RADON FLUX MEASUREMENTS AS PREDICTOR FOR
INDOOR RADON CONCENTRATIONS IN
NEW HOME RESIDENTIAL STRUCTURES
L. Moorman, Ph.D.
Radon Home Measurement and Mitigation, Inc.
Fort Collins, Colorado
USA

ABSTRACT
A method measuring vertical upwards total radon soilgas flow from the ground through
building sites before construction is investigated as a predictor for the radon
concentration inside a home after construction. The theory for this radon risk evaluation
(RRE) is derived and simple analytical and more realistic numerical examples are given.
Data obtained from short term radon tests inside homes are compared with numerical
model calculations leading to additional insights that are validating empirically the
derived connection between radon flux into the building and the radon concentrations.
Special circumstances allowed the comparison of over two orders of magnitude of radon
concentrations of finished homes with RRE radon concentrations that were obtained
following a well defined protocol. Data are presented supporting the usefulness of this
RRE-method as part of a radon resistant new home construction program. Conclusions
are summarized.

MOTIVATION AND GOAL
If radon concentrations for indoor air in finished homes could be predicted before
construction an informed decision could be made about the desirability of incorporating
Radon Resistant New Home Construction (RRNC) methods during construction [1,2,3],
In a few jurisdictions (e.g. Fort Collins, CO) codes have moved towards amending RRNC
requirements via Appendix F of the newly adopted IRC-2000 code, or a modified version,
independent of whether the house is proven to need RRNC within the framework of an
accepted action level [4]. This approach, although understandable in the absence of a
predictive method, is inefficient and unnecessary costly for those homes that do not need
a radon system below the action level.
The proposed RRE tests can be done before the critical parts of the house are built so that
RRNC methods can be incorporated to the appropriate level. If measurements are made
with low results a minimum proposed RRNC method can be implemented. If
measurements are made resulting in high values, maximum protection can be
implemented during the construction of the building. This has the advantage that the
highest efficiency for radon removal can be given to the building by a no-noise, passive,

radon mitigation system. It also means that buildings with little radon infiltration do not
need to set aside extra costs for a radon system.
The goal of this research is to investigate if it is possible and if so determine the accuracy
that can be achieved using a well defined protocol for the predictive nature of a Radon
Risk Evaluation (RRE) based on in-situ measurements. Another goal is to develop the
theoretical formalism resulting in practical graphical tools in which context these data can
be understood.

CONSTANT PARAMETER THEORY
Consider a constant average entry flow rate density, which we will refer to as the radon
flux density, of radon atoms, F, per unit of time and per unit footprint area entering a
building through openings with the soil within the footprint or ground contact area, A, of
the building. Consider furthermore a loss rate through natural radioactive decay by radon,
Γ , into its daughter element polonium-218 with known decay time scale, τ ,
1
Γ= .
(1)

τ

and an average air exchange rate of inside air with outside air, G. Both loss terms will
also be proportional to the number of radon atoms present inside the building, N. Absent
other losses, a differential equation can be written down that describes the dynamic
relationship between the number of radon atoms present in the building, N, its source and
losses leading to the rate of change per time unit given by:
dN
= AF − (Γ + G ) N
(2)
dt
Next we make the assumption that the air exchange rate G is determined by a time scale T
during which a significant part of the air volume, say a fraction 1/e, from inside the home
is exchanges with the outside air environment. Assuming furthermore that the radon in
the outside air is negligible this leads to the model parameter’s relationship:
1
G= .
(3)
T
The ‘density of radioactivity’ by radon measured in Bq/m3, is the disintegration rate of
radon nuclei and, although related, is not the same as the atomic density of radon. This
radioactivity is often referred to as the ‘average radon concentration’ in the radon
mitigation community.
N (t )
R(t ) = Γ
.
(4)
V
Similarly the “flux density of radioactivity” by radon through the footprint into the
building is given by:
ϕ (t ) = ΓF (t ) .
(5)
In practical situations we often want to know the radon concentration on the lowest level
of the building where it is frequently measured when the tester follows EPA guidelines.
The relationship to the overall average concentration can be derived and can be described

2

in terms of a simple multiplicative factor. In order to take into account appropriate
weight factors for radon concentrations measured on different floors of the same
building, µ i , and the different volumes , Vi , on different floors, the radon concentration
on the lowest floor compared to the average radon concentration for the total building is:
(6)
R1 = MR
with
V
M=
.
(7)
m
V1 + ∑ µ iVi
i =2

