Entering values or using a field are not the only way you can specify the size of a buffer using GeoAnalytics Tools. In some cases, you might want to perform a mathematical calculation to set the buffer size. You can perform simple and advanced calculations that can be applied to all records. This calculation is applied to each feature. The sections below include examples of using a buffer expression. Calculations are performed when analysis is run on your ArcGIS GeoAnalytics Server.
At ArcGIS Enterprise 10.6 and later, expressions are formatted using Arcade expressions. Using Arcade, field names are formatted as $feature["field name"] or $feature.fieldname. The first option, $feature["field name"], is required when a field name includes a space. All examples below use this option. GeoAnalytics Server does not use Arcade expressions at Enterprise 10.5 or 10.5.1.
Learn more about Buffer expressions supported at 10.5 and 10.5.1
Learn more about Arcade expressions
Buffer expressions are used by the Reconstruct Tracks and Create Buffers tools.
The following tools use Arcade expressions in GeoAnalytics Server at Enterprise 10.6 and later:
 Reconstruct Tracks to buffer expressions
 Create Buffers to buffer expressions
 Join Features to join expressions
 Calculate Field to calculate field values
 Detect Incidents to detect incidents using start and end expressions
Mathematical operator and function examples
Buffer expressions can mathematically process numbers. The following table shows a sample of available operations.
Learn more about mathematical operations and functions in Arcade
Operator  Explanation  Example 

a + b  Returns the sum of a plus b.  fieldname contains a value of 1.5 $feature["fieldname"] + 2.5 4.0 
a  b  Returns the difference of a minus b.  fieldname contains a value of 3.3 $feature["fieldname"] 2.2 1.1 
a * b  Returns the product of a times b.  fieldname contains a value of 2.0 $feature["fieldname"] * 2.2 4.4 
a / b  Returns the quotient of a divided by b.  fieldname contains a value of 4.0 $feature["fieldname"] / 1.25 3.2 
abs( a )  Returns the absolute (positive) value of a.  fieldname contains a value of 1.5 abs($feature["fieldname"]) 1.5 
log( a )  Returns the natural logarithm (base E) of a.  fieldname contains a value of 1 log($feature["fieldname"]) 0 
sin( a )  Returns the trigonometric sine of a. The input is assumed to be an angle in radians.  fieldname contains a value of 1.5707 sin($feature["fieldname"]) 1 
cos( a )  Returns the trigonometric cosine of a. The input is assumed to be an angle in radians.  fieldname contains a value of 0 cos($feature["fieldname"]) 1 
tan( a )  Returns the tangent of a. The input is assumed to be an angle in radians.  fieldname contains a value of 0 tan($feature["fieldname"]) 0 
sqrt( a )  Returns the square root of a.  fieldname contains a value of 9 sqrt($feature["fieldname"]) 3 
min( a, b )  Returns the lowest valued number between a and b.  fieldname contains a value of 1.5, and a value of 3 min($feature["fieldname"], 3) 3 
max( a, b )  Returns the highest valued number between a and b.  fieldname1 contains a value of 1.5, and fieldname2 contains a value of 3 max($feature["fieldname1"], $feature["fieldname2"]) 1.5 
constrain(<value>,<low>,<high>)  Returns the input value if it's within the constraining bounds. If the value is less than the low value, it returns the low value. If the value is greater than the high value, it returns the high value.  Example 1: constrain( $feature["distance"], 0, 10) Returns 0 if distance is less than 0, 10 if distance is greater than 10, and distance otherwise. Example 2: constrain($feature['Store dist'], 6, distance) Returns 6 if Store dist is less than 6, distance if Store dist is greater than distance, and Store dist otherwise. 
Multiplication
$feature["Distance"] * 2
Logical operator examples
In addition to simple mathematical expressions, more advanced functions can be used to apply buffer expressions.
Function  Explanation  Example  Result 

