This project provides a small massenergy.units file for GNU Units. It redefines the second as the distance light travels in one second and sets the speed of light c = 1. Mass and energy then convert directly via (E = mc^2).
Through this lens, a gram is about 21 kilotons of TNT. A sugar cube is city-scale. The Sun radiates roughly four million tons of mass every second.
You’ll never see the universe quite the same again.
| Doc / package | What it is |
|---|---|
| HYPERFACET.md | Two-line core, project backstory, and “mind-blower” reframe of global energy as mass |
| Data center power | Power plants + data centers, waste heat vs Earth solar absorption — usage examples with units |
| Solar radiance & Earth absorption | Solar luminosity, daily insolation, absorbed/radiated balance, and mass-energy equivalences |
| minkowski_entropy/ | Space-entropy: Python doing what units alone cannot. Geometric compounding along timelike intervals (c = 1) … and yes, it still does compounding finance. |
| Spacetime-Entropy Package(md) | Spacetime Entropy & Growth/Decay Module |
| Twin Paradox Redux | Classic problem looked at as an entropy reduction effect instead of a clock speed effect |
| Finance examples | Same math as entropy for compounding interest (readable help in the module README) |
- Redefines core units:
second ≈ 299792 km,c = 1 - Mass ↔ energy conversions without extra factors
- Named references for familiar nuclear yields and large-scale events
- Real-world examples from physics, history, and energy economics
- Topic notes: data center power, solar radiance / Earth absorption
- Optional Minkowski / space-entropy math package (
minkowski_entropy)
- GNU Units 2.x (tested with 2.23)
- A Unix-like shell (Linux, macOS, WSL, or Cygwin)
# Debian / Ubuntu / WSL
sudo apt install units
# Fedora / RHEL
sudo dnf install units
# macOS (Homebrew)
brew install unitsOn Windows, use WSL or Cygwin and install units inside that environment.
git clone https://github.com/NinerXrayBravoTwoTwo/MassEnergyUnits.git
cd MassEnergyUnitsOr download massenergy.units alone from the repository.
Load the system units database first, then this file (so m, J, g, etc. still exist):
units -f /usr/share/units/definitions.units -f ./massenergy.unitsHomebrew on macOS often uses:
units -f "$(brew --prefix)/share/units/definitions.units" -f ./massenergy.unitsPersonal units file (recommended for multi-user machines — each person configures their own home directory):
# Use the absolute path to your clone
echo "!include $PWD/massenergy.units" >> ~/.unitsThen any normal units session picks up the definitions.
Shell alias (repo-local, no install into /usr):
# Linux / WSL
alias lightunits='units -vf /usr/share/units/definitions.units -f /path/to/MassEnergyUnits/massenergy.units'
# macOS Homebrew
alias lightunits='units -vf "$(brew --prefix)/share/units/definitions.units" -f /path/to/MassEnergyUnits/massenergy.units'Add the alias to ~/.bashrc or ~/.zshrc as you prefer.
Shared install (optional; needs admin rights):
sudo cp massenergy.units /usr/share/units/| Definition | Meaning |
|---|---|
s = 2.99792458e8 m |
One second is the distance light travels in one second |
c = 1 |
Speed of light is unitless |
ton_tnt = 4.184e9 J |
Standard thermochemical ton of TNT |
Mass and energy, space and time, are brought into direct calculable parity.
"Time and distance are the same thing. Ergo, mass and energy are the same thing."
* *
* * * Oh, We're having so much fun, making itty bitty suns!
* *
-- wengland@stephsft.com 1989 — usenetInteractive session (You have: / You want: prompts):
You have: g
You want: kton
g = 21.480764 kton
g = (1 / 0.046553278) kton
You have: gadget
You want: kt
gadget = 19 kt
gadget = 0.8845 g
You have: nagasaki
You want: hiroshima
nagasaki = 1.4 hiroshima
You have: 5g
You want: hiroshima
5g = 7.1602548 hiroshima
You have: g
You want: nagasaki
g = 1.0228935 nagasaki
In spacetime the 'now' manifold requires 4D distance of 186282.4 miles
You have: s
You want: miles
s = 186282.4 miles
Jupiter is about 5.46 earth radi from the sun.