Depending on the type of home the described corrections can be as large as 53% for
individual cases compared to other cases underscoring the significance to obtain the
proper information from the blue prints of the home.
Another aspect that should be mentioned is that all equation so far have been expressed in
SI-units where the radioactivity density or ‘radon concentration’ R1 is expressed in
Bq/m3, all time units in seconds, all length units in meters and the radioactive flux into
the building through the footprint in Bq/m2s.
From a practical point of view we will often use different units that have become
common place in the radon literature: R1 is expressed in pCi/L, the time unit in hours
(e.g. the inverse of the air exchange time scale G in 1/hr, e.g. “air changes per hour”), and
the unit of distance in feet with the only exception that the radioactive flux into the
building through the footprint is expressed in pCi/m2s. These practical choices in units
can be accomplished by inserting the dimensionless constant ‘c’ everywhere with the
3600
(8)
radiation flux, ϕ , in the equations, where:
c =
305

When returning to the equations in SI units the constant c should simply be set to 1.
The behavior for absence of radon in the initial condition is obtained by solving equation
(2) and using (4),(6) and (8) results in the familiar exponential saturation curve
1  A
− ( Γ +G ) t
(9)
)
R1 = cM
  ϕ (1 − e


(Γ + G) V
that can be measured in a house as the example given in Fig 1 with its initial transient
time scale determined by the shorter time scale T rather than the larger time scale τ .

Eq. (9) shows that if the influx rate of radon through the footprint is known and if the
time scale for the loss through the envelope of the building structure is known as well as
the effective height of the building, the long term concentration in the building can be
calculated. This is irrespective of whether the building has been constructed yet. This
insight could make it possible to predict radon levels for buildings before their
construction by measuring flux rates and deriving the other relevant parameters from
architectural plans, even before the building is constructed.
The process of calculating the expected radon concentration will be named the radon risk
evaluation (RRE) in this manuscript since it is an attempt to calculate the best predictor

3

5

R (pCi/L)

4

3

2

1

0
0

10

20

30
Time (h)

40

50

FIG 1: Data from a CRM compared with a numerically evaluated temporal behavior for
an increasing radon concentration by radon trapped in a house with 1/G=T=10 hours
and 1/Γ=τ=3.825 days=91.8 hours. Data taken in a house that was in open conditions
before t=0 h and closed after t=0 h. Notice that the scatter of data is relatively large.
This is because the radon levels are relatively low. (Data taken with femto-Tech CRM510)
for the radon concentration in the finished building, before it is constructed. The
concentration from this calculation will be referred to as the RRE concentration. The
RRE concentration has the same unit as the radon concentration.

TIME DEPENDENT GENERALIZED THEORY
Generalizing the formalism for a time dependence of the radioactive entry flux through
the footprint of the house, ϕ (t ) = ΓF (t ) , and an additional loss factor described by a
strict positive function g(t) and other loss mechanisms, the differential equation
governing the dynamics of the radon radioactivity measured in the lowest level of the
home is:
dR1
+ γ (t ) R1 = cαϕ (t ) ,
(10)
dt
where

γ (t ) = ( Γ + G ) + g (t )

(11)
and where we introduced a parameter for the inverse of the effective height of the
building:

4

1
MA
=
,
(12)
H'
V
Equation (10) is an inhomogeneous, linear, first order differential equation that can be
solved exactly yielding the general solution:

α=

R1 (t ) = R1 (0) +

cα t
f (t ')ϕ (t ' )dt
f (t ) ∫0

(13)

with:
t

t

∫ γ ( t ') dt '

f (t ) = f (0)e 0

∫

γ + g ( t ') dt '

= f (0)e

(14)

0

Using initial conditions N(0)=0 and f(0) =1 we will discuss a few characteristic analytical
and more complicated numerical examples.
Complex looking real data can be well reproduced with a small number of degrees of
freedom using this time dependent formalism. As an example we show here how we
fitted a set of data that had a 24 hour cyclic behavior by using a sinusoidal behavior for
the
40

R (pCi/L)

30

20

10

0
0

10

20
30
Time (h)

40

FIG. 2 Sinusoidal cyclic ventilation function (g(t), red curve) allows a good twoparameter fit with data of radon concentrations, R1, measured with a CRM detector.

excess ventilation function, g (t ) , and fitting the phase (time where maximum occurs)
and amplitude (Strength of the ventilation rate). The resulting curve fits the data well as
the resulting comparison shows in Fig. 2.

