The GNU Emacs Calculator

Calc is an advanced desk calculator and mathematical tool written by Dave Gillespie that runs as part of the GNU Emacs environment.

This manual, also written (mostly) by Dave Gillespie, is divided into three major parts: “Getting Started,” the “Calc Tutorial,” and the “Calc Reference.” The Tutorial introduces all the major aspects of Calculator use in an easy, hands-on way. The remainder of the manual is a complete reference to the features of the Calculator.

This file documents Calc, the GNU Emacs calculator, included with GNU Emacs 30.2.

Copyright © 1990–1991, 2001–2025 Free Software Foundation, Inc.

Permission is granted to copy, distribute and/or modify this document under the terms of the GNU Free Documentation License, Version 1.3 or any later version published by the Free Software Foundation; with the Invariant Sections being just “GNU GENERAL PUBLIC LICENSE”, with the Front-Cover Texts being “A GNU Manual,” and with the Back-Cover Texts as in (a) below. A copy of the license is included in the section entitled “GNU Free Documentation License.”

(a) The FSF’s Back-Cover Text is: “You have the freedom to copy and modify this GNU manual.”

Table of Contents

• 1 Getting Started

  • 1.1 What is Calc?

  • 1.2 About This Manual

  • 1.3 Notations Used in This Manual

  • 1.4 A Demonstration of Calc

  • 1.5 Using Calc

    • 1.5.1 Starting Calc
    • 1.5.2 The Standard Calc Interface
    • 1.5.3 Quick Mode (Overview)
    • 1.5.4 Keypad Mode (Overview)
    • 1.5.5 Standalone Operation
    • 1.5.6 Embedded Mode (Overview)
    • 1.5.7 Other C-x * Commands

  • 1.6 History and Acknowledgments

• 2 Tutorial

  • 2.1 Basic Tutorial

    • 2.1.1 RPN Calculations and the Stack
    • 2.1.2 Algebraic-Style Calculations
    • 2.1.3 Undo and Redo
    • 2.1.4 Mode-Setting Commands

  • 2.2 Arithmetic Tutorial

  • 2.3 Vector/Matrix Tutorial

    • 2.3.1 Vector Analysis
    • 2.3.2 Matrices
    • 2.3.3 Vectors as Lists

  • 2.4 Types Tutorial

  • 2.5 Algebra and Calculus Tutorial

    • 2.5.1 Basic Algebra
    • 2.5.2 Rewrite Rules

  • 2.6 Programming Tutorial

  • 2.7 Answers to Exercises

    • 2.7.1 RPN Tutorial Exercise 1
    • 2.7.2 RPN Tutorial Exercise 2
    • 2.7.3 RPN Tutorial Exercise 3
    • 2.7.4 RPN Tutorial Exercise 4
    • 2.7.5 Algebraic Entry Tutorial Exercise 1
    • 2.7.6 Algebraic Entry Tutorial Exercise 2
    • 2.7.7 Algebraic Entry Tutorial Exercise 3
    • 2.7.8 Modes Tutorial Exercise 1
    • 2.7.9 Modes Tutorial Exercise 2
    • 2.7.10 Modes Tutorial Exercise 3
    • 2.7.11 Modes Tutorial Exercise 4
    • 2.7.12 Arithmetic Tutorial Exercise 1
    • 2.7.13 Arithmetic Tutorial Exercise 2
    • 2.7.14 Vector Tutorial Exercise 1
    • 2.7.15 Vector Tutorial Exercise 2
    • 2.7.16 Matrix Tutorial Exercise 1
    • 2.7.17 Matrix Tutorial Exercise 2
    • 2.7.18 Matrix Tutorial Exercise 3
    • 2.7.19 List Tutorial Exercise 1
    • 2.7.20 List Tutorial Exercise 2
    • 2.7.21 List Tutorial Exercise 3
    • 2.7.22 List Tutorial Exercise 4
    • 2.7.23 List Tutorial Exercise 5
    • 2.7.24 List Tutorial Exercise 6
    • 2.7.25 List Tutorial Exercise 7
    • 2.7.26 List Tutorial Exercise 8
    • 2.7.27 List Tutorial Exercise 9
    • 2.7.28 List Tutorial Exercise 10
    • 2.7.29 List Tutorial Exercise 11
    • 2.7.30 List Tutorial Exercise 12
    • 2.7.31 List Tutorial Exercise 13
    • 2.7.32 List Tutorial Exercise 14
    • 2.7.33 Types Tutorial Exercise 1
    • 2.7.34 Types Tutorial Exercise 2
    • 2.7.35 Types Tutorial Exercise 3
    • 2.7.36 Types Tutorial Exercise 4
    • 2.7.37 Types Tutorial Exercise 5
    • 2.7.38 Types Tutorial Exercise 6
    • 2.7.39 Types Tutorial Exercise 7
    • 2.7.40 Types Tutorial Exercise 8
    • 2.7.41 Types Tutorial Exercise 9
    • 2.7.42 Types Tutorial Exercise 10
    • 2.7.43 Types Tutorial Exercise 11
    • 2.7.44 Types Tutorial Exercise 12
    • 2.7.45 Types Tutorial Exercise 13
    • 2.7.46 Types Tutorial Exercise 14
    • 2.7.47 Types Tutorial Exercise 15
    • 2.7.48 Algebra Tutorial Exercise 1
    • 2.7.49 Algebra Tutorial Exercise 2
    • 2.7.50 Algebra Tutorial Exercise 3
    • 2.7.51 Algebra Tutorial Exercise 4
    • 2.7.52 Rewrites Tutorial Exercise 1
    • 2.7.53 Rewrites Tutorial Exercise 2
    • 2.7.54 Rewrites Tutorial Exercise 3
    • 2.7.55 Rewrites Tutorial Exercise 4
    • 2.7.56 Rewrites Tutorial Exercise 5
    • 2.7.57 Rewrites Tutorial Exercise 6
    • 2.7.58 Programming Tutorial Exercise 1
    • 2.7.59 Programming Tutorial Exercise 2
    • 2.7.60 Programming Tutorial Exercise 3
    • 2.7.61 Programming Tutorial Exercise 4
    • 2.7.62 Programming Tutorial Exercise 5
    • 2.7.63 Programming Tutorial Exercise 6
    • 2.7.64 Programming Tutorial Exercise 7
    • 2.7.65 Programming Tutorial Exercise 8
    • 2.7.66 Programming Tutorial Exercise 9
    • 2.7.67 Programming Tutorial Exercise 10
    • 2.7.68 Programming Tutorial Exercise 11
    • 2.7.69 Programming Tutorial Exercise 12