You have: jupitersundist_max
You want: au
jupitersundist_max = 5.4570496 au
You have: jupitersundist_max
You want: hours
jupitersundist_max = 0.75641496 hours
It takes a day for the 'now' spacetime cone manifold to reach a 4D spaceime diameter of 31.7 jupiter-sol radi.
You have: day
You want: jupitersundist_max
day = 31.728616 jupitersundist_max
Total power used was 823.73 kW hours over 64 days, costing $135.06.
You have: 823.73 kW hours / 64 days
You want: micro g per day
823.73 kW hours / 64 days = 0.51554432 micro g per day
You have: 823.73 kW hours /135.06 dollars
You want: micro g per dollar
823.73 kW hours /135.06 dollars = 0.24429762 micro g per dollar
The city of Seattle charges me $1 for every 0.2443 μg of energy I use. (0.0002443 mg / $)
Image: Pollen
On the other hand, perhaps you are stunned by the fact that the amount of energy I use in my house each day can actually be measured in mass that is meaningfull at all.
... at 0.156 micro gram per day or 32.995 μg for the entire 64 day billing period. This is actually visible under a normal light micoscope, at the scale of a bacteria or grain of pollen. A little bit smaller than the width of a human hair but close.
My take away is that we are not just passing by this energy gradient, we are wading through and into it.
Calculate the mass of your own power bill and see what you get. You might be surprised.
You have: 823.73 kW hours
You want: micro grams
823.73 kW hours = 32.994836 micro gram
| Organism/Stucture | Typical mass | W hours equivalent mass | Visible under microscope? |
|---|---|---|---|
| Pollen grain | 10–100 ng | 0.24965 - 2.5 kW hrs | Yes |
| Tiny plant seeds | 1–10 µg | 25 - 249 kW hrs | Yes |
| Diatom | 2–200 µg | 0.5 - 5 kW hrs | Yes |
| Tardigrade | 100–500 µg | 2.5 - 12.5 kW hrs | Yes |
| Human hair | 50–100 µg | 1.25 - 2.5 kW hrs | Yes |
| Rotifer | 50–500 µg | 1.25 - 12.5 kW hrs | Yes |
| flax seed | 1–2 mg | 24.97 - 49.93 MW hrs | Yes |
Converting mass to energy at 168.5 µg per year, the human brain uses about 20 watts continuous uninterrupted power.
That is about 168.5 µg of mass-energy per year.
You have: 20 watt / hour * day * siderealyear
You want: micro g
20 watt / hour * day * siderealyear = 168.54325 micro g
- I am 65.5 years old. (1960 - 2026)
- At ~168.5 µg of mass per year, I have burned the equivalent of ~11.04 mg of mass with just my brain in 65.5 years.
- Most of that energy scavenged from the solar gradient was spent in fighting entropy, the second law.
- Was it all worth it? 😊
You have: 20 watt / hour * day * siderealyear * 65.5
You want: milligrams
20 watt / hour * day * siderealyear * 65.5 = 11.039583 milligrams
You have: 10000 watt / hour * day * siderealyear
You want: 20 watt / hour * day * siderealyear
10000 watt / hour * day * siderealyear = 500 * 20 watt / hour * day * siderealyear
^^^ 500 human brains worth of power usage
- Human brain burns about 0.17 milligrams of mass-energy per year,
- while a high end AI data server burns about 84 milligrams of mass-energy per year.
That is about 500 times more energy usage than a human brain.
