# What do the units of energy measurement mean in E=mc^2? **URL:** \ **Category:** Factual Questions\ **Created:** [April 1, 2014, 6:11pm UTC](https://boards.straightdope.com/t/what-do-the-units-of-energy-measurement-mean-in-e-mc-2/685104 "2014-04-01T18:11:54Z")\ **Posts on this page:** 20\ **Page:** 1
**Author:** ![filmore](https://avatars.discourse-cdn.com/v4/letter/f/7993a0/32.png) [@filmore](https://boards.straightdope.com/u/filmore)\ **Post date:** [April 1, 2014, 6:11pm UTC](https://boards.straightdope.com/t/what-do-the-units-of-energy-measurement-mean-in-e-mc-2/685104/1 "2014-04-01T18:11:54Z")
If c is meters/second, then the units of measurement of E=mc^2 are E=(mass)(meter^2/second^2). But what does a mass meter squared per second squared mean? I can understand F=ma as (mass)(meter/second^2) as the amount of force required to accelerate mass at a certain rate. But I’m not sure what (mass)(meter^2/second^2) is telling me about the amount of energy. I having trouble understanding what a meter^2/second^2 means in the real world. ---
**Author:** ![Batistuta](https://avatars.discourse-cdn.com/v4/letter/b/58956e/32.png) [@Batistuta](https://boards.straightdope.com/u/Batistuta)\ **Post date:** [April 1, 2014, 6:20pm UTC](https://boards.straightdope.com/t/what-do-the-units-of-energy-measurement-mean-in-e-mc-2/685104/2 "2014-04-01T18:20:43Z")
Bear in mind that energy (E) is equal to Force times displacement; in other words a force exerted along a distance. So that’s where the ‘meter squared’ comes into play. How large a force are you exerting, and over how big a distance ---
**Author:** ![Valgard](https://avatars.discourse-cdn.com/v4/letter/v/7feea3/32.png) [@Valgard](https://boards.straightdope.com/u/Valgard)\ **Post date:** [April 1, 2014, 6:30pm UTC](https://boards.straightdope.com/t/what-do-the-units-of-energy-measurement-mean-in-e-mc-2/685104/3 "2014-04-01T18:30:00Z")
I’m sure an actual physicist will be along to explain it in detail but the metric units of energy are Joules. Energy is “the ability to do work”, where “work” has a particular meaning; IIRC work is force multiplied by the distance over which that force is applied. So work has units of force \* distance, which would be kg m/s^2 \* m, or kg m^2/s^2. A simple example of work would be lifting a mass straight up against the pull of gravity - you lift a 1kg mass 10m straight up against 1g (9.8 m/s^2) and you’ve done 1kg \* 9.8 m/s^2 \* 10m or 98 Joules of work. The mass has gained 98J of gravitational potential energy; if you let it fall down those 10m you can extract (at most) 98J of work. If it’s in a vacuum and still moving (that is, not stopped by something 10m below) then you can calculate the velocity at that instant by turning that 98J of PE into 98J of KE (kinetic energy) and using KE=1/2 \* m \* v^2 to get v. ---
**Author:** ![John\_Mace](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/john_mace/32/185_2.png) [@John\_Mace](https://boards.straightdope.com/u/John_Mace)\ **Post date:** [April 1, 2014, 6:53pm UTC](https://boards.straightdope.com/t/what-do-the-units-of-energy-measurement-mean-in-e-mc-2/685104/4 "2014-04-01T18:53:26Z")
> [@Valgard](#): > > I’m sure an actual physicist… As an actual physicist, I’d say you did just fine without one of us chiming in! I would only quibble with your notation and re-write it thusly to avoid confusion: J = (kg m/s^2 )\* m, ---
**Author:** ![lawbuff](https://avatars.discourse-cdn.com/v4/letter/l/13edae/32.png) [@lawbuff](https://boards.straightdope.com/u/lawbuff)\ **Post date:** [April 1, 2014, 6:58pm UTC](https://boards.straightdope.com/t/what-do-the-units-of-energy-measurement-mean-in-e-mc-2/685104/5 "2014-04-01T18:58:30Z")
Engy = mass x speed of light in a volume/vaccum squared. ---