• 3 Introduction

  • 3.1 Basic Commands

  • 3.2 Help Commands

  • 3.3 Stack Basics

  • 3.4 Numeric Entry

  • 3.5 Algebraic Entry

  • 3.6 “Quick Calculator” Mode

  • 3.7 Numeric Prefix Arguments

  • 3.8 Undoing Mistakes

  • 3.9 Error Messages

  • 3.10 Multiple Calculators

  • 3.11 Troubleshooting Commands

    • 3.11.1 Autoloading Problems
    • 3.11.2 Recursion Depth
    • 3.11.3 Caches
    • 3.11.4 Debugging Calc

• 4 Data Types

  • 4.1 Integers
  • 4.2 Fractions
  • 4.3 Floats
  • 4.4 Complex Numbers
  • 4.5 Infinities
  • 4.6 Vectors and Matrices
  • 4.7 Strings
  • 4.8 HMS Forms
  • 4.9 Date Forms
  • 4.10 Modulo Forms
  • 4.11 Error Forms
  • 4.12 Interval Forms
  • 4.13 Incomplete Objects
  • 4.14 Variables
  • 4.15 Formulas

• 5 Stack and Trail Commands

  • 5.1 Stack Manipulation Commands
  • 5.2 Editing Stack Entries
  • 5.3 Trail Commands
  • 5.4 Keep Arguments

• 6 Mode Settings

  • 6.1 General Mode Commands

  • 6.2 Precision

  • 6.3 Inverse and Hyperbolic Flags

  • 6.4 Calculation Modes

    • 6.4.1 Angular Modes
    • 6.4.2 Polar Mode
    • 6.4.3 Fraction Mode
    • 6.4.4 Infinite Mode
    • 6.4.5 Symbolic Mode
    • 6.4.6 Matrix and Scalar Modes
    • 6.4.7 Automatic Recomputation
    • 6.4.8 Working Messages

  • 6.5 Simplification Modes

  • 6.6 Declarations

    • 6.6.1 Declaration Basics
    • 6.6.2 Kinds of Declarations
    • 6.6.3 Functions for Declarations

  • 6.7 Display Modes

    • 6.7.1 Radix Modes

    • 6.7.2 Grouping Digits

    • 6.7.3 Float Formats

    • 6.7.4 Complex Formats

    • 6.7.5 Fraction Formats

    • 6.7.6 HMS Formats

    • 6.7.7 Date Formats

      • 6.7.7.1 ISO 8601
      • 6.7.7.2 Date Formatting Codes
      • 6.7.7.3 Free-Form Dates
      • 6.7.7.4 Standard Date Formats

