In theory, it should make no difference**.
The difference between different fuel octanes is their resistance to pre-ignition. In short, a higher number means the engine can have compressive higher forces occurring, and the fuel will remain controllable (and not explode before you want it to).
A higher octane gas in an engine that doesn’t need it, shouldn’t change the fuel consumption.
**Only note is that lower grades typically have 10-15% ethanol, whereas the highest grade typically has 0%. Ethanol is less energy dense than gasoline, so mileage may increase with a higher octane **if** the car increases fuel usage to maintain the same power output.
In most cases, using a higher octane gasoline than your owner’s manual recommends offers absolutely no benefit whatsoever. It won’t make your car perform better, go faster, get better mileage, or run cleaner, and high performance vehicles that require high octane gas will tell you so.
Raising the octane rating (also known as the anti-knock index) doesn’t change the energy content of a gallon of gasoline. A higher octane rating indicates greater resistance to knock, the early combustion of the fuel-air mixture that causes cylinder pressure to spike. When higher-octane fuel is flowing through its injectors, the engine controller can take advantage of the elevated knock threshold and dial in more aggressive timing and higher boost pressures to improve performance.
It depends on whether or not your car was designed to use premium gas.
The modern North American market Fiat 500 (with the 1.4 MultiAir engine) is a good example of this. It is a relatively “normal” car, i.e. not a sports car – it’s just for getting around. But it *is* designed to use premium fuel – this lets it use a higher compression ratio to get more energy out of the same amount of gas. You can use regular gas, but the range of the car decreases. In order for it to run ok on regular gas, it has to significantly retard the ignition timing – this is not ideal for efficiency.
A different car (say, a Toyota Yaris with a 1.5 NZFE) would be designed with a lower compression ratio, to get the most out of regular gas. Since the compression ratio is fixed, it doesn’t get anything extra if you put premium gas into it.
It really depends on the vehicle. Most of the time no, in fact many cars get worse mileage with high octane fuel because it actually contains less energy.
High octane fuels can run higher compression ratios without enriching the air fuel ratios. This means there can be a window in some cars where you get better fuel economy but it is very narrow and you would have to adjust your driving to take advantage of a very small gain.
Additionally, most cars are tuned to the fuel they recommend so most cars do not have the technology to actually take advantage of this.
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