Available with Spatial Analyst license.

Available with Image Analyst license.

The Math toolset contains tools that perform mathematical operations on rasters.

The tools are grouped into four main categories:

**Math**The tools at the top level of the math toolset perform basic mathematical operations on rasters in the following categories: Arithmetic, Power, Exponential, and Logarithmic. Also included are tools that alter the sign of the raster values, as well as those involved in converting the values between integer and floating point.

**Conditional**The Conditional math toolset allows you to control the output values based on the conditions placed on the input values.

**Logical**The Logical math toolset contains tools for performing logical evaluations on rasters in the following categories: Bitwise, Boolean, Combinatorial, Relational, and Conditional.

**Trigonometric**The Trigonometric math toolset contains tools for trigonometric calculations in several categories: Regular, Inverse, Hyperbolic, and Inverse Hyperbolic.

##### License:

The Math tools are also available if you have a Spatial Analyst extension license.

Certain Math tools are also available with a 3D Analyst extension license. These tools are: Divide, Float, Int, Minus, Plus, and Times.

The following table lists the available Math toolsets and provides a brief description of each.

Tool | Description |
---|---|

General Math toolset | The general Math tools apply a mathematical function to the input. These tools fall into several categories. The arithmetic tools perform basic mathematical operations, such as addition and multiplication. There are tools that perform various types of exponentiation operations, which includes exponentials and logarithms in addition to the basic power operations. The remaining tools are used either for sign conversion or for conversion between integer and floating point data types. |

Conditional Math toolset | The Conditional Math tools allow you to control the output values based on the conditions placed on the input values. The conditions that can be applied are of two types, those being either queries on the attributes or a condition based on the position of the conditional statement in a list. |

Logical Math toolset | The Logical Math tools evaluate the values of the inputs and determine the output values based on a defined logic. The tools are grouped into four main categories: Bitwise, Boolean, Combinatorial, Logical, and Relational. |

Trigonometric Math toolset | Trigonometric Math tools perform various trigonometric calculations on the values in an input raster. |

## The general Math tools

The following applies only to the tools at the top level of this toolset. For more details on the others, go to the appropriate sections for the Conditional, Logical and Trigonometric mathematical operations.

The general Math tools apply a mathematical function to the input. These tools fall into several categories. The arithmetic tools perform basic mathematical operations, such as addition and multiplication. There are tools that perform various types of exponentiation operations, which includes exponentials and logarithms in addition to the basic power operations. The remaining tools are used either for sign conversion or for conversion between integer and floating point data types.

Certain tools require two inputs:

- Arithmetic: Plus, Minus, Times, Divide, Mod (modulus), Negate
- Power: Power

While other tools only need a single input:

- Arithmetic: Negate
- Exponential: Exp, Exp2, Exp10
- Logarithmic: Ln, Log2, Log10
- Power: Square, Square Root
- Sign: Abs, Negate
- Type conversion: Float, Int, Round Down, Round Up

The following table lists the available general Math tools and provides a brief description of each:

Tool | Description |
---|---|

Calculates the absolute value of the cells in a raster. | |

Divides the values of two rasters on a cell-by-cell basis. | |

Calculates the base e exponential of the cells in a raster. | |

Calculates the base 10 exponential of the cells in a raster. | |

Calculates the base 2 exponential of the cells in a raster. | |

Converts each cell value of a raster into a floating-point representation. | |

Converts each cell value of a raster to an integer by truncation. | |

Calculates the natural logarithm (base e) of cells in a raster. | |

Calculates the base 10 logarithm of cells in a raster. | |

Calculates the base 2 logarithm of cells in a raster. | |

Subtracts the value of the second input raster from the value of the first input raster on a cell-by-cell basis. | |

Finds the remainder (modulo) of the first raster when divided by the second raster on a cell-by-cell basis. | |

Changes the sign (multiplies by -1) of the cell values of the input raster on a cell-by-cell basis. | |

Adds (sums) the values of two rasters on a cell-by-cell basis. | |

Raises the cell values in a raster to the power of the values found in another raster. | |

Returns the next lower integer value, just represented as a floating point, for each cell in a raster. | |

Returns the next higher integer value, just represented as a floating point, for each cell in a raster. | |

Calculates the square of the cell values in a raster. | |

Calculates the square root of the cell values in a raster. | |

Multiplies the values of two rasters on a cell-by-cell basis. |