Does iPhone battery life last longer using Wi-Fi vs Cellular Network?
The Wi-Fi antenna in your phone has a typical range of few meters. It finds a Wi-Fi router within that range. So the power of the signal should be enough that it would be able to survive for few meters.

On the other hand, for 3G data transfer, you need to send the signals to the receiving antenna which could be a up to a few kilometers from where you are. So the signal should be strong enough to survive a few kilometers.

To give an idea, let's assume:


Your Wi-Fi router is at a distance of 5 meters.
The 3G receiver antenna of service provider is at a distance of 2 kilometers (2000 meters).
We know that the signal strength is inversely proportionate to the square of distance.


So, in order that we have the same signal strength at the receivers antenna of wifi and 3G; the transmitted signal should be of ratio:

(2000/5)^2 = 160000


So the 3G signal should be 160,000 times stronger than Wi-Fi signal. Hence 3G data transfer consumes more power.

Note: We have not considered packet loss when sending data over longer distances, which, although less significant, contributes to a greater power requirement of 3G transmission.

Source: Kingsley, K. (2013, December 12). What consumes less battery on a smartphone - WiFi or 3G? Why?