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In physics, weight means the force of gravity on an object (given by acceleration due to gravity times the mass of that object). In common usage, weight can be either the gravitational force or the mass of an object. In the metric system, mass and force are given in different units (kilograms and newtons), so there is no confusion between them. However, both mass and force in imperial units are measured in pounds.

Mage Hand, the cantrip, says it can carry up to 10 pounds. It doesn’t say if those are pounds of mass or pounds of force. I’m trying to find the force that Mage Hand is capable of exerting. Does Mage Hand use the ambiguous term “pounds” to mean pounds of force or pounds of mass?

Bardic Wizard
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    "I’m trying to find the force that Mage Hand is capable of exerting." To what end? That is, what game problem are you trying to solve that would require you to know this? – Kirt Jan 20 '22 at 19:55
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    @Kirt I have an ongoing project to try to model d&d magic with physics; I’m trying to find the energy mage hand can exert, which means I need to know force and distance. If this is pounds of force, I know both things. If this is pounds of mass, there is no acceleration given so I can’t calculate the force. I want to know how many assumptions I have to make. – Bardic Wizard Jan 20 '22 at 20:03
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    @BardicWizard Wow, good luck! I think you're going to struggle a bit with your project, when you get into wish, planar travel, gods, and such. Or maybe a bit before. – Jack Jan 20 '22 at 22:07
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    I don't think this is the right stack to help you model D&D magic with physics. This stack focuses on helping people enjoy playing the TTRPGs, and applying real-world physics is usually counter-productive to that. This sounds like an interesting project, but you might have to rely on your own judgement, or the sorts of sites that happily discuss things like "the peasant railgun." Questions like "how many BTUs does fireball create" are going to get a lot of resistance here. – Carl Kevinson Jan 21 '22 at 16:44
  • Maybe this would be better rephrased such that it's a homebrew/game-design question, as it looks like your trying to figure out "Does it matter which I pick?" – AncientSwordRage Jan 21 '22 at 18:21
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    I'm also wondering how Mage hand behaves in zero-G – AncientSwordRage Jan 21 '22 at 18:26
  • I suggest that you ask this at a forum. This is a brainstorming kind of question. – KorvinStarmast Jan 22 '22 at 02:52

5 Answers5

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This is not a distinction made by the game rules.

We must assume here that in some standard environment1, mage hand can lift with exactly the force required to lift a mass weighing 10 pounds in that environment; this is the most straightforward reading of the spell description.

Then, if we assume that the force output of mage hand is consistent, we would expect mage hand to be able to lift twice the mass in an environment with half the gravity, but again, there are no rules spelled out for this, so ask the DM.

And just so that this answer will appear in this search, I will leave you with the usual wisdom for inquiries of this type: D&D is not a physics simulator.

That said, if you want to put a number on the maximal force output of mage hand, and you assume that the gravitational acceleration of the usual environment (again, see footnote 1) is exactly that of planet Earth, then mage hand has a maximal force of around 44.5 \$\frac{kg\cdot m}{s^2}\$.

1 To use a weasel word here, the "usual" environment. The usual environment that most adventures are set in. The environment where you don't say "Hmmm, I feel heavier/lighter than usual today." The environment where you go to the market and see a 10 pound bag of flour being sold by an honest proprietor and when you pick it up, it feels exactly as heavy as you expect it to be. That one.

Thomas Markov
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The spell refers to units of mass.

Specifically:

The hand can’t... carry more than 10 pounds.

'Pounds' here is a noun - something that can be carried. A force cannot be carried. You can carry 10 pounds of metal, or ten pounds of flour. You cannot carry ten pounds of force.

The fact that Mage Hand is limited by mass rather than weight shows us that D&D is not a physics simulator. If, as per your comment, you were looking to model the physics of 5e, I would just assume that Mage Hand can carry approximately 44.5 N, which is the force that earth gravity exerts on a mass of 10 lbs.

