. You will observe a peak in your data whenever the user takes a step. Apply a filter on this data, and you shall be able to detect the number of steps taken with reasonable accuracy. Multiply it by the step length and you should get an approximation of the distance travelled. Take height of the user as an input argument. Step length is around 0.45*Height of a person. Since this approach is independent of GPS, It will also work indoors. EDIT: You'll need to use the accelerometer values for all three axes to make it fairly independent of the device orientation.You can go with x^2 + y^2 + z^2