5

FLUX SAMPLE TEST EQUIPMENT
Measurements were made sampling the radon flux using a multiple set of H-chambers
(960 ml) with short term electrets (HST) developed and produced by the manufacturer of
the E-PERM system. (Rad-Elec, Inc., Frederick, MD). The half-sphere like chamber (Hchamber, hat chamber[1]) with a diameter of 6 inches has a Tyvek diffusion window
instead of an open center half bottom. The chamber is vented to the sides so that it will
not accumulate the radon concentration. When the H-chamber is placed on a radon
emanating surface the radon enters through the bottom window and exits through the side
vents. The semi- equilibrium radon concentration inside the chamber is representative of
dynamic flux from the surface. The discharge rate of the electret is a measure of the
radon flux. Flux monitors were calibrated by the manufacturer using well characterized
radon flux beds at CANMET (Canada) using 7.7 ± 1.1 pCi/m2s (Flux Units). The HST
chamber-electret combinations have a sensitivity in 8 hours of 0.24 Flux Units.
A shovel and a ladder to be able to enter the space between the freshly built foundation
walls were needed to set up the measurements. A carrying case was made to include all
needed parts for 8 simultaneous measurements: 8 H-chambers, 8 electrets, one electret
reader, roll of paper towels, one cross laminated radon shield and a writing supporting
area (desk). This case was convenient in allowing us to efficiently make a single trip in
and out of the building site with analysis performed in situ instead of the arduous process
of multiple trips moving all attributes seperately in and out.

MEASUREMENT PROTOCOL
The weather conditions used for flux tests described in this manuscript are to be
moderate, not wet and not extreme, See [2]. (1) We require absence of rain for at least 12
hours before the start of flux measurements. (2) We require absence of extreme
temperatures for our region. (3) We require no frozen top soil conditions during the
measurements (4) We require no extended period of severe wind conditions (> 20 mi/hr).
(5) Tests are set up on undisturbed soil under the disturbed top layer inside the excavated
basement, crawlspace or recently poured and hardened foundation walls, before the slab
is poured and under the gravel fill, if possible. (6) Tests are not to be exposed during the
early morning hours [5].
The detection protocol developed during these measurements includes: (α) Set up two
tests for two hours side by side (2 inches apart), A, B, where the filter material of test A is
shielded with 8-mil cross laminated radon barrier material to yield a background
measurement. Test B is unshielded. Use a central location for consistent background
testing and the initial scale measurement if multiple subsequent tests are done. The first
set of two tests is to determine the order of magnitude of the flux density and whether the
use of Short or Long term tests is advisable in the next step. Thus its function is to
estimate the scale, to establish the optimal choice of the type of electrets and an estimated
optimal time exposure for all subsequent measurements on this site. (β) Based on the
outcome of (α) use all short or long term electrets in order to determine how much of the
target area we can reach, and calculate the optimal exposure duration. Given the shape of

6

the footprint choose a test location pattern that divides the total area in equal parts
causing similar weights to the individual test results. (γ) In addition to (α) place 6 tests
on a site with a footprint area up to 1500 sft and add 2 tests for every additional 500 sft
footprint.

RESULTS OF RRE MEASUREMENTS
Nine residences have been investigated that resulted in RRE values of radon
concentrations over a range of two orders of magnitude around the action level. The sites
are named alphabetically from A to I in order to protect exact locations and home owners
identities. All test locations were in three connected Counties in the Rocky Mountains
and Plains area (i.e. Larimer County CO; Albany and Laramie County, WY). The Sites
were chosen based on construction companies’ and home owners’ choice to be part of
this experiment. No attempt was made in any other way to determine the radon content
of the area prior to the RRE measurements except for site B and H due to special
circumstances as will be explained below. Post construction radon tests were two-day,
short term double simultaneous tests under closed house conditions with two E-PERM
detectors identical to the EPA-protocol for real estate transactions for this device.

0.8

7pm-1am

Flux (pCi/m^2 s)

0.7
0.6
0.5
0.4

4/3/01: 12Noon-7pm

4/2/01:
11am-6pm

0.3
0.2
0.1
0

A

B

C

D

E

F

G

H

I

J

Avg

bg

FIG 3 Radon Ground Flux measurements for site A.

As an example two residences out of the nine will here be discussed in more detail.
In residence A, a log home, (See Fig. 3) we placed the detectors on the site after
foundation walls had been constructed and before the concrete slab was poured. Two
detectors were used for the scale measurement (7 hours) and four detectors at one time
(one background and three measurements during 5.7 hours) and the same four detectors
were used the next day (6.75 hours) to avoid the early morning time period.

