# Python as a Calculator¶

Python can be used as a calculator to compute arithmetic operations like addition, subtraction, multiplication and division. Python can also be used for trigonometric calculations and statistical calculations.

## Arithmetic¶

Python can be used as a calculator to make simple arithmetic calculations.

Simple arithmetic calculations can be completed at the Python Prompt, also called the Python REPL. REPL stands for Read Evaluate Print Loop. The Python REPL shows three arrow symbols >>> followed by a blinking cursor. Programmers type commands at the >>> prompt then hit [ENTER] to see the results.

Commands typed into the Python REPL are read by the interpreter, results of running the commands are evaluated, then printed to the command window. After the output is printed, the >>> prompt appears on a new line. This process repeats over and over again in a continuous loop.

Try the following commands at the Python REPL:

Suppose the mass of a battery is 5 kg and the mass of the battery cables is 3 kg. What is the mass of the battery cable assembly?

>>> 5 + 3
8


Suppose one of the cables above is removed and it has a mass of 1.5 kg. What is the mass of the leftover assembly?

>>> 8 - 1.5
6.5


If the battery has a mass of 5000 g and a volume of 2500 $$cm^3$$ What is the density of the battery? The formula for density is below, where $$D$$ is density, $$m$$ is mass and $$v$$ is volume.

$D = \frac{m}{v}$

In the problem above $$m = 5000$$ and $$v=2500$$

Let’s solve this with Python.

>>> 5000 / 2500
2.0


What is the total mass if we have 2 batteries, and each battery weighs 5 kg?

>>> 5 * 2
10


The length, width, and height of each battery is 3 cm. What is the area of the base of the battery? To complete this problem, use the double asterisk symbol ** to raise a number to a power.

>>> 3 ** 2
9


What is the volume of the battery if each the length, width, and height of the battery are all 3 cm?

>>> 3 ** 3
27


Find the mass of the two batteries and two cables.

We can use Python to find the mass of the batteries and then use the answer, which Python saves as an underscore _ to use in our next operation. (The underscore _ in Python is comparable to the ans variable in MATLAB)

>>> 2 * 5
10
>>> _ + 1.5 + 1
12.5


### Section Summary¶

A summary of the arithmetic operations in Python is below:

Operator

Description

Example

Result

+

2 + 3

5

-

subtraction

8 - 6

2

-

negative number

-4

-4

*

multiplication

5 * 2

10

/

division

6 / 3

2

**

raises a number to a power

10**2

100

_

returns last saved value

_ + 7

107

## Trigonometry: sine, cosine, and tangent¶

Trigonometry functions such as sine, cosine, and tangent can also be calculated using the Python REPL.

To use Python’s trig functions, we need to introduce a new concept: importing modules.

In Python, there are many operations built into the language when the REPL starts. These include + , -, *, / like we saw in the previous section. However, not all functions will work right away when Python starts. Say we want to find the sine of an angle. Try the following:

>>> sin(60)
Traceback (most recent call last):
File "<stdin>", line 1, in <module>
NameError: name 'sin' is not defined


This error results because we have not told Python to include the sin function. The sin function is part of the Python Standard Library. The Python Standard Library comes with every Python installation and includes many functions, but not all of these functions are available to us when we start a new Python REPL session. To use Python’s sin function, first import the sin function from the math module which is part of the Python Standard Library.

Importing modules and functions is easy. Use the following syntax:

from module import function


To import the sin() function from the math module try:

>>> from math import sin
>>> sin(60)
-0.3048106211022167


Success! Multiple modules can be imported at the same time. Say we want to use a bunch of different trig functions to solve the following problem.

An angle has a value of $$\pi$$/6 radians. What is the sine, cos, and tangent of the angle?

To solve this problem we need to import the sin(), cos(), and tan() functions. It is also useful to have the value of $$\pi$$, rather than having to write 3.14.... We can import all of these functions at the same time using the syntax:

from module import function1, function2, function3


Note the commas in between the function names.

