What is the real temperature to caramelize sugar?

a lot of recipes caramelize sugar in a simmering water.

Calling the solution "simmering water" isn't a good characterization. The boiling point of pure water is 100C. But the boiling point rises as the concentration of sugar in the solution increases. Once you're above 75% or so, the boiling point increases significantly. For 90% sugar (still 10% water remaining), it's up to around 120C.

As the water evaporates, the sugar concentration, the boiling point, and therefore the temperature all increase. When you reach 160C, there's probably less than 1% water and the decomposition of the sugar (carmelization) rate starts to increase significantly.

There are some charts/tables for different concentrations here, but they only goes up to 90%

Recipes that call for water to be added to the sugar for making a caramel do so to help all the sugar melt, by dissolving some or all of it in the water. This prevents premature crystallization of the sugar. When you keep heating the mixture, all the water will evaporate, at which point the temperature of the (now pure) molten sugar will rise above 100 °C and will go through its different cooking stages. The sugar will caramelize when it reaches a temperature of 160 °C.

While the other answers are right, it should be pointed out that caramelisation does not happen at 160°C - not only at that temperature, at least. Thermal decomposition happens as both a factor of temperature and time. In fact, it is possible for sugar to undergo thermal decomposition well under 160°C: Stella Parks over at Serious Eats does it at 150°C, and Harold McGee has done it at 125°C

Like Agos says, thermal decomposition definitely starts happening below 160°C

I spent a lot of time playing around trying to make Caramel a less dangerous process (ever try making 20lbs of caramel when you're doing it at 160°C? Good luck :D)

In 2017, I came up with an alternative caramel process that never goes above 125°C

It takes hours instead of minutes, but ... it's really easy to do, and doesn't require any thermometer.

https://fearthecowboy.medium.com/caramel-3-0-a-new-beginning-a9a132c87900

Dry carmelization is a colour thing. Melt all the sugar and watch for colour changes. Dry sugar can not and will not prematurely recrystallize as crystalization is a function of sugar coming out of solution in water. Melted sugar is not the same as sugar dissolved in water.

To start wet and keep heating is where crystallization can happen. Indeed you can cook till all moisture is gone at which point you have no more dissolved sugar but melting sugar at which time you can proceed to raise the temp till it colours.

You need to stir so vigorously with dry melted sugar that taking temp would be awkward and dangerous. Some make caramel wet and stop at a pre determined temperature to determine the finished firmness but this is not caramelization but the mallard reaction. Real caramelization of sugar happens 150 or higher.

Try cooking dry sugar (which will require vigorous stirring) till it colours like old copper. Off heat slowly whisk in heavy cream until it is good and fluid and then boil to your terminal temperature of say 118 for caramel for apple dipping and see the difference in flavour.

My point: many confuse the colouring of dairy products in a caramel with the caramelization of sugar which happens way up there in temperature.