Issue 057 - Military spending - Personnel-cost scaling
How large is $38 billion in military terms?
The Congressional Budget Office estimates that U.S. combat operations against Iran cost the Department of Defense about $38 billion through August 1, 2026. That includes expended munitions, lost equipment, additional flying hours, operations, and fuel.
The problem
Estimate how many full years of supporting one active-duty U.S. service member would be equivalent to $38 billion.
Rather than considering only salary, estimate the broader annual cost associated with maintaining a service member, including pay and benefits, housing and healthcare, training, equipment and supplies, transportation, and the military infrastructure and support personnel required to keep that person operational.
Then estimate what fraction of the entire active-duty U.S. military could theoretically be supported for one year by $38 billion.
As an extension, CBO estimates continued operations could cost roughly $2 billion per month at lower combat intensity or $3 billion per month at a higher level similar to July 2026. Estimate how many additional service-member-years of military resources are consumed for every month the conflict continues at those rates.
Because Fermi problems target an order of magnitude, I normally use no more than two significant digits and write most calculations in scientific notation; the Fermi reference explains both conventions.
Before checking sources
Matt's first pass
I considered salary, BAH, food, healthcare, training, and fuel or transportation.
I assumed an average salary of about $50,000 annually, BAH of $12,000, food of $20,000, healthcare of $3,000, training of $5,000, and fuel or transportation of $3,000. That gives a combined estimated annual total of about $93,000 per soldier.
annual support cost
~= $50,000 + $12,000 + $20,000 + $3,000 + $5,000 + $3,000
~= $93,000 per soldier-year
~= $9.3 x 10^4 per soldier-yearDivided into $38 billion, that would support about 400,000 soldiers for a year.
service-member-years
~= $3.8 x 10^10 / $9.3 x 10^4
~= 4 x 10^5 service-member-yearsIf my memory is correct, across all branches of the military there are about 1.2 to 1.4 million active-duty personnel, so if the $38 billion was applied just to personnel support, it would sustain about one-third to one-fourth of the active-duty force for a year.
Calibration Score
Matt's Calibration Score: 55 / 100
Higher is better: earn points for accurate pegs, sound models, correct math, and a result close to the sourced answer. The image shows percent full of it: 100 minus the Calibration Score.
Pegs: 10/30. The active-duty-force size was strong, but the annual support cost per service member was low by about a factor of two because operational and institutional support costs were thinly counted.
Model: 15/30. Dividing war cost by service-member-year cost is the right equivalence model, but the first pass leaned too much toward individual support costs rather than broader military support cost.
Math: 10/10. The arithmetic was clean.
Result: 20/30. The final service-member-year estimate was high by about a factor of two, which is comfortably within one order of magnitude.
Grounding facts
CBO estimates that U.S. combat operations against Iran cost DoD about $38 billion through August 1, 2026. CBO says that reflects replacement of expended munitions and equipment lost in battle, increased flying hours, other operations, and increased fuel costs.
CBO also estimates that continued operations would cost about $2 billion per month at a lower level of violence, or about $3 billion per month if intensity returned to roughly the July 2026 level.
CBO's Atlas of Military Compensation reports that the President's 2026 budget request included about $277 billion in DoD military compensation. USAFacts, using Defense Manpower Data Center data, reports about 1.35 million active-duty troops in March 2026.
The CBO cost report notes an important boundary: the $38 billion estimate does not include basic operating costs of military forces already accounted for in the federal budget. So the calculation below is a scale comparison, not a claim that those exact normal support-years were unfunded or displaced.
After checking sources
Check and recalibrate
Matt's first pass correctly avoided salary-only thinking, but the corrected estimate needs a wider support-cost peg. A service member is not just paid; the military also pays for healthcare systems, family support, housing allowances, training pipelines, unit support, base operations, civilian staff, contractors, equipment upkeep, transportation, and administration.
A simple sourced peg is CBO's DoD military-compensation figure divided by the active-duty force size. That is imperfect because the compensation budget is not only a clean active-duty-support numerator, but it is a useful Fermi anchor for "not just salary."
annual broad support cost per active-duty equivalent
~= $2.77 x 10^11 / 1.35 x 10^6
~= $2.1 x 10^5 per service-member-yearRound that to $200,000 per service-member-year. That is about twice Matt's $93,000 estimate, which matches his post-check assessment: the individual line items were plausible, but operational and institutional support were undercounted.
Now convert CBO's $38 billion cost estimate:
service-member-years equivalent
~= $3.8 x 10^10 / $2 x 10^5
~= 1.9 x 10^5 service-member-yearsSo the best compact answer is about 200,000 active-duty support-years. That is not millions of personnel-years, but it is also far more than a small unit. It is the scale of supporting a very large fraction of one service branch for a year.
Compare that with the whole active-duty force:
fraction of active-duty force
~= 1.9 x 10^5 / 1.35 x 10^6
~= 1.4 x 10^-1
~= 14%That is roughly one-seventh of the active-duty force for a year. Matt's one-fourth to one-third estimate was high because the denominator was too low, but it was in the right order of magnitude.
For the monthly extension:
low-intensity month
~= $2 x 10^9 / $2 x 10^5
~= 1 x 10^4 service-member-years/month
higher-intensity month
~= $3 x 10^9 / $2 x 10^5
~= 1.5 x 10^4 service-member-years/monthSo each additional month at CBO's projected rates is equivalent to about 10,000 to 15,000 active-duty support-years.
The scale lesson is a little subtle. CBO's $38 billion combat-cost estimate is not a full military budget and does not include normal baseline support costs already in DoD's budget. But as a comparison, it is about the same magnitude as supporting hundreds of thousands of active-duty service members for a year, not merely tens of thousands and not millions.
Post-check reflection
Matt's reflection
My estimate for per-soldier support cost was about half what it should have been because I left out operational costs. As a consequence, my total service members supported by $38 billion was about double what it should have been.
Regarding active-duty service members, I did not use an estimation strategy, I just had a recollection of that number.
While it is interesting to put the spend in terms of soldier support, those soldiers are being supported by defense spending anyway, as a consequence of their being active duty, so this is on top of that existing spending. So this is an increase of about one-sixth of what the DOD was spending anyway, which does not seem terribly high.
Recommended memory peg
For U.S. military personnel-scale comparisons, remember: the active-duty force is about 1.3 x 10^6 people, and a broad active-duty support-year is on the order of $2 x 10^5. At that peg, $1 billion buys about 5,000 service-member-years.
Reader results
Bars show how submitted estimates sort into the answer choices from the gut-check prompt.