Blast Radius Calculator

Estimate fireball and shockwave radii for nuclear explosions based on yield (TNT equivalent). Uses empirical cube‑root scaling.

Cube‑root scaling: R = R₀ · (W / W₀)1/3

where R is radius, W is yield in kilotons TNT. Reference values (1 kt):

  • Fireball (peak) ~ 130 m
  • 5 psi overpressure ~ 470 m (severe damage)
  • 1 psi overpressure ~ 1500 m (glass breakage)
Yield in TNT equivalent.
0.3 kt 15 kt 1 Mt
Computing...

Understanding Blast Radii

The effects of a nuclear explosion scale with the cube root of the yield – a consequence of the energy being released in a volume. This means that doubling the yield increases the radius of a given effect by only about 26% (21/3 ≈ 1.26). The empirical reference values used here (1 kt: fireball 130 m, 5 psi 470 m, 1 psi 1500 m) are derived from declassified data in The Effects of Nuclear Weapons (1950s–60s) and are typical for a surface burst.

Overpressure levels – what they mean

  • 20 psi (138 kPa): Heavily reinforced concrete structures severely damaged or demolished. Near‑total casualties.
  • 10 psi (69 kPa): Multi‑story buildings collapse; severe lung damage possible.
  • 5 psi (34 kPa): Residential buildings collapse; widespread injuries. This is often used as the threshold for “severe damage” in nuclear planning.
  • 2 psi (14 kPa): Moderate damage – roofs peel, walls crack.
  • 1 psi (6.9 kPa): Glass windows break; light injuries from flying debris.

Fireball: The luminous sphere of hot gases. At peak size, its radius for a surface burst is roughly 130 · W1/3 meters (W in kt).

The Cube‑Root Law & Scaling Parameter

In blast physics it is common to use the scaled distance:

Z = R / W1/3

where R is the actual distance (m) and W the yield (kt). For a given overpressure, Z is approximately constant. For example, the 5 psi overpressure corresponds to Z ≈ 470 m/kt1/3. Once Z is known, the radius for any yield is simply R = Z · W1/3. This scaling holds over a wide range of yields (from ~0.001 kt to 100 Mt) and is a direct consequence of the self‑similarity of strong explosions (Sedov–Taylor similarity).

Surface Burst vs. Air Burst

  • Surface burst: The fireball touches the ground, crater forms, and the blast wave is hemispherical. This calculator assumes surface burst – a conservative baseline for ground damage.
  • Air burst (optimized height): The fireball does not contact the ground, but the shock wave reflects and merges (Mach reflection), producing a larger low‑pressure radius (e.g., 5 psi radius can be 20‑30% larger). However, the fireball’s thermal pulse affects a wider area.

Illustrative Radii for Selected Yields

Yield Fireball 5 psi (severe damage) 1 psi (glass breakage)
0.1 kt 60 m 220 m 700 m
1 kt 130 m 470 m 1.50 km
10 kt 280 m 1.01 km 3.23 km
100 kt 600 m 2.18 km 6.97 km
1 Mt 1.30 km 4.70 km 15.0 km
10 Mt 2.80 km 10.1 km 32.3 km
50 Mt 4.79 km 17.3 km 55.4 km

Values are rounded. For 1 Mt, the 5 psi radius is ~4.7 km – an area of nearly 70 km² subjected to severe damage.

Limitations & Further Effects

  • Thermal radiation: Can ignite fires and cause burns far beyond the 1 psi radius. Scaling for thermal effects is different (roughly as W1/2).
  • Ionizing radiation: Initial neutron/gamma rays are important only for low‑yield weapons (<10 kt) and within ~1 km.
  • Terrain & atmosphere: Hills, buildings, and weather can locally amplify or reduce blast.
  • Weapon design: The reference radii assume a “typical” fission/fusion weapon. Modern low‑yield or enhanced‑radiation designs may differ.

Calculator Assumptions:

  • Reference radii for 1 kt surface burst: fireball = 130 m, 5 psi = 470 m, 1 psi = 1500 m.
  • Cube‑root scaling is applied for other yields.
  • Valid for yields from ~0.001 kt to 100 Mt (extrapolated).
  • Radii are shown in meters or kilometers for readability.

Frequently Asked Questions

TNT equivalent is a convention for expressing the energy released in explosions. 1 ton of TNT = 4.184 × 10⁹ J. Nuclear weapon yields are commonly given in kilotons (kt) or megatons (Mt) of TNT equivalent.

The energy is released in a volume; the destructive effect propagates outward in three dimensions. For a given overpressure, the radius scales as the cube root of the energy (yield). This is a fundamental property of point explosions (Sedov–Taylor scaling).

The values are based on declassified data from 1950s–60s tests and are reasonably accurate for rough estimates. Modern weapon designs may have different efficiencies, but the cube‑root scaling remains valid.

For an air burst (optimised height), the 5‑psi radius can be about 20‑30% larger, but the fireball does not touch the ground. This calculator assumes a surface burst, which is a common baseline for damage studies.