    • 6.7.8 Truncating the Stack

    • 6.7.9 Justification

    • 6.7.10 Labels

  • 6.8 Language Modes

    • 6.8.1 Normal Language Modes

    • 6.8.2 C, FORTRAN, and Pascal Modes

    • 6.8.3 TeX and LaTeX Language Modes

    • 6.8.4 Eqn Language Mode

    • 6.8.5 Yacas Language Mode

    • 6.8.6 Maxima Language Mode

    • 6.8.7 Giac Language Mode

    • 6.8.8 Mathematica Language Mode

    • 6.8.9 Maple Language Mode

    • 6.8.10 Compositions

      • 6.8.10.1 Composition Basics
      • 6.8.10.2 Horizontal Compositions
      • 6.8.10.3 Vertical Compositions
      • 6.8.10.4 Other Compositions
      • 6.8.10.5 Information about Compositions
      • 6.8.10.6 User-Defined Compositions

    • 6.8.11 Syntax Tables

      • 6.8.11.1 Syntax Table Basics
      • 6.8.11.2 Precedence
      • 6.8.11.3 Advanced Syntax Patterns
      • 6.8.11.4 Conditional Syntax Rules

  • 6.9 The Modes Variable

  • 6.10 The Calc Mode Line

• 7 Arithmetic Functions

  • 7.1 Basic Arithmetic

  • 7.2 Integer Truncation

  • 7.3 Complex Number Functions

  • 7.4 Conversions

  • 7.5 Date Arithmetic

    • 7.5.1 Date Conversions
    • 7.5.2 Date Functions
    • 7.5.3 Business Days
    • 7.5.4 Time Zones

  • 7.6 Financial Functions

    • 7.6.1 Percentages
    • 7.6.2 Future Value
    • 7.6.3 Present Value
    • 7.6.4 Related Financial Functions
    • 7.6.5 Depreciation Functions
    • 7.6.6 Definitions

  • 7.7 Binary Number Functions

• 8 Scientific Functions

  • 8.1 Logarithmic Functions
  • 8.2 Trigonometric/Hyperbolic Functions
  • 8.3 Advanced Mathematical Functions
  • 8.4 Branch Cuts and Principal Values
  • 8.5 Random Numbers
    • 8.5.1 Random Number Generator
  • 8.6 Combinatorial Functions
  • 8.7 Probability Distribution Functions

• 9 Vector/Matrix Functions

  • 9.1 Packing and Unpacking

  • 9.2 Building Vectors

  • 9.3 Extracting Vector Elements

  • 9.4 Manipulating Vectors

  • 9.5 Vector and Matrix Arithmetic

  • 9.6 Set Operations using Vectors

  • 9.7 Statistical Operations on Vectors

    • 9.7.1 Single-Variable Statistics
    • 9.7.2 Paired-Sample Statistics

  • 9.8 Reducing and Mapping Vectors

    • 9.8.1 Specifying Operators
    • 9.8.2 Mapping
    • 9.8.3 Reducing
    • 9.8.4 Nesting and Fixed Points
    • 9.8.5 Generalized Products

  • 9.9 Vector and Matrix Display Formats

• 10 Algebra

  • 10.1 Selecting Sub-Formulas

    • 10.1.1 Making Selections
    • 10.1.2 Changing Selections
    • 10.1.3 Displaying Selections
    • 10.1.4 Operating on Selections
    • 10.1.5 Rearranging Formulas using Selections

  • 10.2 Algebraic Manipulation

  • 10.3 Simplifying Formulas

    • 10.3.1 Basic Simplifications
    • 10.3.2 Algebraic Simplifications
    • 10.3.3 “Unsafe” Simplifications
    • 10.3.4 Simplification of Units

  • 10.4 Polynomials

  • 10.5 Calculus

    • 10.5.1 Differentiation
    • 10.5.2 Integration
    • 10.5.3 Customizing the Integrator
    • 10.5.4 Numerical Integration
    • 10.5.5 Taylor Series

  • 10.6 Solving Equations

    • 10.6.1 Multiple Solutions
    • 10.6.2 Solving Systems of Equations
    • 10.6.3 Decomposing Polynomials

  • 10.7 Numerical Solutions

    • 10.7.1 Root Finding
    • 10.7.2 Minimization
    • 10.7.3 Systems of Equations

  • 10.8 Curve Fitting

    • 10.8.1 Linear Fits
    • 10.8.2 Polynomial and Multilinear Fits
    • 10.8.3 Error Estimates for Fits
    • 10.8.4 Standard Nonlinear Models
    • 10.8.5 Curve Fitting Details
    • 10.8.6 Polynomial Interpolation

