R as a Calculator

Introduction

One of the best ways to start learning R is to use it as a sophisticated calculator. R excels at mathematical operations and provides many built-in functions that go far beyond what a standard calculator can do. In this lesson, we’ll explore R’s mathematical capabilities and start building your confidence with the R console.

Getting Started

Open RStudio and look for the Console pane (usually in the bottom-left). You’ll see a prompt that looks like this:

R version 4.5.1 (2025-06-13) -- "Great Square Root"
Copyright (C) 2025 The R Foundation for Statistical Computing
Platform: x86_64-pc-linux-gnu

R is free software and comes with ABSOLUTELY NO WARRANTY.
You are welcome to redistribute it under certain conditions.
Type 'license()' or 'licence()' for distribution details.

R is a collaborative project with many contributors.
Type 'contributors()' for more information and
'citation()' on how to cite R or R packages in publications.

Type 'demo()' for some demos, 'help()' for on-line help, or
'help.start()' for an HTML browser interface to help.
Type 'q()' to quit R.

>

This prompt is where you can type R commands and see immediate results.

Basic Arithmetic Operations

Let’s start with fundamental arithmetic operations:

Addition and Subtraction

# Addition
5 + 3
[1] 8
# Subtraction
10 - 4
[1] 6
# You can chain operations
15 + 7 - 3
[1] 19

Multiplication and Division

# Multiplication
6 * 7
[1] 42
# Division
20 / 4
[1] 5
# Combined operations
3 * 4 + 2
[1] 14

Exponentiation

# Using ^ operator
2^3
[1] 8
# Using ** operator (alternative)
2**3
[1] 8
# Square root (special case)
sqrt(16)
[1] 4
# nth root using exponentiation
8^(1/3)  # cube root of 8
[1] 2

Modular Arithmetic

# Modulo (remainder after division)
17 %% 5
[1] 2
# Integer division (quotient without remainder)
17 %/% 5
[1] 3

Order of Operations

R follows standard mathematical order of operations (PEMDAS):

# Without parentheses
2 + 3 * 4
[1] 14
# With parentheses to change order
(2 + 3) * 4
[1] 20
# Complex expression
2^3 + 4 * (5 - 2) / 6
[1] 10

Mathematical Functions

R includes many built-in mathematical functions:

Basic Functions

# Absolute value
abs(-5)
[1] 5
# Rounding functions
round(3.14159, 2)    # Round to 2 decimal places
[1] 3.14
ceiling(3.2)         # Round up
[1] 4
floor(3.9)           # Round down
[1] 3
# Sign function
sign(-42)            # Returns -1, 0, or 1
[1] -1

Logarithmic and Exponential Functions

# Natural logarithm
log(10)
[1] 2.302585
# Logarithm base 10
log10(100)
[1] 2
# Logarithm with custom base
log(8, base = 2)
[1] 3
# Exponential function
exp(1)               # e^1
[1] 2.718282
# Power of 10
10^2
[1] 100

Trigonometric Functions

# Basic trigonometric functions (in radians)
sin(pi/2)
[1] 1
cos(0)
[1] 1
tan(pi/4)
[1] 1
# Inverse functions
asin(1)
[1] 1.570796
acos(1)
[1] 0
atan(1)
[1] 0.7853982
# Convert degrees to radians
degrees_to_radians <- function(degrees) degrees * pi / 180
sin(degrees_to_radians(90))
[1] 1

Special Numbers and Constants

R has several built-in constants:

# Pi
pi
[1] 3.141593
# Euler's number
exp(1)
[1] 2.718282
# Infinity
Inf
[1] Inf
1/0                  # Also gives Inf
[1] Inf
# Not a Number
NaN
[1] NaN
0/0                  # Results in NaN
[1] NaN
# Not Available (missing value)
NA
[1] NA

Working with Vectors

One of R’s superpowers is vectorized operations:

Creating Vectors

# Using c() function to combine values
numbers <- c(1, 2, 3, 4, 5)
numbers
[1] 1 2 3 4 5
# Creating sequences
1:10                 # Numbers 1 through 10
 [1]  1  2  3  4  5  6  7  8  9 10
seq(0, 20, by = 2)   # Even numbers from 0 to 20
 [1]  0  2  4  6  8 10 12 14 16 18 20

Vector Arithmetic

# Operations on entire vectors
x <- c(1, 2, 3, 4)
y <- c(5, 6, 7, 8)

# Element-wise operations
x + y
[1]  6  8 10 12
x * y
[1]  5 12 21 32
x^2
[1]  1  4  9 16
# Operations with single numbers (recycling)
x + 10
[1] 11 12 13 14
x * 2
[1] 2 4 6 8

Useful Vector Functions

# Create some data
scores <- c(85, 92, 78, 96, 88, 75, 89)

# Summary statistics
sum(scores)          # Total
[1] 603
mean(scores)         # Average
[1] 86.14286
median(scores)       # Middle value
[1] 88
max(scores)          # Maximum
[1] 96
min(scores)          # Minimum
[1] 75
range(scores)        # Min and max
[1] 75 96
length(scores)       # Number of elements
[1] 7
# More advanced statistics
var(scores)          # Variance
[1] 55.80952
sd(scores)           # Standard deviation
[1] 7.470577