iif(<condition>,<true value>,<false value>)  Returns one value if a condition evaluates to true and returns another value if that condition evaluates to false. <true value> and <false value> can be the following:
 iif($feature["field1"] > $feature["field2"], $feature["field1"], 0) iif($feature["field1"] > $feature["field2"], iif($feature["field2"] = 0, $feature["field3"], $feature["field4"]), 0)  Returns field1 if field1 is greater than field2, and 0 otherwise. Returns the result of the second iif function if field1 is greater than field2, and 0 otherwise. 
when(<expression1> , <result1> , <expression2> , <result2> , ... , <expressionN> , <resultN>, <default>)  Evaluates a series of expressions in order until one evaluates to true.
 when(($feature["field1"] + 10) > 1, 1,($feature["field2"] + 10) > 2 , 2, $feature["field3"])  If field1 + 10 is greater than 1, returns 1. If not, checks if field2 + 10 is greater than 2. If yes, it returns 2. If not, it returns field3. 
decode(<conditional val> , <case1> , <result1>, <case2>, <result2>, ... <caseN>, <resultN>, <defaultValue> )  Evaluates an expression and compares its value with subsequent parameters. If the expression matches, it returns the next parameter value. If none match, there is the option for the last parameter to be a default return value.
 decode($feature["field1"] + 3 , $feature["field1"], 1, $feature["field2"], 2, 0)  Compares equality between the conditional val field1 + 3 and case1 field1. If true, it returns 1. If false, it compares the equality between field1 + 3 and field2. If true, it returns 2; otherwise, it returns 0. 
As distance function examples
Buffer expressions can cast numeric values to a linear distance.
Function  Explanation  Example  Result 

as_meters(<value>)  Applies a calculation assuming the input values are in meters.  as_meters( $feature["fieldname"] ) as_meters(150)  Results are buffered by 150 meters. 
as_kilometers(<value>)  Applies a calculation assuming the input values are in kilometers.  as_kilometers( $feature["fieldname"] ) as_kilometers(150)  Results are buffered by 150 kilometers. 
as_feet(<value>)  Applies a calculation assuming the input values are in feet.  as_feet( $feature["fieldname"] ) as_feet(150)  Results are buffered by 150 feet. 
as_yards(<value>)  Applies a calculation assuming the input values are in yards.  as_yards( $feature["fieldname"] ) as_yards(150)  Results are buffered by 150 yards. 
as_nautical_miles(<value>)  Applies a calculation assuming the input values are in nautical miles.  as_nautical_miles( $feature["fieldname"] ) as_nautical_miles(150)  Results are buffered by 150 nautical miles. 
as_miles(<value>)  Applies a calculation assuming the input values are in miles.  as_miles( $feature["fieldname"] ) as_miles(150)  Results are buffered by 150 miles. 
Conditional operators
Conditional statements can use the following operators:
Operator  Explanation  Example  Results 

a > b a < b  a is greater than b a is less than b  10 > 2  False 
a >= b a <= b  a is greater than or equal to b a is less than or equal to b  abs(10) >= 10  True 
a != b  a is not equal to b  abs(3) != 3  True 
a == b  a is equal to b  abs(5) == 5  True 
<condition1>  <condition2>  Condition 1 or condition 2 is met.  (abs(5) == 5)  (10 < 2)  True 
<condition1> && <condition2>  Condition 1 and condition 2 are met.  (abs(5) == 5) && (10 < 2)  False 
Track aware examples
At ArcGIS Enterprise 10.6.1 or later, you can use trackaware equations in Arcade with the Reconstruct Tracks tool.
Function  Explanation  Example  Result  

