Working at a think tank with lots of proliferation specialists offers certain advantages, especially the casual conversations.

It turns out Ferenc Dalnoki-Veress, Miles Pomper and I all share a pet-peeve: When people incorrectly convert amounts of plutonium and especially highly enriched uranium from kilograms into some arbitrary number of nuclear weapons.

There is a right way and a wrong way to do this.

Significantly Wrong on Significant Quantities


A cautionary tale by way of a slightly technical rant about the proper use of certain concepts pertaining to the conversion of actual units of measure into hypothetical units of destruction and the pitfalls encountered therein


Ferenc Dalnoki-Veress, Jeffrey Lewis and Miles Pomper

James Martin Center for Nonproliferation Studies

If you are a casual reader, you may be forgiven for thinking that the official unit of measure for plutonium and highly enriched uranium is a “bomb’s worth” – so often is the term employed by pundits, wonks and other forms of ink-stained wretches attempting to describe how much the United States, Russia, Iran or North Korea has of this or that.  Of course, the proper measure is the kilogram.  Even if you are an American and stubborn, you should still go metric.

Of course, kilograms are not the least bit exciting, certainly not when compared with nuclear weapons.  Tell an audience that the US and Russia, though the “Megatons to Megawatts” program, have downblended more than 400 metric tons of weapon-grade HEU and you may receive some polite applause.  Tell them it is enough for thousands of nuclear weapons and you have their attention.

With that attention, however, comes a responsibility to be accurate.  All too often, pundits make serious mistakes when converting a real measurement like kilograms into the more evocative “bombs worth.” Few pundits make clear their assumptions on how much nuclear material is needed for a weapon in which context.  Invariably, the result is to exaggerate either the danger faced or averted.  The problem is especially bad when the topic is an amount of highly enriched uranium.

For example, this week’s Economist cover story on Iran paraphrases an Israeli official, Director of Military Intelligence Major-General Aviv Kochavi, explaining that “if further enriched to 90 percent,” Iran’s stockpile of 100 kg of 20percent HEU “would be enough for up to four nuclear weapons.”  Similarly, a recent White House blog post on the upcoming Nuclear Security Summit, for example, notes that since the last summit in April 2010, the United States has removed more than 400 kg of highly enriched uranium removed from over 10 countries – “enough for 16 nuclear bombs.”   These calculations are just plain wrong.  Perhaps it doesn’t matter to the casual reader, but it matters to us.  And, if you read this blog, it should matter to you, too.

The obvious place to begin our discussion is the IAEA safeguards concept of a “significant quantity” of HEU. Readers certainly know that current IAEA safeguards standards define a significant quantity as “the approximate amount of nuclear material for which the possibility of manufacturing a nuclear explosive device cannot be excluded. Significant quantities take into account unavoidable losses due to conversion and manufacturing processes and should not be confused with critical masses.” And the current IAEA glossary defines that threshold amount for HEU as 25kg of U-235 in HEU.    (U235 is the stuff that goes boom.)

Now, “significant quantity” is not a perfect measure. Tom Cochran and Chris Paine have long and convincingly argued that the IAEA should lower the definition of a significant quantity, at least in some contexts.  State actors using implosion designs can and do build devices with much smaller amounts of material, even accounting for material lost along the way.  A “bomb’s worth” of HEU for China is much less than a “bomb’s worth” for a terrorist group willing to settle for a gun-type device.  Still, for all its flaws, the Significant Quantity is the standard agreed to by the international community as the basis for safeguards.  As such, it serves as a handy reference point without respect to the design expertise of a particular state or group.  Moreover, a White House official will find it much easier to clear the IAEA’s concept of a “bomb’s worth” than asking Z Division for an estimate.  So, for all its flaws, the SQ remains useful.  Now, would it be so difficult to use the concept correctly?

Think about it.  Twenty-five kg of U235 is not the same thing as 25 kg of “highly enriched” uranium – highly enriched can mean anything from 20 percent U-235 to well over 90 percent U-235.  Let’s revisit the comment of the Israeli intelligence official.  He says the material in Iran is sufficient for four nuclear weapons.  The Economist does not detail his assumptions, but if his estimates are based on IAEA significant quantities, then he is way off base. One hundred kilograms of 20 percent HEU contains 20 kg of U-235 — less than one significant quantity.    Similarly, the recent White House blog post also overlooks the fact that some of material is former Soviet HEU with enrichment levels of 30 or 40 percent.  For example, Soviet-origin HEU fuel removed from the WWR-M reactor in Ukraine is at a 36 percent enrichment level.  Using 36 percent as an estimate of the average level of enrichment, the material might contain as little 144 kilograms of U235.  (Of course, some of the material may be of a higher enrichment.)

Moreover, in both cases, the material would need to be further enriched to make a nuclear weapon.  If you grandmother had balls, the old saying goes, she’d have been your grandfather. A better measure of how many “bomb’s worth” of material is how many bombs one might make from the material at its existing level of enrichment – after all, one can theoretically build a bomb with material of lesser enrichment.  This would involve large amounts of fissile material in a ginormous device, but it is possible. As Frank von Hippel and Alexander Glaser demonstrate, the critical mass needed for a bomb is roughly inversely proportional to enrichment level. So at 20 percent U235, the critical mass is about 400 kilograms of HEU assuming a 5-cm-thick beryllium neutron reflector.  At 90 percent U235, the similarly reflected critical mass is 28 kg.*

As Matt Bunn likes to point out, the IAEA actually has a rule of thumb to estimate a “bomb’s worth” of material across different enrichment values: the notion of the effective kilogram.  In the case of uranium with an enrichment of 0.01 (1%) or greater, the IAEA calculates the number of effective kilograms in the material as “its weight in kilograms multiplied by the square of its enrichment.”  Using this method, Iran’s stockpile of 100 kg of 20 percent HEU is just 4 effective kilograms – well below the 25 kilogram “significant quantity” threshold.  Similarly, the 400 kilograms of “HEU” removed since the last nuclear security summit, again assuming an average enrichment level of 36 percent, could shrink to a mere 52 effective kilograms – just enough for two significant quantities.

This is the correct way to do these calculations.  It is fine if someone wants to point out why, in a particular context, significant quantities and effective kilograms don’t capture an important feature of the real world. (Your proverbial Iranian grandmother, for example, could grow balls and further enrich her stockpile of uranium.)  That’s the sort of expert discussion that makes this field interesting and fun, especially if one can make grandmother jokes.  But understanding how these measures relate to the real world is different from simply not understanding them at all.  There is a right and wrong way to use these measures.  If you don’t know the difference, stick to kilograms.

*What’s a technical gripe without a footnote? Twenty-eight kilograms of 90 percent HEU just happens to be almost exactly one Significant Quantity.  (Such material would contain 25 kilograms of U235.)  Although one would expect the reflected critical mass of weapons-grade highly enriched uranium to be very similar to a Significant Quantity, the fact that they are identical is just a coincidence.  The IAEA Significant Quantity is not a critical mass calculation.  A panel of experts recommended twenty-five kilograms to the IAEA.  We know they included an allowance for material lost to processing, but the three of us have not seen further discussion about device design. We are comparing apples to, well, applesauce.  But it’s still nice the numbers are copacetic.