Logical Operations

R can also perform logical operations:

Comparison Operators

# Equal to
5 == 5
[1] TRUE
# Not equal to
5 != 3
[1] TRUE
# Greater than / Less than
10 > 5
[1] TRUE
3 < 7
[1] TRUE
# Greater than or equal to / Less than or equal to
5 >= 5
[1] TRUE
4 <= 3
[1] FALSE

Logical Operators

# AND operator
TRUE & TRUE
[1] TRUE
(5 > 3) & (2 < 4)
[1] TRUE
# OR operator
TRUE | FALSE
[1] TRUE
(5 > 10) | (2 < 4)
[1] TRUE
# NOT operator
!TRUE
[1] FALSE
!(5 > 10)
[1] TRUE

Practical Examples

Let’s work through some practical calculation examples:

Example 1: Compound Interest

# Calculate compound interest
# Formula: A = P(1 + r/n)^(nt)
principal <- 1000    # Initial amount
rate <- 0.05         # 5% annual interest rate
n <- 12              # Compounded monthly
t <- 5               # 5 years

final_amount <- principal * (1 + rate/n)^(n*t)
final_amount
[1] 1283.359
# Interest earned
interest_earned <- final_amount - principal
interest_earned
[1] 283.3587

Example 2: Body Mass Index (BMI)

# BMI calculation: weight (kg) / height (m)^2
weight_kg <- 70
height_m <- 1.75

bmi <- weight_kg / height_m^2
round(bmi, 1)
[1] 22.9
# BMI for multiple people
weights <- c(65, 70, 80, 55)
heights <- c(1.70, 1.75, 1.80, 1.60)
bmis <- weights / heights^2
round(bmis, 1)
[1] 22.5 22.9 24.7 21.5

Example 3: Temperature Conversion

# Celsius to Fahrenheit: F = (C * 9/5) + 32
celsius_temps <- c(0, 20, 30, 37, 100)
fahrenheit_temps <- (celsius_temps * 9/5) + 32
fahrenheit_temps
[1]  32.0  68.0  86.0  98.6 212.0
# Fahrenheit to Celsius: C = (F - 32) * 5/9
fahrenheit_example <- c(32, 68, 86, 98.6, 212)
celsius_converted <- (fahrenheit_example - 32) * 5/9
celsius_converted
[1]   0  20  30  37 100

Comments in R

Notice the use of # for comments in the examples above. Comments are crucial for explaining your code:

# This is a comment - R ignores this line
2 + 2    # You can also add comments at the end of lines
[1] 4
# Comments can span multiple lines
# Use them to explain what your calculations do
# Future you (and others) will thank you!

Tips for Using R as a Calculator

Use the Up Arrow

  • Press the up arrow key in the console to recall previous commands
  • This saves time when you want to modify a calculation slightly

Scientific Notation

# R uses scientific notation for very large or small numbers
1000000
[1] 1e+06
0.0001
[1] 1e-04
# You can control the display
options(scipen = 999)  # Avoid scientific notation
1000000
[1] 1000000
options(scipen = 0)    # Reset to default

Assignment vs. Printing

# This just calculates and displays the result
5 + 3
[1] 8
# This calculates and stores the result in a variable
result <- 5 + 3

# To see the stored value, type the variable name
result
[1] 8
# Or use parentheses to assign and display
(result2 <- 10 * 2)
[1] 20

Common Mistakes to Avoid

Case Sensitivity

# R is case-sensitive
PI        # This will give an error
pi        # This works

Missing Parentheses

# Incorrect
mean c(1, 2, 3)    # Missing parentheses - ERROR

# Correct
mean(c(1, 2, 3))

Division by Zero

# Be careful with division
5 / 0    # Returns Inf
[1] Inf
0 / 0    # Returns NaN
[1] NaN

Practice Exercises

Try these calculations on your own:

  1. Calculate the area of a circle with radius 7 (use π)
  2. Find the hypotenuse of a right triangle with sides 3 and 4
  3. Calculate the average of these test scores: 88, 92, 76, 95, 89, 82
  4. Convert 25°C to Fahrenheit
  5. Calculate 15% tip on a $47.50 restaurant bill
Solutions
  1. pi * 7^2 = 153.94
  2. sqrt(3^2 + 4^2) = 5
  3. mean(c(88, 92, 76, 95, 89, 82)) = 87
  4. (25 * 9/5) + 32 = 77°F
  5. 47.50 * 0.15 = $7.125

Summary

In this lesson, you’ve learned to use R as a powerful calculator that can:

  • Perform basic and advanced mathematical operations
  • Work with vectors for batch calculations
  • Use built-in mathematical functions
  • Handle logical operations
  • Apply mathematical concepts to real-world problems

Next Steps

Now that you’re comfortable with R’s calculation capabilities, let’s explore:

Pro Tip

The more you practice using R for calculations, the more natural it becomes. Try replacing your regular calculator with R for daily calculations – you’ll be surprised how quickly you improve!