Issue 064 - Energy and defense - Kinetic energy
How much momentum and kinetic energy does a hypersonic missile carry?
North Korea recently tested a missile system it describes as hypersonic, with state-media images showing a reported speed of about 2,146 m/s while South Korea reported flight distances of roughly 450 to 600 km.
Energy and infrastructureAbout 1 minute
Sources checked September 25, 2026. Figures and circumstances may have changed.
The problem
If a missile is traveling at about 2,100 m/s, about how much kinetic energy does one missile carry?
Then compare momentum and kinetic energy with familiar vehicles, remembering that momentum scales with velocity but kinetic energy scales with velocity squared.
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.
Grounding facts
The reported speed anchor is about 2.1 x 10^3 m/s, roughly Mach 6 at ordinary atmospheric conditions. ChosunBiz reported that the North Korean image display showed 2,146 m/s, while also noting that the displayed telemetry differed from the 450 km and 600 km ranges reported by South Korea.
The exact missile type and mass are uncertain, so a checked Fermi range matters more than a single fake-precise value. CSIS Missile Threat lists the KN-23 short-range ballistic missile at about 3,400 kg. A 2026 38 North assessment cites a UN estimate of about 3,800 kg for the Hwasong-11A and discusses later evidence that some variants may be larger and heavier.
For this check, a reasonable missile-mass range is therefore a few tonnes to perhaps 10 tonnes. I will use 5 x 10^3 kg as the central value and keep the range visible.
After checking sources
Checked answer and calculation
Using a central mass of 5 tonnes and speed of 2,100 m/s:
momentum
= m x v
~= 5 x 10^3 kg x 2.1 x 10^3 m/s
~= 1.1 x 10^7 kg m/skinetic energy
= 1/2 x m x v^2
~= 0.5 x 5 x 10^3 kg x (2.1 x 10^3 m/s)^2
~= 1.1 x 10^10 J
~= 10 billion JAcross a rough 3.5-to-10-tonne missile range, that is about 8 x 10^9 to 2 x 10^10 J of kinetic energy and about 7 x 10^6 to 2 x 10^7 kg m/s of momentum.
For comparison, a passenger jet at cruise might have more momentum because it is so massive:
passenger jet momentum
~= 7 x 10^4 kg x 250 m/s
~= 2 x 10^7 kg m/sBut the missile can still carry several times the jet's kinetic energy, because velocity is squared:
passenger jet kinetic energy
~= 0.5 x 7 x 10^4 kg x (250 m/s)^2
~= 2 x 10^9 JA freight train can have much larger momentum, but at ordinary speeds its kinetic energy can still be comparable to or below the missile:
heavy freight train
momentum ~= 5 x 10^6 kg x 20 m/s ~= 1 x 10^8 kg m/s
KE ~= 0.5 x 5 x 10^6 kg x (20 m/s)^2 ~= 1 x 10^9 JThe useful lesson is not that kinetic energy alone measures military effectiveness. It does not. But speed matters brutally: if the missile's speed fell by half, momentum would fall by half, while kinetic energy would fall to one quarter. The lost kinetic energy would be about 75% of the original value.
Before checking sources
Matt's original estimate
This is the unverified estimate Matt wrote before checking sources, not the checked answer.
I assumed: the supersonic rocket is going to have a launch mass of around 10^5 kg. This could be low by an order of magnitude, but I was basing this assumption on the space shuttle launch mass of about 10^6 kg, and that a supersonic ballistic missile test launch mass would be lower than that.
Momentum = m x v, so 10^5 kg x 2.1 x 10^3 m/s gives about 2.1 x 10^8 kg m/s.
KE = 1/2mv^2, so 1/2 x 10^5 x (2.1 x 10^3)^2 = about 2.2 x 10^11 J.
Right away I can compare the KE to the energy contained in a single L of gasoline, which is about 4.5 x 10^7 J, so the KE of the supersonic missile at the given speed is about 5,000x more than that L of fuel. That feels like it might be right.
Next I wanted to compare both momentum and KE to a 1 ton car moving at highway speed, about 60 mph or about 30 m/s.
p = m x v = 10^3 x 30 m/s = about 30,000 kg m/s; so the rocket has a moment of about 7,500x greater than the car on the highway.
KE = 1/2mv^2 = 1/2 x 10^3 x 900 = about 4.5 x 10^5 J, which is 1/100th the energy of a L of gasoline, and that means the rocket has a KE of 500,000x the highway car.
Reasoning score
Matt's reasoning score: 70 / 100
Higher is better: earn points for useful facts, a sound reasoning approach, correct math, and a final estimate close to the sourced answer. The owl meter shows percent full of it: 100 minus the reasoning score.
Useful facts: 10/30. The given speed, gasoline-energy comparison, and car comparison were useful, but the missile mass peg was about an order of magnitude or more too high.
Reasoning approach: 30/30. The right physics models were used: momentum equals mass times velocity, and kinetic energy equals one half mass times velocity squared.
Math: 10/10. The arithmetic followed correctly from the stated assumptions.
Final estimate: 20/30. The kinetic-energy estimate was high by roughly one order of magnitude, but still close enough to capture the broad scale.
Post-check reflection
Matt's reflection
Looks like the main failure was the estimate for the rocket mass. It should have been about 1/10th of what I landed on - or similar to the mass of a large elephant. This is surprising to me.
Regarding the news item, I don't think this problem did much to move me on the importance of the news item. It might be interesting to see how that velocity compares to the ballistic missiles of other nations, or how it relates to defensive capabilities.
Recommended memory peg
For short-range ballistic missile scale, remember a few tonnes to 10 tonnes, not hundreds of tonnes. At hypersonic speed, velocity squared can make a few tonnes behave energetically like something much larger.
Reader results
Bars show how submitted estimates sort into the answer choices from the gut-check prompt.