**Author:** ![BrightNShiny](https://avatars.discourse-cdn.com/v4/letter/b/7bcc69/32.png) [@BrightNShiny](https://boards.straightdope.com/u/BrightNShiny)\ **Post date:** [April 1, 2014, 7:33pm UTC](https://boards.straightdope.com/t/what-do-the-units-of-energy-measurement-mean-in-e-mc-2/685104/6 "2014-04-01T19:33:53Z")
If you really want to start getting into it, the wiki article on [Work](http://en.wikipedia.org/wiki/Work_(physics)) provides a pretty good intro into the relationship between Force, distance, Work and Energy. But the math here might be a bit complex for a lot of people. ---
**Author:** ![Chronos](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/chronos/32/134_2.png) [@Chronos](https://boards.straightdope.com/u/Chronos)\ **Post date:** [April 1, 2014, 7:40pm UTC](https://boards.straightdope.com/t/what-do-the-units-of-energy-measurement-mean-in-e-mc-2/685104/7 "2014-04-01T19:40:48Z")
And a kilogram_meter^2/second^2 is also known as a joule, since it’s such a commonly-used unit of energy. Similarly, a gram_centimeter^2/second^2 is an erg. ---
**Author:** ![BrightNShiny](https://avatars.discourse-cdn.com/v4/letter/b/7bcc69/32.png) [@BrightNShiny](https://boards.straightdope.com/u/BrightNShiny)\ **Post date:** [April 1, 2014, 7:54pm UTC](https://boards.straightdope.com/t/what-do-the-units-of-energy-measurement-mean-in-e-mc-2/685104/8 "2014-04-01T19:54:10Z")
> [@lawbuff](#): > > Engy = mass x speed of light in a volume/vaccum squared. Thank god you came in to post an answer which doesn’t answer the OP in the least bit.:dubious: ---
**Author:** ![lawbuff](https://avatars.discourse-cdn.com/v4/letter/l/13edae/32.png) [@lawbuff](https://boards.straightdope.com/u/lawbuff)\ **Post date:** [April 1, 2014, 7:55pm UTC](https://boards.straightdope.com/t/what-do-the-units-of-energy-measurement-mean-in-e-mc-2/685104/9 "2014-04-01T19:55:50Z")
> [@BrightNShiny](#): > > Thank god you came in to post an answer which doesn’t answer the OP in the least bit.:dubious: Too bad for you then huh! ---
**Author:** ![lawbuff](https://avatars.discourse-cdn.com/v4/letter/l/13edae/32.png) [@lawbuff](https://boards.straightdope.com/u/lawbuff)\ **Post date:** [April 1, 2014, 7:58pm UTC](https://boards.straightdope.com/t/what-do-the-units-of-energy-measurement-mean-in-e-mc-2/685104/10 "2014-04-01T19:58:06Z")
> [@lawbuff](#): > > Engy = mass x speed of light in a volume/vaccum squared. To clarify for bright and shiny boy; Energy is E; M is MASS; C is speed of light in a volume, 2= squared. that good enough sport. ---
**Author:** ![kenobi\_65](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/kenobi_65/32/13178_2.png) [@kenobi\_65](https://boards.straightdope.com/u/kenobi_65)\ **Post date:** [April 1, 2014, 8:20pm UTC](https://boards.straightdope.com/t/what-do-the-units-of-energy-measurement-mean-in-e-mc-2/685104/11 "2014-04-01T20:20:08Z")
> [@lawbuff](#): > > To clarify for bright and shiny boy; > > Energy is E; M is MASS; C is speed of light in a volume, 2= squared. that good enough sport. If you re-read the OP, he understood the basics of the elements of equation. His question was: what does the E in the equation actually **mean** – and that goes beyond “E = Energy”. ---
**Author:** ![BrightNShiny](https://avatars.discourse-cdn.com/v4/letter/b/7bcc69/32.png) [@BrightNShiny](https://boards.straightdope.com/u/BrightNShiny)\ **Post date:** [April 1, 2014, 8:22pm UTC](https://boards.straightdope.com/t/what-do-the-units-of-energy-measurement-mean-in-e-mc-2/685104/12 "2014-04-01T20:22:21Z")
> [@lawbuff](#): > > To clarify for bright and shiny boy; > > Energy is E; M is MASS; C is speed of light in a volume, 2= squared. that good enough sport. To clarify for you, that doesn’t answer his question at all. Boy. ---
