It is the sort of question that comes up on road trips, in internet comment sections, and when talking to your friends: Is it more efficient to put the car in neutral (or push in the clutch) and coast, or leave it in gear and let the engine slow the car down? Obviously, this situation only comes up when going downhill, or rolling up to a red light or stop sign with no traffic.
Of course, the answer is going to vary based on what car you are driving. Older fuel injected cars (more than 25 years or so) most likely don’t have the ability to shut down the injectors completely, and carburetted cars will always allow fuel into the motor based solely on engine vacuum, because that is how a carb works. Diesel-powered and hybrid cars will be different as well, based on how their computers are programed. But the general answer for modern EFI equipped gas engined cars is to just leave it in gear and take your foot off the gas.
It used to be one of the ten commandments of hypermiling your car (driving in an extreme manner to maximize fuel economy) that you should put the car in neutral, or even turn the engine off when coasting for any length of time. But the computers have now been programed to basically shut off all fuel to the motor, making that redundant. Another trick hypermilers used to use, that has also been integrated into modern engine management systems, is turning off the charging system completely when not needed or when maximum power is demanded by the accelerator and load..
Let’s assume you are cruising on a road with a long downhill section, steep enough that you don’t need to use the gas to maintain the speed limit. Get off the throttle completely and (if you have one) your instant MPG reading will likely go to 99.9 mpg, or whatever the maximum reading is. Shift into neutral (or hold in the clutch) instead and it will go way up, but never quite so high. There is a simple reason for this and Engineering Explained made a video explaining it all very well here.
At idle, in neutral or not, the engine computer gives the engine enough fuel to keep it running smoothly and turning all the accessories. The AC compressor, power steering pump, water pump, engine fan, and charging system all need a little horsepower to turn and do their jobs, and that requires fuel. Leave the car in gear and gravity pulls the car, making the wheels turn, and turning the engine; yes, even in an automatic. Because gravity and momentum turn the motor, the fuel injection system can shut down entirely and the accessories will still turn.
However, If you are in hilly country, and want to use momentum gained while coasting downhill to get up the next hill, neutral coasting is the way to go. If you leave the car in gear, the engine braking will slow you down a bit, limiting how much energy from gravity you can store up for getting up the next hill. Of course, in the end, even after miles of hills, the difference isn’t likely to be very noticeable, unless you are in a very heavy or un-aerodynamic vehicle, like a motorhome.