You have: 20 watt / hour * day * siderealyear
You want: mg
20 watt / hour * day * siderealyear = 0.16854325 mg
You have: 10000 watt / hour * day * siderealyear
You want: mg
10000 watt / hour * day * siderealyear = 84.271624 mg
units -f /usr/share/units/definitions.units -f ./massenergy.units '1 g' 'kton'
units -f /usr/share/units/definitions.units -f ./massenergy.units 'castlebravo' 'g'
units -f /usr/share/units/definitions.units -f ./massenergy.units '1 s' 'km'| Name | Definition |
|---|---|
s, c |
Second as light-travel distance; speed of light = 1 |
ton_tnt, ton_e, ton_tnt_energy |
1 ton TNT = 4.184 GJ |
kton/kt, Mton/Mt |
10³ and 10⁶ tons TNT |
trinity, gadget |
19 kt |
hiroshima, littleboy |
15 kt |
nagasaki, fatman |
21 kt |
castlebravo, shrimp |
15 Mt |
chicxulub, dinokill |
K–Pg impact energy (~4.184×10²³ J) |
solarluminosity, sunpower |
Solar power (382.8 yotta W) |
nova |
Order-of-magnitude supernova (~10⁴⁴ J) |
everestmass |
Mass of Mt. Everest (approx.) |
Yields are common public figures; historical estimates have ranges. Device and convenience names alias the primary units so mass-energy stays consistent when c = 1.
| Event | Energy (J) | Mass equivalent (g) |
|---|---|---|
| Trinity test (19 kt) | ~8.0 × 10¹³ | ~0.88 g |
| Hiroshima (~15 kt) | ~6.3 × 10¹³ | ~0.70 g |
| Nagasaki (~21 kt) | ~8.8 × 10¹³ | ~0.98 g |
| Castle Bravo (15 Mt) | ~6.3 × 10¹⁶ | ~700 g |
| Solar luminosity (per sec) | 3.828 × 10²⁶ | ~4.25 × 10⁹ g |
| Chicxulub impact | 4.184 × 10²³ | ~4.65 × 10⁶ g |
The nunits authors have since incorported these constants into the default "/units/definitions.units" data file. Several additional 'shots' are defined.
$ grep -i tnt /usr/share/units/definitions.units
# The unit "tnt" is defined so that you can write "tons tnt". The
# explosive energy released by TNT range from 900 to 1,100 calories per
# "kiloton" of TNT referred to a short kiloton (2*10^6 pounds), a metric
# equivalent to 1 short kiloton of TNT if the energy release is 1,102
# per gram of TNT.
# It is therefore not well-defined how much energy a "gram of tnt" is,
tnt 1e9 cal_th / ton # Defined exact value
davycrocket 10 ton tnt # lightest US tactical nuclear weapon
hiroshima 15.5 kiloton tnt # Uranium-235 fission bomb
nagasaki 21 kiloton tnt # Plutonium-239 fission bomb
ivyking 500 kiloton tnt # most powerful fission bomb
castlebravo 15 megaton tnt # most powerful US test
tsarbomba 50 megaton tnt # most powerful test ever: USSR,
b53bomb 9 megaton tnt
trinity 18 kiloton tnt # July 16, 1945
- Relatable: Grams and kilograms are everyday units.
- Tangible: “This release was about one gram” is easier than “25 giga watt hours”
- Intuitive scaling: Cosmic and industrial energy use become comparable.
- Physics: Mass and energy are interchangeable (E = mc^2).
- Or just (E = m) in our case since we are using naural units
- Which is actually the fundemental insight of relativity, that mass and energy are the same thing, time and distance are the same units of measure. Not equilvent, the same with 'restrictions'
People have said;
"A loaf of bread converted entirely to energy could power the Earth for a day."
But is that really true? You now know how to actually check.
- If a loaf of bread is about 567g;
- Electricity used by humans in 2023 was about 27.047 PW hours (Petawatt hours)
You have: 27.047 PW hr per (siderealyear/day)
You want: 567 g
27.047 PW hr per (siderealyear/day) = 5.2311762 * 567 g
^^^^^ actual number of loaves of bread needed
So No- They were incorrect, it would actually require 5.23 loaves of bread, converted to energy, to power the human race for a day.