**Author:** ![leahcim](https://avatars.discourse-cdn.com/v4/letter/l/b4bc9f/32.png) [@leahcim](https://boards.straightdope.com/u/leahcim)\ **Post date:** [April 1, 2014, 8:28pm UTC](https://boards.straightdope.com/t/what-do-the-units-of-energy-measurement-mean-in-e-mc-2/685104/13 "2014-04-01T20:28:35Z")
> [@filmore](#): > > I having trouble understanding what a meter^2/second^2 means in the real world. I think it’s fallacious to expect the meter^2/second^2 to “mean” anything in particular in the same way that the acceleration in F=ma means something. “c” is a constant baked into the universe that relates distances in space to distances in time. It’s not even a “speed” really, just a conversion factor. As it happens, the same conversion factor that converts time intervals to space intervals can be applied twice to convert mass measurements to energy measurements. ---
**Author:** ![ThisUsernameIsForbidden](https://avatars.discourse-cdn.com/v4/letter/t/b4bc9f/32.png) [@ThisUsernameIsForbidden](https://boards.straightdope.com/u/ThisUsernameIsForbidden)\ **Post date:** [April 1, 2014, 8:43pm UTC](https://boards.straightdope.com/t/what-do-the-units-of-energy-measurement-mean-in-e-mc-2/685104/14 "2014-04-01T20:43:55Z")
Sometimes I can’t tell whether the responses are from grouchy old men or pedantic youths. ---
**Author:** ![tracer](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/tracer/32/20578_2.png) [@tracer](https://boards.straightdope.com/u/tracer)\ **Post date:** [April 1, 2014, 8:51pm UTC](https://boards.straightdope.com/t/what-do-the-units-of-energy-measurement-mean-in-e-mc-2/685104/15 "2014-04-01T20:51:14Z")
Energy is at least understandable. It’s work, that is, a force applied over a distance, hence Force x distance. The one unit I have more trouble understanding is Entropy. I know what it means (the disorderliness of a system), but the units of entropy work out to “Joules per Kelvin”. I have trouble turning Joules-per-Kelvin into disorderliness in my head. ---
**Author:** ![Smeghead](https://avatars.discourse-cdn.com/v4/letter/s/f1d935/32.png) [@Smeghead](https://boards.straightdope.com/u/Smeghead)\ **Post date:** [April 1, 2014, 8:54pm UTC](https://boards.straightdope.com/t/what-do-the-units-of-energy-measurement-mean-in-e-mc-2/685104/16 "2014-04-01T20:54:31Z")
> [@ThisUsernameIsForbidden](#): > > Sometimes I can’t tell whether the responses are from grouchy old men or pedantic youths. Around here, probably both. ---
**Author:** ![filmore](https://avatars.discourse-cdn.com/v4/letter/f/7993a0/32.png) [@filmore](https://boards.straightdope.com/u/filmore)\ **Post date:** [April 1, 2014, 9:17pm UTC](https://boards.straightdope.com/t/what-do-the-units-of-energy-measurement-mean-in-e-mc-2/685104/17 "2014-04-01T21:17:48Z")
Force over distance. That makes sense. So if c is about 3x10^8 m/s^2, then 1 kg has 3x10^8 Joules of energy. If gravity is about 10m/s^2, does that mean that amount of energy could lift 3x10^7 kg up 1 meter? That’s 30000 metric tons. A car is about 4 metric tons. 30000/4 = 7500 cars lifted 1 meter? ---
