Tutorial: Arduino Math Library

Arduino’s math library provides a wide range of functions to perform mathematical operations.

These functions can be used to solve complex problems, process sensor data, and create advanced algorithms.

This tutorial explains how to use the Arduino math library and demonstrates its functionality with examples.

Table of Contents

1. What Is the Math Library in Arduino?

The math library in Arduino is a collection of functions that help perform arithmetic, trigonometric, logarithmic, and rounding operations. These functions are part of the C standard library (math.h) and are included by default in Arduino.

2. Common Math Functions

2.1 Trigonometric Functions

Used for angle-based calculations.

Function	Description
sin(x)	Sine of angle x (radians).
cos(x)	Cosine of angle x (radians).
tan(x)	Tangent of angle x (radians).
asin(x)	Arc sine of x (returns radians).
acos(x)	Arc cosine of x (returns radians).
atan(x)	Arc tangent of x (returns radians).

Example: Calculate Sine

void setup() {
  Serial.begin(9600);
  float angle = 1.0;  // Angle in radians
  float result = sin(angle);
  Serial.print("Sine of angle: ");
  Serial.println(result);
}

void loop() {
  // Empty
}

2.2 Power and Exponentiation

Function	Description
pow(base, exp)	Base raised to the power of exponent.
exp(x)	Exponential of x (e^x).
log(x)	Natural logarithm of x (base e).
log10(x)	Logarithm of x (base 10).

Example: Calculate Power

void setup() {
  Serial.begin(9600);
  float base = 2.0;
  float exponent = 3.0;
  float result = pow(base, exponent);
  Serial.print("2 raised to the power of 3 is: ");
  Serial.println(result);
}

void loop() {
  // Empty
}

2.3 Square Root and Absolute Value

Function	Description
sqrt(x)	Square root of x.
abs(x)	Absolute value of x.

Example: Calculate Square Root

void setup() {
  Serial.begin(9600);
  float number = 16.0;
  float result = sqrt(number);
  Serial.print("Square root of 16 is: ");
  Serial.println(result);
}

void loop() {
  // Empty
}

2.4 Rounding and Modulo

Function	Description
ceil(x)	Rounds x up to the nearest integer.
floor(x)	Rounds x down to the nearest integer.
round(x)	Rounds x to the nearest integer.
fmod(x, y)	Returns the remainder of x divided by y.

Example: Rounding and Modulo

void setup() {
  Serial.begin(9600);

  float number = 4.7;
  Serial.print("Ceiling: ");
  Serial.println(ceil(number));

  Serial.print("Floor: ");
  Serial.println(floor(number));

  Serial.print("Rounded: ");
  Serial.println(round(number));

  Serial.print("Modulo (5.3 % 2): ");
  Serial.println(fmod(5.3, 2));
}

void loop() {
  // Empty
}

3. Practical Examples

3.1 Calculate Distance Using Pythagoras

void setup() {
  Serial.begin(9600);

  float x = 3.0;
  float y = 4.0;
  float distance = sqrt(pow(x, 2) + pow(y, 2));  // Pythagorean theorem

  Serial.print("Distance: ");
  Serial.println(distance);
}

void loop() {
  // Empty
}

3.2 Normalize Sensor Data

Normalize a sensor value to a range of 0 to 1.

const int sensorPin = A0;

void setup() {
  Serial.begin(9600);
}

void loop() {
  int sensorValue = analogRead(sensorPin);
  float normalizedValue = sensorValue / 1023.0;  // Normalize to range 0-1

  Serial.print("Normalized Value: ");
  Serial.println(normalizedValue);
  delay(500);
}

3.3 Generate a Sine Wave for PWM Output

Create a smooth sine wave pattern for an LED using analogWrite().

const int ledPin = 9;
const float pi = 3.14159;

void setup() {
  pinMode(ledPin, OUTPUT);
}

void loop() {
  for (int i = 0; i < 360; i++) {
    float angle = i * (pi / 180);         // Convert degrees to radians
    float brightness = (sin(angle) + 1) * 127.5;  // Map sine value to 0-255
    analogWrite(ledPin, (int)brightness); // Output PWM signal
    delay(10);                            // Delay for smooth transition
  }
}

4. Best Practices for Using the Math Library

Use Appropriate Data Types:
- Use float for functions like sin() or pow() to handle decimal precision.
Convert Degrees to Radians:
- Trigonometric functions require angles in radians. Convert degrees using:
```
float radians = degrees * (PI / 180);
```
Avoid Integer Division:
- When working with integers, remember that division truncates decimals. Use float if precision is required.
Optimize for Performance:
- Some functions like pow() can be computationally expensive. Simplify calculations where possible.
Test Boundary Cases:
- Ensure that inputs to functions like sqrt() or log() are within valid ranges.

Conclusion

The Arduino math library provides powerful tools for performing a wide range of calculations, from simple arithmetic to complex trigonometry and logarithms.

Whether you’re normalizing sensor data, generating waveforms, or solving geometric problems, these functions can help simplify your code.

This tutorial covers the most commonly used math functions and demonstrates practical examples to help you integrate them into your Arduino projects.

For more details, visit the official Arduino reference.

Arduino Math Library