Technical Note TN-119
rev 3 wh.5-06
Calculating STEL, TWA, Min, Max, And Average Values For ToxiRAE PIDs
TWA = (2 h exposed x 20 ppm)/(8 h/day) = 5 ppm-days
This document gives an overview of the general
meanings of TWA (Time-Weighted Average) and
STEL (Short-Term Exposure Limit) and gives details
on how these and other concentration data are
determined and datalogged on RAE Systems
instruments. Examples are given for the ToxiRAE
PID, Model PGM-30, through version 1.22 firmware.
Depending on the datalogging options chosen, there
may be differences between the instantaneously
displayed values and the final datalogged values, for
some instruments. All averages are calculated as
arithmetic averages, rather than geometric.
TWA vs. Running Average. Figure 2 illustrates the
difference between TWA readings and running average.
Like STEL readings, the running average concentration
(dashed line in Figure 2) tracks the instantaneous
readings and can rise and fall. In contrast, the TWA is a
cumulative dose that can never fall for the first 8 hours.
Concentration (ppm)
Introduction
Definition of TWA, STEL and Ceiling
Figures 1 and 2 give a conceptual view of TWA,
STEL and Ceiling values for a hypothetical compound
having a TWA of 10 ppm, STEL of 20 ppm, and
Ceiling of 50 ppm. Typically the TWA is the lowest
value, STEL is somewhat higher and the Ceiling is the
highest. The Ceiling is the concentration that should
never be exceeded, even for one instant.
Ceiling
50
Instantaneous
Reading
40
STEL
Reading
30
STEL
20
TWA
10
0
0
STEL. The STEL is a running average concentration
over the immediately previous 15-minute window, as
shown in Figure 1. The instantaneous concentrations
may exceed the STEL value as long as they never
exceed the Ceiling, and the 15-minute running average
never exceeds the STEL limit. If the STEL alarm is
reached, the worker must be removed from STEL
level exposure for at least one hour. Workers can be
exposed to a maximum of four STEL periods per 8
hour shift, with at least one hour between exposure
periods.
10
20
30 40 50
Time (minutes)
60
70
Figure 1. Exposure limit illustration: STEL.
35
Instantaneous
Reading
Concentration (ppm)
30
TWA. TWA is different from the other parameters
because it is an accumulated exposure dose instead of
and instantaneous or average concentration.
Although TWA is usually given in units of ppm,
which is a concentration unit, it is understood that the
actual units are equivalent to ppm-days. It is
calculated as the running average concentration times
the number of hours exposed, divided by the number
of hours in a working day. OSHA and ACGIH
define a working day as 8 hours, while NIOSH
defines it as 10 hours. Thus, if one is exposed to 20
ppm of a substance for two hours, the OSHA or
ACGIH TWA reading is calculated as:
25
STEL
20
Running Average
15
TWA Reading
TWA
10
5
0
0
2
4
6
8
10
Time (hours)
Figure 2. Exposure limit illustration: ACGIH TWA
vs. Running Average.
RAE Systems Inc.
1
3775 N. First St., San Jose, CA 95134-1708 USA
Phone: +1.888.723.8823
Email: raesales@raesystems.com
Web Site: www.raesystems.com
Technical Note TN-119
rev 3 wh.5-06
minutes in an eight-hour day (480). The TWA is
the value accumulated from the time the
instrument is turned on, until the time of the last
Minute Average; it assumes no further exposure
from then on. The TWA continues to accumulate
after eight hours until the instrument is turned off.
• Peak Value: The Peak Value is updated every
second and is the highest measured Second Value
since the unit was turned on.
ACGIH vs. OSHA TWA. The ACGIH and OSHA
methods of calculating TWA differ after 8 hours of
exposure data. The OSHA TWA is a cumulative
dose over a moving 8-hour window, whereas the
ACGIH TWA continues to accumulate even after 8
hours and can never decrease. Figure 3 shows that if
the work shift is more than 8 hours, the ACGIH
TWA continues to accumulate and can even exceed
the Peak value. In the OSHA method, however, the
TWA can not exceed the Peak value. All RAE
monitors use the ACGIH TWA method as a default.
Logged Values
The ProRAE-30 Program downloads minimum,
average and/or maximum values within a defined
datalogging period. The datalogging period is
defined as a time interval within the total datalogging
event. The user defines the datalogging period in
one-second increments from one second to one hour.
Concentration (ppm)
30
ACGIH TWA
Reading
25
20
Instantaneous
Reading
OSHA TWA
Reading
15
STEL and TWA values are not downloaded directly,
but are recalculated from the downloaded minima,
averages or maxima.
Peak
TWA
10
• The Minimum Value is the lowest Second Value
measured during each datalogging period.
5
• The Average Value is the arithmetic average of all
Second Values measured during each datalogging
period.
0
0
10
20
30
Time (hours)
40
• The Maximum Value is the highest Second Value
measured during each datalogging period.
Figure 3. ACGIH TWA can exceed the Peak value if
readings are accumulated for more than 8 hours.