Trish
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Lovell
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    approximately, and depending on this being British pounds. in contrast, 10 roman pounds (libra) are 3,289 kg and exert 32.26 N of force on sea level. 10 Nuremberg Pharmacy Pounds are 3.576 kg and exert 35.07 N – Trish Jan 20 '22 at 20:57
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    Pounds are both a unit of Mass and a unit of Force. As the text does not specify which version is being spoken of, we must use the common definition, which is a unit of Force. – ValhallaGH Jan 20 '22 at 22:11
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    I would have thought mass would be a far more common usage/definition than force. – BBeast Jan 20 '22 at 23:13
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    @ValhallaGH the most common definition is by far weight: the pound stems from the Latin word pondus, which means literally weight, mass. The roman libra pondo is the literal scale-weight. If you ask any engineer or physicist to define you a force, they tell it to you in Newtons or tell you specifically it is a force pounds (lbf) but never just pound. – Trish Jan 22 '22 at 02:09
  • @Trish Weight is a Force - a mass affected by an acceleration (gravity) - in physics discussions. Mass is the amount of matter (stuff) being talked about, but Weight is the force. As a trained engineer related to a physicist, we use Newtons because the world uses SI units; when we talk in freedom units, Pounds are a force - mass is the Slug. Weight and Mass are not interchangeable. – ValhallaGH Jan 22 '22 at 04:33
  • Mol is amount. Mass is amount times density. Force is mass times acceleration. Weight is the force under an acceleration of 9.806 m/s². Happy now? There are no units of freedom, only degrees of freedom defining how a body can move. The pound-inch-system is Imperial. Some of the early presidents even proposed to make America SI by law. But all that doesn't change that weight is interchangeable with mass in a fixed frame of reference. – Trish Jan 22 '22 at 09:05
  • If you look at all places where you encounter the markings lbf or lbs/lbm/lb, then you'll find it on far more cases to indicate a weighted mass of something than the force it applies. You package has a mass of 3 lbs and so on - on every packaging it is mass (generally measured by dividing the force it applies by g). – Trish Jan 22 '22 at 09:26
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    Please don't use comments for extended discussion - especially not extended discussion on mechanical physics on an RPG game stack – Lovell Jan 22 '22 at 09:41
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In DnD and most games, the terms are interchangeable. This is because the games generally take place on Earth or an Earth analog. On Earth, it takes 10 pounds of force to hold 10 pounds of mass.

The difference only matters if the characters end up in an area with a significantly different local gravity.

That means that you can push open a door that takes 10 pounds of force or less to open. Alternatively, you could hold down something that has 10 pounds of lift or less.

Also, lest you get ideas, you cannot apply that force instantaneously as an impact or to a point source or they would give the spell a damage stat.

Could you press the carotid artery of a helpless person to eventually kill them? Yes but if they can move at all, you probably can't maintain the pressure. If the opponent is merely asleep, they are likely to wake up and "do something about it". Also, there are much easier and faster ways to kill a helpless opponent.

ShadoCat
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Don't try this at home

Most DM's have no reason to even consider trying to determine the force of a mage hand; such real world physics calculations are unnecessary and, given that D&D is not a physics simulator, quickly break down by generating contradictory results. Why can a hand lift 10 pounds at one speed, but 10.01 pounds at only 1/6th that speed? It is sufficient for the vast majority of use cases for the DM to ask themselves questions such as 'Would a hand that could carry 10 pounds be able to do this in my game'?

However, the OP has stated in comments that they have an 'ongoing project to try to model d&d magic with physics'. As an end unto itself then, they will need to consider the following:

The hand can carry 10 pounds.

The hand can’t attack, activate magic items, or carry more than 10 pounds.

