# How can potential energy be negative?

In my physics class I was told that potential energy can be negative because it relative, but i thought as long as something has room to fall it has a positive amount of potential energy. So how can potential energy be negative?

I like Serena
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In my physics class I was told that potential energy can be negative because it relative, but i thought as long as something has room to fall it has a positive amount of potential energy. So how can potential energy be negative?

Hi LoganNagol! Welcome to PF!

We are free to set a reference point.
Usually we set a reference point for potential energy at ground level.
Consequently, the potential energy is typically ##mgh##, where ##h## is the height above ground level.
This works just fine as long as we stay above ground level.
But of course we can get below ground level, giving us a negative potential energy.
This doesn't mean that the total energy is negative, since that is not possible.
It only means that the potential energy, as we defined it, becomes negative.

LoganNagol
sophiecentaur
Gold Member
In my physics class I was told that potential energy can be negative because it relative, but i thought as long as something has room to fall it has a positive amount of potential energy. So how can potential energy be negative?
Potential is always referred to some location.
Using the definition of Potential as the Work Done to take a unit mass from the reference point gives you a negative amount of work to do, bringing your mass in from a reference location at infinity but a positive value if your reference point is at the bottom of a hill.
The only location that is the same for everyone on Earth, The Solar System or the Galaxy is a location that's an infinite distance away. Taking that definition of Potential gives a conveniently consistant answer.
This is just one of the many occasions where you have to choose a sign at the beginning of your calculations and maintain consistency right up until the answer. IF you do that then the numbers take care of themselves and you get the right answer.

LoganNagol
Note that if we use Sophie's reference point of infinity as zero and note that gravity only attracts, then gravitational potential energy would always be negative. We are always in a gravitational hole. You always have to climb out to get to infinity. Maybe negative potential should surprise you less than positive!

I think the English word "potential" is what sets people's expectations. For positive potential it makes perfect sense. You have the "potential" to do some work with this energy. However it is kind of the wrong word when it is negative. Perhaps it should be called "relative configurational energy". Then the idea that it is relative to some reference configuration is explicit and there is no linguistic bias on the sign. It may take work to get to the reference configuration, or it may give work. On the other hand, what a horrible mouthful. You can't even pronounce it as an acronym.

Electron Spin and LoganNagol
sophiecentaur