You may think that this is nitpicking, however this is extreenly precise math. There is a big difference between one loaf verses five times that amount.
- This file is for intuition and conversion, not Lorentz transforms or tensor calculus.
- For spacetime intuition, see Spacetime Physics (Taylor & Wheeler).
- Not affiliated with the GNU Units project.
- Historical nuclear yields are estimates; modern analyses sometimes revise them.
At first you will doubt this reality. Have patience,and you will see the universe in a new light where a second really is a distance measured in meters and electricity measured in micrograms.
| ElecProd ekg | Std x ekg/G$ | Std x ekg/TT | CapFF ekg | Std x ekg/G$ | Std x ekg/TT | EmissionTT TT | GDP G$ | Country |
|---|---|---|---|---|---|---|---|---|
| 947.3 | -28.154 | 17.312 | 1412.612 | -32.698 | 11.967 | 33620.0 | 127800.0 | World |
| 235.6 | 0.739 | -2.564 | 359.847 | 0.085 | -3.455 | 11670.0 | 23210.0 | China |
| 164.0 | -2.494 | 4.201 | 267.166 | -1.970 | 4.601 | 5242.0 | 19490.0 | United States |
| 121.9 | -7.598 | 3.995 | 150.630 | -9.990 | 1.506 | 3475.0 | 20850.0 | European Union |
| 55.5 | -3.440 | 0.157 | 91.690 | -3.184 | 0.356 | 2383.0 | 9474.0 | India |
| 41.3 | 0.176 | -0.038 | 58.472 | -0.206 | -0.458 | 1847.0 | 4016.0 | Russia |
| 39.6 | -1.265 | 1.012 | 73.766 | -0.599 | 1.646 | 1268.0 | 5443.0 | Japan |
| 26.0 | 0.793 | 1.063 | 11.589 | -0.922 | -0.666 | 640.6 | 1774.0 | Canada |
| 24.5 | -1.530 | 0.497 | 30.015 | -2.030 | -0.025 | 847.6 | 4199.0 | Germany |
| 22.7 | -0.838 | 1.025 | 9.001 | -2.400 | -0.551 | 513.8 | 3248.0 | Brazil |
| 21.2 | -0.627 | 1.241 | 7.807 | -2.116 | -0.259 | 341.2 | 2856.0 | France |
- ekg means kilograms of mass-energy (the antimatter-equivalent sense).
- GDP is gross domestic product.
Data from the CIA World Factbook (circa 2016–2017).
| Independent (X) | Dependent (Y) | Correlation | Mean X | Slope |
|---|---|---|---|---|
| Electric Consumption | Generating Capacity Fossil Fuel | 0.993 | 29.1 | 1.7 ekg/ekg |
| Generating Capacity Fossil Fuel | GDP | 0.984 | 46.9 | 64.8 ekg/G$ |
| Electric Production | GDP | 0.982 | 31.5 | 102.0 ekg/G$ |
| Electric Production | CO₂ Emissions (Tt) | 0.977 | 31.5 | 44.3 ekg/TT |
| Fossil Fuel Gen Capacity | CO₂ Emissions (Tt) | 0.969 | 46.9 | 27.8 ekg/TT |
| Nat Gas Produced | Nat Gas Consumed | 0.955 | 102.8 | 0.8 Gcm/Gcm |
| Oil Reserves | Oil % GDP | 0.946 | 30974.6 | 0.0 Gbbl/% |
| GDP | CO₂ Emissions (Tt) | 0.942 | 4090.6 | 0.4 G$/TT |
| Electric Consumption | Renewable Gen Capacity | 0.934 | 29.1 | 0.4 ekg/ekg |
| Renewable Gen Capacity | CO₂ Emissions (Tt) | 0.932 | 12.9 | 97.9 ekg/TT |
| Oil Export | Oil % GDP | 0.927 | 0.9 | 1.3 Mbbl/% |
| Renewable Gen Capacity | GDP | 0.923 | 12.9 | 222.1 ekg/G$ |
| Fossil Fuel Gen Capacity | Renewable Gen Capacity | 0.921 | 46.9 | 0.3 ekg/ekg |
