Nuclear weapons are described by a single number — yield, in kilotons or megatons of TNT equivalent. But yield does not translate directly into damage radius. A weapon ten times more powerful than another is only roughly 2.15 times as wide in its blast effects. [1] This counterintuitive scaling shapes everything from arsenal design to targeting strategy.
What "yield" actually measures
Nuclear yield is the total energy released by a weapon, expressed in TNT equivalent: 1 kiloton equals 1,000 tons of TNT, or 4.184 × 10¹² joules. [2] The Hiroshima bomb released 15 kilotons; Tsar Bomba released 50,000 kilotons; modern strategic warheads typically release 100–500 kilotons. [3]
But that energy is distributed across multiple effects. For a fission weapon exploded in the air below about 40,000 ft, roughly 50% of the energy goes into blast, 35% into thermal radiation, 5% into initial nuclear radiation and 10% into residual (delayed) radiation, carried mainly by fallout. [2] The exact split depends on burst altitude and weapon design.
The cube-root scaling law
Blast overpressure radius scales with the cube root of yield. The reason is geometric: the energy released expands roughly as a sphere, so the volume scales linearly with energy and the radius scales as the cube root of the volume. Specifically, the radius for a given overpressure (5 PSI, 1 PSI, etc.) grows as yield to the one-third power. [1]
In practice, this means a 100-kiloton weapon has a 5 PSI radius of about 2.9 km. A 1-megaton weapon (10× more energy) has a 5 PSI radius of about 6.2 km, only about 2.15× larger. To double the blast radius, you need to multiply yield by about 8. [4]
Thermal radiation scales differently
Thermal radiation radius grows roughly as yield to the 0.4 power, slightly faster than blast (yield to the 1/3 power). [4] This is because thermal energy is delivered as a brief flash that radiates more efficiently to longer distances. For very large weapons, the thermal radius can exceed the blast radius. Tsar Bomba's blast wave broke windows hundreds of kilometers away, reportedly up to about 900 km. [5]
For most modern strategic weapons (100 kt to 1 Mt), thermal and blast radii are comparable. The differences become noticeable only for very small (sub-kiloton) or very large (multi-megaton) weapons.
Air burst vs surface burst
The same weapon produces different effects depending on detonation altitude. An air burst — detonated above the ground at the optimal altitude — maximizes the area affected by blast and thermal radiation, because the shock wave reflects off the ground and reinforces the direct wave (the "Mach stem" effect). Air bursts produce minimal fallout because the fireball does not touch the ground.
A surface burst — detonated at ground level — produces a smaller blast radius than an air burst at the optimum height, for most overpressures, because much of the bomb's energy goes into cratering and ground shock. [1] But the fireball touches the ground and vaporizes soil, lofting it into the upper atmosphere as radioactive fallout. Surface bursts produce heavy lethal fallout plumes that drift far downwind; fallout from the Castle Bravo test contaminated an area more than 530 km long. [6]
Hiroshima and Nagasaki were both air bursts, optimized for area destruction at the cost of fallout. Surface bursts are typically reserved for hardened targets — missile silos, command bunkers, deep-buried command-and-control nodes.
Why arsenals shrunk in yield
Cold-War arsenals featured single warheads in the multi-megaton range — the W53 warhead on the Titan II missile yielded 9 megatons. [7] Modern arsenals have moved to lower yields (100-500 kt) for two reasons. First, MIRVing — putting multiple warheads on one missile — works better with smaller, lighter warheads. A Trident II can carry up to eight W88 warheads (about 455 kt each) instead of one large warhead. [3]
Second, accuracy improved dramatically. Early ICBMs could land within a kilometer or two of target; modern ICBMs are very accurate, with accuracy given as circular error probable (CEP), the radius within which half the warheads are expected to land. [8] With high accuracy, a smaller warhead does the same damage to the target while reducing collateral effects. The cube-root scaling means that the blast radius of a 455 kt warhead is "only" about 4.8 km for the 5 PSI zone — but that is more than enough to destroy any city center if the missile lands accurately. [4]
How the simulator uses these formulas
The radii come from the scaling laws in The Effects of Nuclear Weapons (Glasstone & Dolan, 1977) and the standard scaling-law table derived from it. The fireball radius is computed as about 0.061 × yield_kt^0.4 km (from Glasstone & Dolan §2.127); blast and burn radii are interpolated from a published table of ranges for 1 kt to 20 Mt air bursts. [9] See the full methodology page for all formulas.
These formulas are calibrated against decades of nuclear test data. They idealize conditions — flat terrain, clear weather, no buildings — but provide a useful first-order picture of nuclear effects. Real-world casualties depend strongly on time of day, sheltering, building construction, and weather. The simulator's number should be interpreted as an order-of-magnitude estimate, not a precise prediction.