Try:

>>> from math import sin, cos, tan, pi
>>> pi
3.141592653589793
>>> sin(pi/6)
0.49999999999999994
>>> cos(pi/6)
0.8660254037844387
>>> tan(pi/6)
0.5773502691896257


### Section Summary¶

The following trig functions are part of Python’s math module:

Trig function

Name

Description

Example

Result

math.pi

pi

mathematical constant $$\pi$$

math.pi

3.14

math.sin()

sine

sine of an angle in radians

math.sin(4)

9.025

math.cos()

cosine

cosine of an angle in radians

cos(3.1)

400

math.tan()

tangent

tangent of an angle in radians

 tan(100)

2.0

math.asin()

arc sine

 math.sin(4)

9.025

math.acos()

arc cosine

log(3.1)

400

math.atan()

arc tangent

atan(100)

2.0

math.radians()

math.radians(90)

1.57

math.degrees()

degree conversion

math.degrees(2)

114.59

## Exponents and Logarithms¶

Calculating exponents and logarithms with Python is easy. Note the exponent and logarithm functions are imported from the math module just like the trig functions were imported from the math module above.

The following exponents and logarithms functions can be imported from Python’s math module:

• log

• log10

• exp

• e

• pow(x,y)

• sqrt

Let’s try a couple of examples:

>>> from math import log, log10, exp, e, pow, sqrt
>>> log(3.0*e**3.4)         # note: natural log
4.4986122886681095


A right triangle has side lengths 3 and 4. What is the length of the hypotenuse?

>>> sqrt(3**2 + 4**2)
5.0


The power function pow() works like the ** operator. pow() raises a number to a power.

>>> 5**2
25


>>> pow(5,2)
25.0


### Section Summary¶

The following exponent and logarithm functions are part of Python’s math module:

Math function

Name

Description

Example

Result

math.e

Euler’s number

mathematical constant $$e$$

math.e

2.718

math.exp()

exponent

$$e$$ raised to a power

math.exp(2.2)

9.025

math.log()

natural logarithm

log base e

math.log(3.1)

400

math.log10()

base 10 logarithm

log base 10

math.log10(100)

2.0

math.pow()

power

raises a number to a power

math.pow(2,3)

8.0

math.sqrt()

square root

square root of a number

math.sqrt(16)

4.0

## Statistics¶

To round out this section, we will look at a couple of statistics functions. These functions are part of the Python Standard Library, but not part of the math module. To access Python’s statistics functions, we need to import them from the statistics module using the statement from statistics import mean, median, mode, stdev. Then the functions mean, median, mode and stdev (standard deviation) can be used.

>>> from statistics import mean, median, mode, stdev

>>> test_scores = [60, 83, 83, 91, 100]

>>> mean(test_scores)
83.4

>>> median(test_scores)
83

>>> mode(test_scores)
83

>>> stdev(test_scores)
14.842506526863986


Alternatively, we can import the entire statistics module using the statement import statistics. Then to use the functions, we need to use the names statistics.mean, statistics.median, statistics.mode, and statistics.stdev. See below:

>>> import statistics

>>> test_scores = [60, 83, 83, 91, 100 ]

>>> statistics.mean(test_scores)
83.4

>>> statistics.median(test_scores)
83

>>> statistics.mode(test_scores)
83

>>> statistics.stdev(test_scores)
14.842506526863986


### Section Summary¶

The following functions are part of Python’s statistics module. These functions need to be imported from the statistics module before they are used.

Statistics function

Name

Description

Example

Result

mean()

mean

mean or average

mean([1,4,5,5])

3.75

median()

median

middle value

median([1,4,5,5])

4.5

mode()

mode

most often

mode([1,4,5,5])

5

stdev()

standard deviation

stdev([1,4,5,5])

1.892

variance()

variance

variance of data

variance([1,4,5,5])

3.583