Is three hours long enough to transfer from Stansted to Heathrow?

Can I make this connection?

It is possible but extremely risky to rely on doing so.

Is three hours long enough to transfer from Stansted to Heathrow?

Ample, in most circumstances, if you mean pavement to pavement. The distance by road is only about 62 miles.

What you did not ask:

What is the minimum time difference between ETA at Stansted and ETD of a transatlantic fight out of Heathrow T2/T3 under normal conditions, that allows a reasonable contingency?

It is possible to clear Stansted in ½ hr – ¾ hr. Half an hour, 40 minutes max - as long as there's no industrial action going on per battybilly 14/9/11 and I recently collected my daughter there and even with checked luggage she was rapidly through from landing to meeting me in 40 minutes per taurean_traveller 4/3/13. However it seems more variable than at some larger airports. Nationality could be a factor (eg take longer for non-EU citizens), luggage will be and of course how busy the airport happens to be.

Assuming ¾ hr, the earliest available for ground transport from a 13:25 arrival would be 14:10. National Express has a departure (I chose for 1/12/16 – a weekday) at 14:15. Later in December activity in the airport on its own makes aiming for that coach very risky. And there is also significant chance of weather delays, not necessarily at Stansted but having a knock on effect when too little slack is built into the aircraft's schedule.

So the next coach departs 15:40:

2hr 15m is ample to clear Stansted in all but the most extreme conditions. It should take about 1hr 30m to T2/T3, with allowance of about 20 minutes more for the journey than a car might take. (But Expect your coach journey to Heathrow to take between 80-125 minutes.) Arrival at T2/T3 therefore around 17:10, which is no good for a 16:30 departure. Taking AA as an example, their minimum ticket counter check-in time at LHR for international flights is one hour and you would probably want to add at least 15 minutes to collect your bag and make your way to the check-in counter. Hence on the above basis the earliest flight out you should consider seriously is 18:25, for a total ETA>ETD of five hours.

However, by say taxi you could depart Stansted around 14:25 at the latest (if landing to schedule), arrive T2/T3 around 15:35 and so catch a flight out around 16:50, for a total ETA>ETD of 3hr 25m. This is consistent with BA's advice: We recommended that you allow at least: … 3.5 hours if you're connecting between London Stansted and London Heathrow.

At 3hr 25m the earliest outbound would be 16:50 – still after the flight time you mention, though only by 20 minutes. However departing Stansted at 14:25 allows an hour for clearing the airport, assuming an on time arrival. This is generous and could easily be 20 minutes less. As mentioned, it is possible to make such a connection but with no time at all to spare so unwise when what is at stake is missing a transatlantic flight and requiring quite an expensive taxi ride (if prebooked about £80) or, if to reduce somewhat the risk of delays due to traffic and assuming limited luggage, an even more expensive motorcycle ride (~£210 according to @David Marshall in a Comment).

The timing of your arrival relative to the coach schedule is about as bad as possible. So in general 5 hours is a sensible minimum interval between ETA and ETD without spending more than £50 over and above what is necessary (longer is to be preferred).

The time of day, day of the week, whether your bag is first or last off the conveyor and lots of other factors may also each make a difference of a few minutes.

So if 3hr 5m is possible (even 3 hrs) why 5 hrs a sensible minimum? Mainly because of gaps in the coach schedule of as much as 1hr 25m.

Not a doable itinerary I'm afraid. The direct bus departs Stansted at 13:40, arriving at Heathrow at 15:45. 45 minutes is unlikely to be enough to drop off baggage and get to the gate