# How the relational math tools work

The relational math tools compare the values of inputs and return the results as a Boolean value of 0 for False and 1 for True. The input rasters are tested on a cell-by-cell basis.

There are six tools for performing relational logical operations: Equal To, Not Equal, Greater Than, Greater Than Equal, Less Than, and Less Than Equal.

## Relational tool logic

### Equal To

If both values are equal, the output is 1. If the values are not equal, the output is 0.

``` Input1 = Input2, Output = 1
Input1 ≠ Input2, Output = 0```

### Not Equal

If both values are not equal, the output is 1. If the values are equal, the output is 0.

``` Input1 = Input2, Output = 0
Input1 ≠ Input2, Output = 1```

### Greater Than

If the first input is greater than the second, the output is 1. If not, the output is 0.

``` Input1 > Input2, Output = 1
Input1 = Input2, Output = 0
Input1 < Input2, Output = 0```

### Greater Than Equal

If the first input is greater than or equal to the second, the output is 1. If not, the output is 0.

``` Input1 > Input2, Output = 1
Input1 = Input2, Output = 1
Input1 < Input2, Output = 0```

### Less Than

If the first input is less than the second, the output is 1. If not, the output is 0.

``` Input1 > Input2, Output = 0
Input1 = Input2, Output = 0
Input1 < Input2, Output = 1```

### Less Than Equal

If the first input is less than or equal to the second, the output is 1. If not, the output is 0.

``` Input1 > Input2, Output = 0
Input1 = Input2, Output = 1
Input1 < Input2, Output = 1```

## NoData handling

If any of the input cell values is NoData, the output value will be NoData.