7

The results given in Fig. 3 shows a diagram with measured flux values based on standard
handling of SST-electrets and manufacturers calibration of reader that is used to read the
electrets. A flux measurement of this nature is based on manufacturers procedure as
described in Ref. [5]. The variation among the measurements is significant as the values
range from 0.038 to 0.63 pCi/m2s with an average of 0.25 pCi/m2s. The resulting RRE
value is 1.9 pCi/L The radon concentration measured in the basement of this house later
was found to be 4.05 pCi/L and above a crawlspace section 1.6 pCi/L. The bar diagram
shows indeed a much lower influx of radon under the crawlspace which is measurement
H. After the RRE test result was known the owner of this new home construction
building opted not to install a radon system. Based on the post construction radon test the
owner was satisfied with the final radon concentration and no further mitigation was
requested.

Flux (pCi/m^2 s)

4

3

2

1

0

A

B

C

D

E

F

Avg

bg

FIG 4 Example of Radon Ground Flux measurements with two sets
of tests seperated by a week for site H.

Residence H provided a unique opportunity to test the RRE- radon concentration
comparison. A Ranch style home without basement and sub-floor heating supply ducts
built in the 1960’s was tested for radon and came high (16.4 pCi/L). A radon mitigation
system was proposed but its implementation was delayed. A year later the home owners
decided to demolish the existing building and planned to build an entirely new residence
with basement on the same Site. Flux measurements from the ground were obtained
before the construction of the new building and these could be (a posteriori) compared
with the measurements in the original ranch style building (that had no RRNC methods
implemented). Two sets of flux measurements a week apart were performed in order to
probe for the internal consistency of measurements at different times on the same site, the
results are shown in Fig. 4. The first set of six flux measurements were 2.34 pCi/m2s
corresponding to an RRE value of 20.6 pCi/L. The second set of six measurements a
8

week later were 1.78 pCi/m2s corresponding to and RRE value of 15.2 pCi/L. Because
the old home had a ranch style without basement the volume correction factor (M) was
1.00 since grade level was the lowest level.

Radon Concentration (pCi/L)

20
15
10
5
0
0

5

10

15

20

Radon Risk Evaluation (pCi/L)

Fig. 5: Comparison via a correlation diagram for RRE measurements on sites and
Radon test values in completed buildings (blue squares). Black line: best linear fit.
Circles and triangles: various types of RRNC implemented.
.
Fig. 5 summarizes the results in a correlation diagram comparing the predicted RRE and
actual radon concentrations for homes with no mitigation installed. Only data below 20
pCi/L are shown. If the correlation had been perfect all blue squared data points would
be located on the continuous line. Further analysis using the linear regression method
shows that the best fit for the blue data points using the linear assumption is described by
the black line (with an R-squared value of 0.89). This correlation diagram indicates a
good correlation between RRE values and Radon concentrations within appropriate error
bars.
In order to obtain a separation between the measured parameter, which is the average
radon flux from the ground on the Site and a parameter that represents the building’s
dR1
= 0 to Eq. (10) or
construction characteristics we apply the steady state condition:
dt
by going to the long time limit of Eq. (9). The resulting linear relationship between

9

average radon flux through footprint and average radon concentration for an individual
home can be written as:
ϕ = XR1
(15)
with X a parameter that characterizes the building dynamics under steady state radon
flow:
( Γ + G )V 1 L
(16)
X =
= ∑ µ i [( Γ + G ) H i ]
cMA
c i =1
in which the effective height of floor i compared to the footprint is defined by:
V
Hi = i
(17)
A
The inclusion of the atomic decay rate Γ and ventilation rate G for closed building
conditions G give X the unit of a length per time, i.e. a speed. Therefore X can be
interpreted as a measure of the removal rate of radon from the building including
transportation speed with which radon on the average moves through the building as well
as the loss rate via decay to its daughter element, Po-218, inside the building.
This removal speed through the building thus contains the relevant building
characteristics. Since the radon removal speed is specific to each building, indicated here
with index j, we can make a graph of the measured fluxes ϕ j before construction against
the corresponding buildings’ radon transportation speeds Xj.
In Fig. 6 we present this graph and have included all buildings (with fluxes less than 2.5
pCi/m2s) for which RRE testing was done with the measured flux on the vertical axis and
with the effective removal speed on the horizontal axis. In this diagram the blue squares
are the data points corresponding to the various buildings discussed in the correlation
diagram. Other buildings for which post-construction concentrations could not be
compared with RRE values because Radon Resistant New Home Construction were
applied can still be shown in this type of diagram.
At this point it is helpful to recognize from Eq. (15) that for a fixed radon concentration
the relationship between flux and removal speeds is also a linear relationship:
ϕ j = R1 X j .
(18)
Thus this relationship is represented in the graph by a line through the origin with fixed
slope. The red line starting in the origin marks for all transportation speeds the
corresponding fluxes that result in a radon concentration of 4.0 pCi/L, i.e. it is the equiconcentration line for 4.0 pCi/L. The blue arrows mark the boundaries of the region
within which the radon removal speeds of all nine buildings we studied fall, although it is
not impossible for other buildings to be positioned outside these lines.
The grey arrow on the horizontal axis marks the value of the speed of radon due to
diffusion through still air [5]. From the data one can conclude that the average radon
removal speed for all buildings studied is larger than the radon diffusion speed and thus
the vertical transportation of radon in these buildings must be of different origin. This
origin is the pressure differences such as the stack effect and any other cause influencing
the buildings air exchange rate with the outside environment. As an example for a ranch
style home without basement the radon removal speed equals the diffusion speed when
the air exchange time scale is 23 hours representing an extremely airtight home.

