The modified Berggren formula was developed in the early 1950s to address the shortcomings of the Stefan formula. The modified Berggren formula assumes that the soil is a semiinfinite mass with uniform properties and existing initially at a uniform temperature (T_{i}). It is further assumed that surface temperature is suddenly changed from T_{i} to T_{s} (below freezing). The modified Berggren formula is simply the Stefan formula corrected for the effects of temperature changes in the soil mass:
where:  x  =  depth of freeze or thaw, (ft)) 
λ  =  dimensionless coefficient which takes into consideration the effect of temperature changes in the soil mass (i.e., a fudge factor). Corrects the Stefan formula for the neglected effects of volumetric heats (accounts for “sensible heat” changes)  
k_{avg}  =  thermal conductivity of soil, average of frozen and unfrozen (BTU/hr • ft • °F) 

n  =  conversion factor for air freezing (or thawing) index to surface freezing (or thawing) index 

FI  =  air freezing index (°F • days)  
TI  =  air thawing index (°F • days)  
L  =  latent heat (BTU/ft^{3}) 
Determination of λ
l can be determined by chart (Figure 1) based on inputs of a (thermal ratio) and m (fusion parameter).
λ  =  f (FI (or TI), mean annual air or ground temperature, thermal properties of soil) 
=  f(m,a) and can be read from Figure 1  
μ  =  fusion parameter 
C  =  average volumetric heat capacity of a soil (BTU/ft^{3} • °F) 
L  =  latent heat (BTU/ft^{3}) 
=  surface freezing (or thawing) index, nFI (or nTI) divided by length of freezing (or thawing) season. Represents temperature differential between average surface temperature and 32 °F taken over the entire freeze (or thaw) season.  
=  
d  =  length of freezing or thawing duration. For example, if the winter freezing season is December through February, then the duration of freezing (d) equals about 90 days. 
T_{f}  =  32 °F 
T_{s}  =  average surface temperature for the freezing (or thawing) period 
α  =  thermal ratio 
T  =  average annual air or ground temperature 
T – T_{f}  =  represents the amount that the mean annual temperature exceeds (or is less than) the freezing point of the soil moisture (assumed to be 32 °F). 
Modified Berggren Formula Example
Determine the depth of frost penetration into a homogeneous sandy silt for the following conditions:
Given:
 Mean annual temperature = 48 °F
 Surface freezing index = nFI = 750 °F • days
 Duration of freezing season = d = 100 days
 Soil properties:
 Dry density = g_{d }= 100 lb/ft^{3}
 Water content = w = 15% ‘‘
Solution
 Calculate soil thermal properties
Volumetric latent heat of fusion:
L = (144 BTU/lb) (100 lb/ft^{3}) (15/100) = 2160 BTU/ft^{3}
Average volumetric specific heat:
C_{avg} = 100 (lb/ft^{3}) (0.15) = 28.2 BTU/ft^{3 }• °F
Average thermal conductivity:
k_{f} @ 0.80 BTU/hr • ft • °F (refer to Frost Terminology page Figure 1 (left graph))
k_{u} @ 0.72 BTU/hr • ft • °F (refer to Frost Terminology page Figure 1 (right graph)
Therefore, k_{avg} = 0.76 BTU/hr • ft • °F
 Calculate λ (recall λ = f(α, μ))
From the chart, λ= 0.74
 Calculate depth of freezing