Ten pounds here is a mass. It is the amount of object that the hand can hold aloft. We can get to this conclusion simply from grammar. One doesn't 'carry' a force, but rather a mass. Or, as the PHB section on Lifting and Carrying says,

Lifting and Carrying Your Strength score determines the amount of weight you can bear. The following terms define what you can lift or carry.
Carrying Capacity. Your carrying capacity is your Strength score multiplied by 15. This is the weight (in pounds) that you can carry, which is high enough that most characters don't usually have to worry about it.

After excusing the common colloquialism that by 'weight' the PHB means mass, we can see that your Strength score (a measure of the force you can generate or apply) determines the pounds (a measure of mass) that you can carry. The 'pounds you can carry' are clearly a mass, not a force. [Incidentally, we also see from this quote that a creature with a Strength of 1 can carry 15 pounds, which means that the 'Strength' or force of the mage hand must be less than 1]

We have answered the titular question of the OP from grammar and context alone, but the OP says they want this information because they are "trying to find the force that Mage Hand is capable of exerting," so let's see how far we can get with that.

The spell makes no mention of the fact that carrying weight slows it down. Thus, it is not exerting a constant force, but rather a variable force with a maximum capable of carrying ten pounds. Further, the spell makes no mention that lifting slows it down either. We know that the hand can hold or sustain a mass of ten pounds against the force of gravity. But it can do more than this; it can lift such a mass up. What's more, it can take a mass that it is sustaining in the air, and accelerate it upwards, hinting at an even more powerful force.

Traditionally, we can solve for the force exerted when lifting a mass upward with acceleration with the formula F = ma. We can specify this further as F = m (a + g), where F equals the force exerted, m is the mass of the object, a is the acceleration observed on the object, and g is the acceleration due to gravity.

Gravity? Yes, gravity is apparently the cause of acceleration towards the ground in 5e, as described in the section of the PHB on opportunity attacks (emphasis mine):

You also don't provoke an opportunity attack when you teleport or when someone or something moves you without using your movement, action, or reaction. For example, you don't provoke an opportunity attack if an explosion hurls you out of a foe's reach or if gravity causes you to fall past an enemy.

Note that while the acceleration due to gravity on Earth is usually rounded to a constant 32 feet per second squared, 5e rules (at least the optional falling rules from XGtE) assume that falling objects accelerate at 27.78 feet per second squared for the first six seconds, until they reach a speed of 83 feet / second (500 feet in six seconds), and after that fall at a constant speed.

As previously stated, the hand is not only capable of sustaining an object - it can accelerate the object upward.

You can use your action to control the hand...You can move the hand up to 30 feet each time you use it.

Assuming the hand starts your turn not moving, over the course of your turn (6 seconds) you can move it 30 feet. Using the 'distance traveled' formula, we can solve for an acceleration of 1.67 feet / second squared.

Adding these two accelerations (a + g) together, we get a total acceleration of 29.45 feet per second squared. Thus, the maximum force exerted by the hand can be calculated as:

F = 10 pounds (29.45 feet per second squared)
F = ~295 pound feet / second squared
F = ~41 Newtons

This is our estimation for the maximum force produced by the hand.

Kirt
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  • This is interesting, but I think most of it is unnecessary. You answer the 'force/mass' question in the first few paragraphs, then go on to simulate physics in 5e. OP is not asking about how to simulate physics in 5e, only mentioning that this is their motivation. The question 'how can I best simulate the physics of Mage Hand?' would likely be closed as opinion based. – Lovell Jan 21 '22 at 23:04
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    @Lovell That is a fair criticism, but I also note that my answer follows the same structure as the two currently-most upvoted answers, only that is illustrates its calculations more explicitly. – Kirt Jan 21 '22 at 23:45
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To the extent Mage Hand behaves physically, it's an amount of force.

To "carry" something is to move it around while supporting its weight. (Contrast "drag", which is to move it while its weight is supported by the ground.) It indicates a static (near-)equilibrium in the direction of gravity. The inertial mass of the object is not relevant in a static situation; it comes up only if you try to accelerate it.

Mark Wells
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