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@HughB
It could be done. We would need to define a calculation based on steps for walking then maybe heart rate when moving faster than 5km/hr. 5k/hr is about the upper limit of most people's fast walk speed, anything faster is jogging. We would also need an app to store your weight and maybe height.
Note that fitbit would just say you burned so many calories per hour just sat still. Just breathing burns calories. I think about 1800 per day, depending on weight and heart rate.
As having heart rate on all the time uses a lot of battery the app would maybe have to be a widget that turned heart rate on when faster walking was detected.
A basic approximation could just use weight, elapsed time and steps. I suspect early fitbits did not do much more than that.