TrackStartTime()  Calculates the start time of a track in milliseconds from epoch.  Using a track that starts on January 2, 2017. TrackStartTime()  1483315200000  
TrackDuration()  Calculates the duration of a track in milliseconds from the start until the current time step.  Using a track that starts on January 2, 2017, and the current time is January 4, 2017. TrackDuration()  172800000  
TrackCurrentTime()  Calculates the current time in a track.  Using a feature that occurs on January 3, 2017, at 9:00 a.m. TrackCurrentTime()  1483434000000  
TrackIndex  Returns the time index of the feature being calculated.  Calculating this value on the first feature in a track. TrackIndex  0  
TrackFieldWindow(<fieldName>, <startIndex>, <endIndex>)  Returns an array of values in the given field for the specified time index. The window function allows you to go forward and backward in time. The expression is evaluated at each feature in the track.
 MyField has sequentially ordered values of [10, 20, 30, 40, 50]. The expression is evaluated at each feature in the track. Results are returned inclusive of the start feature and exclusive of the end feature. Example 1:TrackFieldWindow("MyField,1,2) Example 2:TrackFieldWindow("MyField,2,0)[0] Example 3:TrackFieldWindow("MyField,0,3)[2]  Example 1: When evaluated at each feature, the table shows the following results.
Example 2: When evaluated at index 2 (value is 30), it returns: 10. Example 3: When evaluated at index 2 (value is 30), it returns: 50.  
TrackGeometryWindow(<startIndex>, <endIndex>)  Returns an array of values representing geometry for the specified time index. The window function allows you to go forward and backward in time. The expression is evaluated at each feature in the track.
 MyField has sequentially ordered values of [10, 20, 30, 40, 50]. The geometry of the features are [{x: 1, y: 1},{x: 2, y: 2} ,{x: null, y: null},{x: 4, y: 4}, {x: 5, y: 5}] The expression is evaluated at each feature in the track. Results are returned inclusive of the start feature and exclusive of the end feature. Example 1: TrackGeometryWindow(1,2) Example 2: TrackGeometryWindow(0,1)[0] on a polyline dataset Example 3: TrackGeometryWindow(0,1)[0] on a polygon dataset Example 4: Find the X value of the previous point TrackGeometryWindow(1,0)[0]["x"]  Example 1: When evaluated at each feature, the table shows the following results.
Example 2: Polylines are returned in the following format: [{"paths":[[[180,22.88],[177.6,23.6]],[[180,18.099999999999994],[179.7,18.4],[179.4,18.7],[178.9,18.9],[178.5,19.3],[178.2,19.7],[178.4,20],[178.8,20.2],[178.9,21.8],[179,22.2],[179.4,22.7],[180,22.88]],[[178,17],[178.8,17.3],[179.2,17.5],[179.6,17.8],[179.9,18],[180,18.099999999999994]]]}] Example 3: Polygons are returned in the following format: [{"rings":[[[7882559.1197999995,6376090.883500002],[7893142.474300001,6042715.216800004],[8544018.775999999,6045361.0554000065],[8544018.775999999,6376090.883500002],[7882559.1197999995,6376090.883500002]]]}] Example 4: Evaluated at index 2 (value is 30): 2  
TrackWindow(<value1>, <value2>)  Returns an array of values representing geometry and all attributes for the specified time index. The window function allows you to go forward and backward in time.
 MyField has sequentially ordered values of [10, 20, 30, 40, 50], in addition to the objectID, globalID, and instant_datetime fields. The geometry of the features are [{x: 1, y: 1},{x: 2, y: 2} ,{x: null, y: null},{x: 4, y: 4}, {x: 5, y: 5}]. The expression is evaluated at each feature in the track. Results are returned inclusive of the start feature and exclusive of the end feature. Example 1:TrackWindow(1,0)[0] Example 2:geometry(TrackWindow(1,0)[0]["x"]  Example 1: When evaluated at each feature, the table shows the following results.
Example 2: Evaluated at index 2 (value is 30): 2 
Use the following track expressions to calculate distance, speed, and acceleration on tracks in ArcGIS Enterprise 10.9 or later.
All distance calculations are calculated in meters, speed in meters per second, and acceleration in meters per second squared. Distances are measured using geodesic distances.
Function  Explanation 

TrackCurrentDistance()  The sum of the distances travelled between observations from the first to current observation. 
TrackDistanceAt(value)  The sum of the distances travelled between observations from the first to the current observation plus the given value. 
TrackDistanceWindow(value1, value2)  The distances between the first value (inclusive) to the last value (exclusive) in a window about the current observation (0). 
TrackCurrentSpeed()  The speed between the previous observation and the current observation. 
TrackSpeedAt(value1)  The speed at the observation relative to the current observation. For example, at value 2, it's the speed at the observation two observations after the current. 
TrackSpeedWindow(value1, value2)  The speed values between the first value (inclusive) to the last value (exclusive) in a window around the current observation (0). 
TrackCurrentAcceleration()  The acceleration between the previous observation and the current observation. 
TrackAccelerationAt(value1)  The acceleration at the observation relative to the current observation. 
TrackAccelerationWindow(value1, value2)  The acceleration values between the first value (inclusive) to the last value (exclusive) in a window around the current observation (0). 
The example calculations for distance, speed, and acceleration use examples from the following image.
Function  Example result  

TrackCurrentDistance() 
 
TrackDistanceAt(2) 
 
TrackDistanceWindow(1, 2) 
 
TrackCurrentSpeed() 
 
TrackSpeedAt(2) 
 
TrackSpeedWindow(1, 2) 
 
TrackCurrentAcceleration() 
 
TrackAccelerationAt(2) 
 
TrackAccelerationWindow(1, 2) 
