References:

The Nukes We Need: Preserving the American Deterrent by Keir A. Lieber and Daryl G. Press (PDF Link)

MS Excel 97-2003 Worksheet with pre-worked out equations based on this page available HERE.

Converting from CEP (Circular Error Probable) to R95

The Circular Error Probable is actually the radius in which 50% of all weapons fired would land. The 95% Radius (R95) is the radius in which pretty much all of the weapons would land. To convert from CEP to R95; use the following formula:

R95 = CEP * 2.1

Calculating the Single Shot Survivability Probability (SSPS)

SSPS: 0.5 ^{(LR/CEP)^2}

Where:

LR = Lethal Radius
CEP = Circular Error Probability

Example:

A missile with a CEP of 1,000 meters is attacking a hardened target. The lethal radius of the warhead against that type of target is about 250 meters. What is the SSPS?

0.5 ^{(250/1000)^2} = 0.957603 or 95%

Calculating the Lethal Radius of a Warhead versus a Target for a Groundburst

LR = 2.62 * Y^(1/3) / H^(1/3)

Where:

Y = Yield in Megatons
H = Hardness of target in PSI
LR = Lethal Radius expressed in nautical miles.

Example:

A nuclear warhead with a yield of 1.2 megatons is attacking a target with a hardness of 10 PSI. What is the Lethal Radius?

Y: 1.2^(1/3) = 1.062659
H: 10^(1/3) = 2.154435

2.62 * (1.062659 / 2.154435) = 1.29 nautical miles

Calculating the Single Shot Probability of Kill (SSPK)

SSPK: 1 – 0.5 ^{(LR/CEP)^2}

Where:

CEP: Circular Error Probable
LR: Lethal Radius

Note: The measurements can be in Feet/Meters/Nautical miles; but the measurement system must be consistent for both variables!

Example:

A Nuclear missile with a CEP of 1.39 nautical miles and a Lethal Radius of 1.29 nautical miles is attacking a point target. What is the SSPK?

1 – 0.5 ^{(1.29/1.39)^2} = 0.4495 or 44.95%

Calculating the Terminal Kill Probability (TKP)

TKP = R * SSPK

Where

R = Probability of the Delivery System AND warhead functioning correctly.
SSPK: Single Shot Probability of Kill

Calculating the Kill Probability for multiple warheads

p(kill)_n = 1 – (1-TKP)ⁿ

Where:

TKP = Terminal Kill Probability
n = Amount of weapons targeted on target.

Example:

Five warheads are fired at a target for which the TKP of each individual warhead is 25%. What is the P(kill)_n?

1-(1-0.45)⁵ = 0.7627 or 76.27%

Computing the Equivalent Megatonnage (EMT) of a Weapons System

EMT = N x Y^2/3

Where:

EMT: Equivalent Megatonnage against Soft Targets
N: Number of Re-Entry Vehicles or Bombs carried
Y: Yield of each bomb or re-entry vehicle in megatons

Example:

The SS-90 SYPHILLIS missile carries 30 x 550 kiloton warheads. What is it's EMT?

30 x 0.55^2/3 = 20.14 Megatons of EMT