25 Billion Hiroshimas??? Wrong, Wrong, Very Wrong!

I’ve been seeing “25 billion Hiroshima bombs worth of heating” in the media for well over a year now. This number is supposed to represent a way to help the average person visualize the total amount of heating of the planet caused by GHGs since 1971. And it’s wrong, wrong, very wrong! In this article I’m going to explain why it’s wrong, give a possible explanation for how this wrong number was computed, and give the correct answer. (Spoiler. 6.05 billion through 2023, 6.4 billion through early 2025.)

The origin of the “25 billion Hiroshimas” claim appears to be from this article in The Conversation, published May 2, 2023, written by Australian climate scientists Andrew King and Steven Sherwood:

Unfortunately, their nonsense got picked up by multiple media outlets. For example:

Live Science, May 5, 2023

“Energy of ’25 billion atomic bombs’ trapped on Earth in just 50 years, all because of global warming”

Econai, May 6, 2023

“A new study has found that global warming trapped an explosive amount of energy-the equivalent of about 25 billion atomic bombs- in Earth’s atmosphere in the past half-century.”

The Guardian, May 15, 2023

“How much heat is that? Scientists have calculated it is the equivalent energy of more than 25bn Hiroshima atomic bombs.”

Mongabay, October 11, 2023

“between 1971 and 2018, the sea took in about 396 zettajoules of heat, equivalent to the energy in about 25 billion Hiroshima atomic bombs.”

I’ve known this is wrong, wrong, very wrong since the first day this number caught my attention. For the last few years I’ve been keeping very close track of total heating via the Hiroshima bomb analogy, using data from the Earth Energy Imbalance available from CERES. I wrote about my methodology and results in this post. My independent work has been fact-checked by the same scientist, Dan Miller, who advised James Hansen on his 2011 Ted Talk, which was the first documented use of the Hiroshima analogy. And what I’ve computed is that from February, 2001 through September, 2024, the planet has heated by an equivalent total of 5.28 billion Hiroshima bombs.

What’s more, the rate of heating has been increasing over time. The planet is heating at almost 4 times the rate today that it was heating in 2001. Going back, pre-2001, the rate of heating was even slower. What this implies is that we should not expect the total Hiroshimas since 1971 to be too much higher than 5.28 billion, certainly nowhere near 25 billion.

So what went wrong and where did their 25 billion Hiroshimas come from?

First, a quote from the LiveScience article:

In an article for The Conversation, Andrew King, a climate scientist at the University of Melbourne in Australia, and Steven Sherwood, a climate scientist at the University of New South Wales in Sydney, calculated that 380 zettajoules is equivalent to around 25 billion times the energy released during the detonation of “Little Boy,” the atomic bomb dropped on Hiroshima, Japan, on Aug. 6, 1945.

I just want to note that they are very specific about it being a Hiroshima bomb, and not some tactical bomb or other unknown bomb. And being a Hiroshima, this bomb has a definite and well-documented theoretical yield of 62.76 terajoules. This exact number is used as the standard when refering to the yield, even though the actual bomb’s yield when it exploded over Hiroshima on August 6, 1945 is not known to the same high degree of accuracy.

Next, we return to the original “The Conversation” article, where the authors write:

“Little Boy, the nuclear bomb which destroyed Hiroshima, produced energy estimated at 15,000,000,000,000 joules [15 terajoules]. This means the effect of humanity’s greenhouse gas emissions in that 50-year period to 2020 is about 25 billion times the energy emitted by the Hiroshima nuclear bomb.”

So, how did Andrew King and Steven Sherwood come up with 15 terajoules per Hiroshima when the actual number is 62.76 terajoules per Hiroshima? I think I know.

If you look up the “Little Boy” bomb on Wikipedia, you will find it described as a “15 kiloton bomb.” To save you the trouble, here is the pertinent quote from the Wikipedia article:

“It exploded with an energy of approximately 15 kilotons of TNT (63 TJ) and had an explosion radius of approximately 1.3 kilometres (0.81 mi) which caused widespread death across the city.”

Somehow 15 kilotons per Hiroshima became 15 terajoules per Hiroshima in their minds, as if 1 kiloton of TNT equaled 1 terajoule. I don’t know quite how they made that mistake, it’s sloppy work at best. And the actual conversion factor is easy enough to find:

>>Siri, how many joules are there in one kiloton of TNT?

>>Good evening, Eliot! There are 4.184 terajoules in one kiloton of TNT, and would you like me to spy on your children (some more)?

These two climate scientists simply divided 380 zettajoules of heating by 15 kilotons per Hiroshima mistakenly converted to 15 terajoules per Hiroshima, and got

(380 zettajoules of heating)/(15 terajoules per Hiroshima) = 25.33 billion Hiroshimas.

They then rounded down to 25 billion. And that’s wrong, wrong, very wrong!

Here’s a self-check they could have done, but didn’t. Suppose they wanted to double-check that they were correct about 25 billion bombs. From January 1, 1971 to May 1, 2023 there were 19,113 days. Dividing gives:

(25 billion Hiroshimas)/(19,113 days) = 1.3 million Hiroshimas per day.

That means their calculation imples 1.3 million Hiroshimas per day on average worth of heating, every day, since January 1, 1971!

At the time James Hansen gave his 2011 Ted Talk, he quoted 400,000 Hiroshimas per day. My post, at the height of the recent Earth energy imbalance spike, gave 1.15 million per day. But they got 1.3 million Hiroshimas per day as an average since 1971. A Google search or AI query gives nowhere near 1.3 million per day, most often reporting Hansen’s out-of-date 400,000. This simple check would have told the authors that something was wrong, wrong, very wrong with their math.

What is the right answer? How many total Hiroshimas worth of heating has there been from 1971 through 2023?

Here’s the right math:

(380 zettajoules of heating)/(62.76 terajoules per Hiroshima) = 6.05 billion Hiroshimas.

With heating continuing at a near record pace since this number was first published, today, in early 2025 we are at about 6.4 billion Hiroshimas worth of heating and rising fast. But 6.4 billion is a very long way from 25 billion. Again, I trust you know that the numbers 25 and 6.4 are different. And even though 25 billion and 6.4 billion are both a lot of heating, the planet would be beyond toast if it were indeed 25 billion.

As the climate catastrophe accelerates and truth becomes muddied by politicians, institutions, religious leaders and corporations, the physical world is quickly becoming the last refuge of facts. The response of the planet and climate to the forcing humans have created can be correctly quantified. Let’s stop f&%king up these simple calculations, please!

A retraction is overdue.