• The STEL is calculated as the average of the
maximum logged results of the previous fifteenminute window:
__Σ (All max logged values in last 15 min)__
# values in 15 min = (15 * 60) / period (sec)
ToxiRAE Displayed Values
• Second Values: Every second, the signal is
sampled for several milliseconds and the data are
averaged to give the instantaneous reading.
• Minute Average: The Second Values are added to
a running sum and every minute this sum is
divided by 60 to obtain a minute average. The
Minute Average is not displayed, but is used to
calculate the TWA and STEL. The Second Value,
after being used to calculate the Minute Average,
is overwritten when the next instantaneous reading
is made.
• STEL: The Minute Average values are then stored
in a rolling buffer for fifteen minutes to calculate
the STELs and then overwritten. The STEL is
updated every minute as an average of the most
recent fifteen Average Minutes.
• TWA: The Minute Average values are also used to
update the TWA every minute, by adding to a
running sum and dividing by the number of
• The TWA is calculated as:
Previous TWA + max logged value * period (sec)
480 * 60
Unlike a Running Average, the ACGIH TWA is an
accumulated exposure dose, and thus the value can
never decrease.
As noted before, the logged values can be different
from the displayed values if inappropriate
datalogging parameters are chosen. The program
always uses the highest values available to calculate
the TWA and STEL. To ensure that the displayed
and logged values are identical, the user should chose
a datalogging period of fifteen minutes or less. It is
also suggested that the user log average only or
average and minimum values, but not peak values.
RAE Systems Inc.
2
3775 N. First St., San Jose, CA 95134-1708 USA
Phone: +1.888.723.8823
Email: raesales@raesystems.com
Web Site: www.raesystems.com
Technical Note TN-119
rev 3 wh.5-06
Example 2 shows an improper set-up that leads to
false and missing data.
Examples
Example 1 shows how to properly set up the PGM-30
to obtain correct TWA and STEL values, and
Example ONE: Proper Set-up to Obtain Correct TWA and STEL Values
S/N: 001403
Year: 1996
Date Time
User ID: 1
Site ID: 1
Cal: 9/20 16:56 100.4 ppm
Period(s): 60 Data Pts: 40
Chk: 9/20 14:40 100.5 ppm
Min
Avg
Max High Low STEL TWA
ppm
100.0 50.0
25.0
10.0
---------------------------------------------------------------------------------------------11/05 10:52 10.7
0.7
0.0
10:53 9.7
1.4
0.0
10:54 8.7
1.9
0.1
10:55 8.0
2.5
0.1
10:56 7.4
3.0
0.1
10:57 7.0
3.4
0.1
10:58 6.7
3.9
0.1
10:59 6.4
4.3
0.1
11:00 6.2
4.7
0.1
11:01 6.0
5.1
0.2
11:02 5.8
5.5
0.2
11:03 5.7
5.9
0.2
11:04 5.5
6.3
0.2
11:05 5.4
6.6
0.2
11:06 5.3
7.0
0.2
11:07 5.2
6.6
0.2
11:08 5.1
6.3
0.2
11:09 5.0
6.0
0.2
11:10 4.9
5.8
0.3
11:11 4.8
5.7
0.3
11:12 4.7
5.5
0.3
1. Logged Avg Values only;
TWA & STEL agree with
the readout.
2. The first Fourteen minutes of
STEL values always increase
because they assume zero
concentration before the first
time point.
3. After Fifteen minutes STEL
is correct because Period <
7.5 minutes and divides
evenly into Fifteen.
Example TWO: Improper Set-up to Obtain Correct TWA & STEL
S/N: 001403
Year: 1996
Date Time
User ID: 1
Site ID: 1
Cal: 6/20 45:29 106.6 ppm
Period(s): 600 Data Pts: 11
Chk: 4/3 15:41 100.3 ppm
Min
Avg
Max High Low STEL TWA
ppm
100.0 50.0
25.0
10.0
---------------------------------------------------------------------------------------------5/10 11:24 2.7
3.6
3.6
0.1
11:34 1.7
2.7
2.7
0.2
11:44 1.6
2.7
2.7
0.2
11:54 2.2
4.4
4.4
0.3
12:04 3.9
4.6
4.6
0.4
12:14 4.1
5.4
5.4
0.5
12:24 2.9
3.8
3.8
0.6
12:34 1.4
1.9
1.9
0.6
12:44 2.2
4.0
4.0
0.7
12:54 3.0
3.9
3.9
0.8
13:04 1.8
3.8
3.8
0.9
1. Logged Avg & Max values;
TWA & STEL differ from
the readout because they are
calculated from Max values.
2. Period > 7.5 minutes; STEL
does not average the last
Fifteen minutes correctly;
it only tracks the Max value.
RAE Systems Inc.
3
3775 N. First St., San Jose, CA 95134-1708 USA
Phone: +1.888.723.8823
Email: raesales@raesystems.com
Web Site: www.raesystems.com