bc - arithmetic expression calculator

Bash's built-in math support is very limited.
bc is a calculator that supports mathematic expressions.
It's available on a lot of Linux distributions.

bc is essentially a programming language of its own.

Table of Contents

• Basics of bc
  • Options
• Converting Celsuis to Fahrenheit
  • Getting around scale with -l
• Syntax
  • Comments
• Variables in bc
• Converting Base10 (Decimal) to Base8 (Octal)
  • Example Conversion Script

Basics of bc

bc uses integer division by default.
scale needs to be set in order to use floating point division.
Compound operators are supported.
i.e., +=, *=, /=, etc..

Options

Option	Description
-h, --help	Print the usage and exit.
-i, --interactive	Force interactive mode.
-l, --mathlib	Define the standard math library.
-w, --warn	Give warnings for extensions to POSIX bc.
-s, --standard	Process exactly the POSIX bc language.
-q, --quiet	Do not print the normal GNU bc welcome.
-v, --version	Print the version number and copyright and quit.

Using -l will give a more precise decimal result:

echo "(79 + 79 + 80 + 80 + 45) / 5" | bc
# 72
echo "(79 + 79 + 80 + 80 + 45) / 5" | bc -l
# 72.60000000000000000000

Passing Strings to bc

Some strings passed to bc will change the way it behaves.

• scale=2; sets the decimal precision to 2 decimal places.
  

  echo "scale=2;10/3" | bc
  # 3.33
  

• ibase and obase: Set the input base and output base (for base number conversion).

  • Useful for converting binary, octal, decimal, and hexadecimal numbers.
    

    echo "ibase=16;obase=2; A" | bc  # Convert A from hexadecimal to binary
    # 1010
    echo "ibase=10;obase=8; 160" | bc  # Convert 160 from deciaml to octal
    # 240
    

Converting Celsuis to Fahrenheit

Formulas:

• °F = (°C × 9/5) + 32
• °C = (°F − 32) x 5/9

Here's how you can use the bc command in a Unix/Linux terminal to convert a
temperature from Celsius to Fahrenheit:

Run the bc command with the Fahrenheit conversion formula.
Convert 20 degrees Celsius to Fahrenheit:

echo "scale=2;(9/5)*20+32" | bc  
# or  
printf "scale=2;%s*1.8+32\n" "$1" | bc  

• echo is used to output the formula to the terminal.
• scale=2; sets the precision to 2 decimal places.
• (9/5)*20+32 is the formula that converts Celsius to Fahrenheit.
• | pipes the output from the echo command to the bc command, which performs
  the arithmetic operation.

You should see 68.00 as the output, which is 20 degrees Celsius in Fahrenheit.

• Remember that bc uses integer division by default.
• We're using scale to force bc to do decimal calculations.
• If you do not provide the scale, or -l (see below), the result will either
  be 68 instead of 68.00, or it could be entirely wrong.

Getting around scale with -l

Instead of using scale=2, you can just append -l to the bc command.

echo "(9/5)*20+32" | bc -l  
# or  
printf "%s*1.8+32\n" "$1" | bc -l  

Syntax

Comments

Comments in bc are the same as C-style multi-line comments, using the syntax /* comment */.

Variables in bc

Numbers are stored in two types of variables:

• Simple variables
• Arrays

Both simple variables and array variables are named.

Names begin with a letter followed by any number of letters, digits and underscores.
All letters in the variable names must be lower case.

• Full alpha-numeric names are an extension.
• In POSIX bc, all names are a single lowercase letter.

The type of variable is clear by the context; all array variable names will be followed by brackets ([]).

There are four special variables:

• scale
  • Defines how some operations use digits after the decimal point.
  • The default value of scale is 0.
• ibase
• obase
  • ibase and obase define the conversion base for input and output numbers.
  • The default for both input base and output base is base 10.
• last
  • (an extension) A variable that has the value of the last printed number.

Converting Base10 (Decimal) to Base8 (Octal)

It's really easy to do base conversion in bc using the ibase (input base) and obase (output base) variables.

Set the ibase to the base you want to convert from, and obase to the base you want to convert to.

Example Conversion Script

An example script of converting a number from decimal (base10) to octal (base 8):

#!/bin/bash
NUM=$1
OUTPUT="$(echo "ibase=10; obase=8; $NUM" | bc)"
printf "Decimal: %s\nOctal: %s\n" "$NUM" "$OUTPUT"

To reverse it, just change the ibase and obase variables.

Converting a number from octal (base 8) to decimal (base10):

#!/bin/bash
NUM=$1
OUTPUT="$(echo "ibase=8; obase=10; $NUM" | bc)"
printf "Octal: %s\nDecimal: %s\n" "$NUM" "$OUTPUT"