10

2.5

Phi (pCi/m^2s)

2
1.5
1
4 pCi/L

0.5
0
0

5E-05

0.0001

0.00015

0.0002

X: Radon removal speed(m/s)

Fig. 6: Ground Flux (Radon Source) versus Radon Removal Speed (A
Building Characteristic). Buildings above the line are predicted to be
high after construction if no RRNC is applied.
Two (blue) data points have a flux value below the critical line of 4.0 pCi/L. These two
data were buildings in which the radon concentrations were measured 4.05 pCi/L and
lower. All pre-construction data points above the critical line resulted in finished
buildings with radon levels well over 4.0 pCi/L, except in those cases when RRNC
techniques were implemented.
The correlation diagram (Fig. 5) and the radon removal speed diagram (Fig. 6) are
evidence that predictions can be made when the described method with adherence to the
proposed conditions and protocol is followed, absent other abnormalities of the site not
included in this study. It has been pointed out elsewhere that the gravel fill under the
slab, when certain gravel pits are used, may add a substantial amount of radon to the final
indoor radon concentration. Such an additional effect was not included, although it is
possible to measure the radon emanation of the gravel ahead of time and apply a shift
correction to the flux on the vertical axis in Fig. (6) in order to include such an effect.
Other exceptions that are not included are results in KARST areas, where extremely large
temporal variations can occur through naturally formed pipe and cavity structures
underground.

11

CONCLUSIONS
In this presentation we have derived a theory that is shown to apply to radon risk
evaluation concentrations of future buildings based on flux sample measurements on the
pre-construction building sites. By comparing flux measurements with actual radon
concentrations of constructed buildings on these sites via a correlation diagram we have
investigated the practical appropriateness of this method. We conclude that in principle
this is a valid method when appropriate steps are taken against extreme weather
conditions that could interfere with the flux measurements. A proposed measurement
protocol is given which is the protocol adhered to by us for most of the measurements
presented in this manuscript. A graphical devise was analytically derived in which two
independent parameters are used, the measured flux from the ground, and the radon
removal speed that entirely depends on the building characteristics. It is shown that high
and low predictions based on flux measurements can easily be discerned by using this
diagram.

ACKNOWLEDGMENTS
The total set of data could not have been measured without the cooperation of several
construction companies and home owners. We thank the individual home owners. We
also thank Elk Ridge Design Builders, Inc., Delta Construction, Inc., Prima Construction,
LLC and Under the Hammer Construction, LLC. for their cooperation.

REFERENCES
[1] J.V. Livingston, W.A. Jester and P. Kotrappa, 1990 Annual Meeting of American
Nuclear Society, V. 61 p. 38-39. L. Stief, P. Kotrappa:” Passive E-PERM radon flux
monitors for measuring undisturbed radon from the ground.” Proc. International Radon
Symposium, AARST, (1996)
[2] M.E. Kitto “Relationship of Soil Radon Flux to Indoor Radon Entry Rates”.
Proc. 12th International Radon Symposium, AARST, Reno NV, (2002).
[3] William L. Nieman and Christie Trifone. “ A method for Time-integrated
measurement of radon soil gas: description and significance” Technical Note 2005.
[4] L. Moorman, ‘Lung cancer prevention through radon mitigation: Urgency and
effectiveness from a local perspective’. Proc. 14th International Conference, AARST,
Newport, RI (2004)
[5] E-Perm System Manual 1999, Part II.10B Flux 1994, Rev.Nov. 1997, Rad Elec Inc.
Frederick, Maryland.
[6] A user’s guide to vacuum technology, 2nd Ed.john F. O’Hanlon. using Table B-2 of
Diffusion parameters for all other rare gasses, an extrapolation is made for Rn based on
section 2.3. Based on this derived diffusion parameter a calculation of the speed of the
diffusion front through still air is made following Section 2.3.3. The result is that the
diffusive front through still air moves at a low speed of 4.4 10-5 m/s or 0.51 ft/hr.

12