  • 10.9 Summations

  • 10.10 Logical Operations

  • 10.11 Rewrite Rules

    • 10.11.1 Entering Rewrite Rules
    • 10.11.2 Basic Rewrite Rules
    • 10.11.3 Conditional Rewrite Rules
    • 10.11.4 Algebraic Properties of Rewrite Rules
    • 10.11.5 Other Features of Rewrite Rules
    • 10.11.6 Composing Patterns in Rewrite Rules
    • 10.11.7 Nested Formulas with Rewrite Rules
    • 10.11.8 Multi-Phase Rewrite Rules
    • 10.11.9 Selections with Rewrite Rules
    • 10.11.10 Matching Commands
    • 10.11.11 Automatic Rewrites
    • 10.11.12 Debugging Rewrites
    • 10.11.13 Examples of Rewrite Rules

• 11 Operating on Units

  • 11.1 Basic Operations on Units
  • 11.2 The Units Table
  • 11.3 Predefined Units
  • 11.4 User-Defined Units
  • 11.5 Logarithmic Units
  • 11.6 Musical Notes

• 12 Storing and Recalling

  • 12.1 Storing Variables
  • 12.2 Recalling Variables
  • 12.3 Other Operations on Variables
  • 12.4 The Let Command
  • 12.5 The Evaluates-To Operator

• 13 Graphics

  • 13.1 Basic Graphics
  • 13.2 Three-Dimensional Graphics
  • 13.3 Managing Curves
  • 13.4 Graphics Options
  • 13.5 Graphical Devices

• 14 Kill and Yank Functions

  • 14.1 Killing from the Stack
  • 14.2 Yanking into the Stack
  • 14.3 Saving into Registers
  • 14.4 Inserting from Registers
  • 14.5 Grabbing from Other Buffers
  • 14.6 Yanking into Other Buffers
  • 14.7 X Cut and Paste

• 15 Keypad Mode

  • 15.1 Main Menu
  • 15.2 Functions Menu
  • 15.3 Binary Menu
  • 15.4 Vectors Menu
  • 15.5 Modes Menu

• 16 Embedded Mode

  • 16.1 Basic Embedded Mode
  • 16.2 More About Embedded Mode
  • 16.3 Assignments in Embedded Mode
  • 16.4 Mode Settings in Embedded Mode
  • 16.5 Customizing Embedded Mode

• 17 Programming

  • 17.1 Creating User Keys

  • 17.2 Programming with Keyboard Macros

    • 17.2.1 Naming Keyboard Macros
    • 17.2.2 Conditionals in Keyboard Macros
    • 17.2.3 Loops in Keyboard Macros
    • 17.2.4 Local Values in Macros
    • 17.2.5 Queries in Keyboard Macros

  • 17.3 Invocation Macros

  • 17.4 Programming with Formulas

  • 17.5 Programming Calc, with Lisp

    • 17.5.1 Defining New Functions

    • 17.5.2 Defining New Simple Commands

    • 17.5.3 Defining New Stack-Based Commands

    • 17.5.4 Argument Qualifiers

    • 17.5.5 Example Definitions

      • 17.5.5.1 Bit-Counting
      • 17.5.5.2 The Sine Function

    • 17.5.6 Calling Calc from Your Lisp Programs

      • 17.5.6.1 Additional Arguments to calc-eval
      • 17.5.6.2 Error Handling
      • 17.5.6.3 Numbers Only
      • 17.5.6.4 Default Modes
      • 17.5.6.5 Raw Numbers
      • 17.5.6.6 Predicates
      • 17.5.6.7 Variable Values
      • 17.5.6.8 Stack Access
      • 17.5.6.9 Keyboard Macros
      • 17.5.6.10 Lisp Evaluation
      • 17.5.6.11 Example

    • 17.5.7 Calculator Internals

      • 17.5.7.1 Data Type Formats
      • 17.5.7.2 Interactive Functions
      • 17.5.7.3 Stack-Oriented Functions
      • 17.5.7.4 Predicates
      • 17.5.7.5 Computational Functions
      • 17.5.7.6 Vector Functions
      • 17.5.7.7 Symbolic Functions
      • 17.5.7.8 I/O and Formatting Functions
      • 17.5.7.9 Hooks

• Appendix A GNU GENERAL PUBLIC LICENSE

• Appendix B GNU Free Documentation License

• Appendix C Customizing Calc

• Appendix D Reporting Bugs

• Appendix E Calc Summary

• Index of Key Sequences

• Index of Calculator Commands

• Index of Algebraic Functions

• Concept Index

• Index of Variables

• Index of Lisp Math Functions