| Refined Fuel Consumed | GDP | 0.918 | 3.1 | 1193.9 Mbbl/G$ |
| Oil Import | GDP | 0.914 | 1.5 | 2432.9 Mbbl/G$ |
| Hydro Gen Capacity | CO₂ Emissions (Tt) | 0.909 | 11.4 | 101.5 ekg/TT |
| Fossil Fuel Gen Capacity | Refined Fuel Consumed | 0.903 | 46.9 | 0.0 ekg/Mbbl |
| Refined Export | Nat Gas Consumed | 0.900 | 0.8 | 132.7 Mbbl/Gcm |
| Electric Consumption | Refined Fuel Consumed | 0.895 | 29.1 | 0.1 ekg/Mbbl |
| Electric Production | Refined Fuel Consumed | 0.893 | 31.5 | 0.1 ekg/Mbbl |
| Refined Fuel Produced | GDP | 0.892 | 2.9 | 1132.5 Mbbl/G$ |
| Fossil Fuel Gen Capacity | Oil Import | 0.889 | 46.9 | 0.0 ekg/Mbbl |
| Refined Fuel Produced | Nat Gas Consumed | 0.883 | 2.9 | 33.6 Mbbl/Gcm |
| Oil Export | Growth Rate | -0.545 | 0.9 | -0.6 Mbbl/% |
Energy is hard to grasp in abstract SI form. U.S. electricity use of about 3,900 TWh in 2016 is hard to picture — until you notice that as pure mass-energy it is only a few hundred pounds.
Time is not a special dimension separate from space; measuring the second as ~300,000 km makes c = 1. Substituting that into everyday energy formulas makes mass and energy the same unit. One kilogram is about 89.9 PJ or 25 TWh.
When you realize that time is just another distance, then in basic work-energy equations time cancels out and we are left with the realization that, as far as the math is concerned, Energy is equal to mass.
There is no actual complicated math or even calculus required to see or use this. Just Algebra 😄
A single gram of mass is about 21 kilotons of TNT.
You have: g
You want: kt
g = 21.480764 kt
You have: g
You want: GW hr
g = 24.965422 GW hr
You have: g
You want: TJ
g = 89.875518 TJ
# A tera watt hour is 40 grams of mass by the way.
# I mention it only because this conversion seems to come up often.
You have: TW hr
You want: g
TW hr = 40.055402 g
| Name | Yield | Mass-energy | Date | Device | Notes |
|---|---|---|---|---|---|
| Trinity | 19 kt | ~0.88 g | 1945-07-16 | Gadget | First test, White Sands, NM |
| Hiroshima | ~15 kt | ~0.70 g | 1945-08-06 | Little Boy | U-235 gun-type |
| Nagasaki | ~21 kt | ~0.98 g | 1945-08-09 | Fat Man | Pu-239 implosion |
| Castle Bravo | 15 Mt / ~63 PJ | ~701 g | 1954-03-01 | Shrimp | Largest U.S. test |
| Chicxulub | 4.184×10²³ J | ~4.65×10⁶ g | 66 Ma | — | K–Pg extinction impact |
| Solar (1 s) | 3.828×10²⁶ J | ~4.25×10⁹ g | Present | — | Solar luminosity |
| Nova | ~10⁴⁴ J | ~10²⁷ g | — | — | Order-of-magnitude |
See CONTRIBUTING.md for issues, pull requests, and testing.
- The core deliverable is
massenergy.units— keep it small and commented. - Historical yield numbers may be updated when better public estimates appear; keep device aliases (
gadget,littleboy, …) linked to the yield names. - Longer essay material and exercise ideas live in
README-original.mdandProjects.md.
MIT — Copyright (c) 1995, 2008, 2017, 2026 Jillian England.