If I use regular gas on a car that requires premium gas do I save money?

Yes, I had this same question in the past and actually tested it on a vehicle.  The most careful test was conducted on Lexus GS300 in the spring of 2006.  I filled a near empty fuel tank with 1 gallon of gasoline and drove around in as much controlled manner as possible along a route twice, using different grade of fuel each time.
Results were that you do save fuel cost, MPG suffered a little, but not enough to offset fuel cost savings.  I ended up with roughly 5% lower MPG when fuel cost savings was 10%.  This was before youtube existed, but I taped it on my Hi8 camera, so if I ever figure out how to digitize it, I will post it on youtube one day.

Most modern engines have knocking protection feature, meaning if lower octane fuel is pumped into the engine, it'll reduce the compression as to prevent knocking.  Knocking is a premature combustion of air/fuel mixture in a cylinder of an engine.

Maybe.  Maybe not.  Most likely, though, the savings are negligible and the cost could be dramatic. 

Around here, premium is usually $.20 to $.30 more a gallon than regular unleaded.  Over a standard-ish 16 gallon tank, you will be saving under $5.  Say you fill up weekly, that is $20 a month.  I bet you spend more than that on some other non-necessity every month.  Starbucks?  Fuzzy socks?  Pay someone from Craigslist to demean you while you eat cheesecake in the nude?

The difference between regular and premium gas isn't always understood by the average consumer.  It isn't so much "better" in the sense that a 1080p TV is better than a 720p one.  Regular is perfectly fine in engines that call for it, but putting premium in a regular engine could actually degrade performance.  And, at the same time, using regular in place of premium in a car that requires premium, might be asking for similar problems. 

Octane ratings are enigmatic at best for most consumers.  It has nothing to do with the amount of potential energy in the fuel, but the compressibility of the fuel.  Performance cars have high compression engines.  Premium fuel can be compressed more before "spontaneous" ignition than regular.  If you run regular in a premium engine, you might experience a knock.  If you use premium in a lower compression car, you also might experience mistimed ignition, poor ignition, or run hot. 

Let's say you have a performance car that requires premium.  That car cost $60,000.  A new engine for that car might cost $12,000.  If you have that car for 10 years and fill up once a week, you are only saving $2,400 over the life of the car.  That is neglecting the possibility of poor efficiency because of your fuel choice, too.  That new engine, or even just the maintenance potentially required, will easily outweigh the savings.  And these are just the monetary costs, not the performance costs of having a car that ignites too soon. 

So, yes, you do save a couple bucks at the pump, but then you might lose more on your mechanic/parts store/lease violations/performance. 

It might be negligible, but $.30/gallon is a fair price for the insurance against the worst.
You save money for a while. But there is a reason why the manufacturer specifies premium gas. The Octane rating of a gas determines how it burns and premium gas burns better. The regular gas will cause "pinging" if it used under power. This pinging is pre-ignition, and can and will cause damage to the piston, as well as the rings. Over time it can burn a hole in the piston.

The key for drivers is to know whether premium gasoline is merely recommended or if it's required. In today's automobiles, advances in engine technology mean that even if the owner's manual recommends premium gasoline, the car will typically run on regular without issue and won't damage the engine in any other way. The car's performance might suffer only slightly: it might be a half-second slower from zero to 60 mph, for instance. But the average driver isn't likely to notice this drop-off.
No.  The car needs premium gasoline because the pistons are high compression and the engine timing is advanced.  A lower grade gasoline will lead to reduced power and worse gas mileage.  The couple cents you save per gallon at the pump will disappear with the reduction in gas mileage.

Personally, I find that you get the same mileage regardless of the quality of the gas. Yes you would be saving money. But some say that the premium fuel protects the engine. I would say that maintain your car by doing the services on time and perhaps the fuel wouldn't matter. Unless Ofcourse you're driving a high end super car. Perhaps then you would be so wealthy that the premium fuel cost wouldn't matter.

I bought a 370z recently and filled it with regular 87 fuel as everything I have read says unless you car requires premium fuel you are wasting money. Well you could definitely feel a difference in performance as I had just got the car I drove the hell out of it. The car does in fact require premium fuel, unlike other performance cars I have owned Nissan does not tell you on the fuel gauge you need premium. It's only indication is a little sticker on the fuel door, and probably the owners manual.

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