Calculating Transformer Voltage Ratio: Correct Formula U2/U1 vs U1/U2 Debate Clarified

Hello. I have a question about transformer ratio calculation. The definitions that can be found on the Internet show that the transformer voltage ratio is calculated from the formula n = U2 / U1, i.e. the secondary side voltage divided by the primary side voltage. On the other hand, in the textbook for electrical engineering and in some sources on the Internet, there is a completely opposite formula, i.e. n = U1 / U2. My question is: what is the correct formula to calculate the voltage ratio of a transformer? I know this is a question from the absolute basics of electrical engineering, but I would like to know why some sources say yes and others quite the opposite, and of course learn the correct formula.

Actually, the definition is the ratio of the input parameter to the output parameter.

I understand that the formula n = U1 / U2 is correct, i.e. the ratio of the primary side voltage to the secondary side voltage. Can someone explain this discrepancy in the definitions given in the manual and on the Internet?

If you read it, you would find it. It is also mentioned whether the transformer lowers or increases the voltage, or what you will find more often - the ratio is the ratio of the upper voltage to the lower voltage - it is different here. Not only is the transformer fun, but not all parameters are in the same proportion, but must be in the opposite way.

I know that it matters whether the transformer increases or decreases the voltage, but I am wondering about the contradiction in definitions. Let us assume that we have a step-up transformer with rated parameters U1 = 127V and U2 = 220V. According to the definition in the manual, the ratio will be n = 0.58, while according to the definition of the high-to-low voltage ratio, it will be n = 1.73, so which value is correct?

Assuming that the definition of the high to low voltage ratio is correct, we will always obtain a ratio of n = 1.73 for both the step-up transformer, i.e. U1 = 127V and U2 = 220V, and the step-down transformer U1 = 220V and U2 = 127V.
Assuming that the definition of the ratio of the primary to the secondary side (or vice versa) is correct, for a step-up transformer U1 = 127V and U2 = 220V, we will get a ratio of n = 0.58, and for a step-down transformer U1 = 220V and U2 = 127V, we will obtain a ratio of n = 1.73 .
From my point of view, these definitions are mutually exclusive, but please correct me if I am wrong.

Transformer gear n it is the ratio of the upper voltage Ug to the lower voltage measured Ud on the transformer terminals in idle state. The gear ratio is always greater than (or at least equal to) one. That's how the standards put it.
The higher voltage winding is called the upper winding, the quantities relating to this winding are called upper and denoted by the index g.
The winding of the lower voltage is called the lower winding, the quantities relating to this winding are called the lower and denoted by the index d.

Regardless of these terms, the terms referring to the primary (supply) and secondary (receiving) side are used. The quantities referring to the primary (supplied) side are marked with the index 1, the secondary side with the index 2.
Depending on whether the primary side voltage U1 is higher or lower by the secondary side voltage U2, the transformer is called a step-up or a step-up voltage.
The ratio can be determined by the ratio U1 / U2 or U2 / U1 depending on what kind of transformer we are dealing with.

Thanks for the clarification. The lack of mention of the type of transformer (step-up or step-up) in the definition of the gear was misleading me. Subject to be closed.