**Author:** ![Colophon](https://avatars.discourse-cdn.com/v4/letter/c/f05b48/32.png) [@Colophon](https://boards.straightdope.com/u/Colophon)\ **Post date:** [April 1, 2014, 9:26pm UTC](https://boards.straightdope.com/t/what-do-the-units-of-energy-measurement-mean-in-e-mc-2/685104/18 "2014-04-01T21:26:18Z")
> [@leahcim](#): > > I think it’s fallacious to expect the meter^2/second^2 to “mean” anything in particular in the same way that the acceleration in F=ma means something. “c” is a constant baked into the universe that relates distances in space to distances in time. It’s not even a “speed” really, just a conversion factor. As it happens, the same conversion factor that converts time intervals to space intervals can be applied twice to convert mass measurements to energy measurements. Of course the units “mean something”. That’s the beauty of using units in equations. If you multiply kilograms by (metres per second) squared, then you get joules, so you know that you are talking energy. And the joule is defined as 1 kg m[sup]2[/sup] s[sup]-2[/sup], so if the mass is given in kilos and the speed is given in metres per second then the energy will be given in joules. Just think about what energy represents: work. Force x distance. Force = mass x acceleration. Mass in kilograms, acceleration in metres per (second squared). Now to get the work done you have to multiply force by distance. So: mass x acceleration x distance. In other words, kilograms x metres per (second squared) x metres. Which makes kilograms x (metres squared) per (second squared). ---
**Author:** ![Valgard](https://avatars.discourse-cdn.com/v4/letter/v/7feea3/32.png) [@Valgard](https://boards.straightdope.com/u/Valgard)\ **Post date:** [April 1, 2014, 9:48pm UTC](https://boards.straightdope.com/t/what-do-the-units-of-energy-measurement-mean-in-e-mc-2/685104/19 "2014-04-01T21:48:06Z")
> [@filmore](#): > > Force over distance. That makes sense. So if c is about 3x10^8 m/s^2, then 1 kg has 3x10^8 Joules of energy. If gravity is about 10m/s^2, does that mean that amount of energy could lift 3x10^7 kg up 1 meter? That’s 30000 metric tons. A car is about 4 metric tons. 30000/4 = 7500 cars lifted 1 meter? c is 3x10^8 m/s (not m/s^2) and you forgot to square it so you’re off by a factor of 300 million 😃 E=mc^2 so in your example, the energy equivalent of 1kg of matter is (1kg)(3x10^8m/s)^2 which is 9x10^16 kg m^2/s^2 or 9x10^16 Joules (90 petajoules if I’m reading wiki right). That is a huge amount of energy. That would be a 21.5MT explosion if that helps visualize it. ---
**Author:** ![ThisUsernameIsForbidden](https://avatars.discourse-cdn.com/v4/letter/t/b4bc9f/32.png) [@ThisUsernameIsForbidden](https://boards.straightdope.com/u/ThisUsernameIsForbidden)\ **Post date:** [April 1, 2014, 10:10pm UTC](https://boards.straightdope.com/t/what-do-the-units-of-energy-measurement-mean-in-e-mc-2/685104/20 "2014-04-01T22:10:57Z")
Just in case I’ve got it wrong then someone can correct me: > [@](#): > > I can understand F=ma as (mass)(meter/second^2) as the amount of force required to accelerate mass at a certain rate. But I’m not sure what (mass)(meter^2/second^2) is telling me about the amount of energy. I having trouble understanding what a meter^2/second^2 means in the real world. Let’s break it down yo: Force = MA = M x V/t [kg x m/s/s] E = Fd = M x V/t x d [kg x m/s/s x m] In the first equation, imagine a sailboat. It has mass M and the wind blows it around with force F, this causes the boat to accelerate until the forces are in equilibrium where the drag of the boat (force of friction of the water) is the same as the force of the wind. It’s a simplification, but you get the picture. In the second equation, imagine the same sailboat. There is an amount of energy required to apply that force to the sailboat over some distance d. You could translate that into an amount of fuel you would use if you used an engine rather than a sail, for example. [Next page](https://boards.straightdope.com/t/what-do-the-units-of-energy-measurement-mean-in-e-mc-2/685104.md?page=2)