C++ Math Operations

Introduction to C++ Math

C++ provides a wide range of mathematical operations using both built-in operators and the library. These tools allow you to perform everything from simple arithmetic to advanced calculations.

The header includes functions for common operations, while arithmetic operators handle fundamental math directly.

Basic Arithmetic Operators

ℹ️ Note: Integer division discards the fractional part. Use floating-point operands to preserve decimals.

Operator	Operation	Example	Result
+	Addition	5 + 2	7
-	Subtraction	5 - 2	3
*	Multiplication	5 * 2	10
/	Division	5.0 / 2	2.5
%	Modulus (remainder)	5 % 2	1
++	Increment	x++ (x starts 5)	x becomes 6
--	Decrement	x-- (x starts 5)	x becomes 4

Common Math Functions

The library provides many helpful functions for numerical calculations:

⚠️ Warning: Remember to #include <cmath> before using these functions.

Function	Description	Example	Result
sqrt(x)	Square root	sqrt(25)	5
pow(x,y)	x raised to the power y	pow(2,3)	8
abs(x)	Absolute value	abs(-5)	5
ceil(x)	Round upward	ceil(3.2)	4
floor(x)	Round downward	floor(3.8)	3
round(x)	Round to nearest	round(3.5)	4
fmod(x,y)	Floating-point remainder	fmod(5.5,2)	1.5

Trigonometric Functions

C++ includes standard trigonometric functions that use radians:

Example

#include <iostream>
#include <cmath>
using namespace std;

int main() {
    constexpr double PI = 3.141592653589793;
    double angle = 45.0;
    double radians = angle * PI / 180.0;

    cout << "sin(45°): " << sin(radians) << endl;
    cout << "cos(45°): " << cos(radians) << endl;
    cout << "tan(45°): " << tan(radians) << endl;
    return 0;
}

Output

sin(45°): 0.707107
cos(45°): 0.707107
tan(45°): 1

ℹ️ Note: M_PI is not part of the C++ standard. Prefer a constant you define yourself (as shown) or C++20's std::numbers::pi.

Exponential and Logarithmic Functions

For exponents and logarithms, offers several functions:

Example

#include <iostream>
#include <cmath>
using namespace std;

int main() {
    cout << "exp(1): " << exp(1) << endl;     // e^1
    cout << "log(10): " << log(10) << endl;   // Natural logarithm
    cout << "log10(100): " << log10(100) << endl; // Base-10 logarithm
    return 0;
}

Output

exp(1): 2.71828
log(10): 2.30259
log10(100): 2

Random Number Generation

Modern C++ (C++11 and later) provides robust random number facilities in :

Example

#include <iostream>
#include <random>
using namespace std;

int main() {
    random_device rd;
    mt19937 gen(rd());
    uniform_int_distribution<> dist(1, 6);

    cout << "Dice roll: " << dist(gen) << endl;

    uniform_real_distribution<> float_dist(0.0, 1.0);
    cout << "Random float: " << float_dist(gen);
    return 0;
}

ℹ️ Note: This method is preferred over rand()/srand() due to better randomness quality.

Mathematical Constants

C++20 introduced standardized mathematical constants in . Before that, implementations often provided macros like M_PI, which are not portable.

⚠️ Warning: Prefer std::numbers (C++20). On older standards, define your own constants; do not rely on non-standard macros like M_PI/M_E.

Example

// C++20 (preferred)
#include <iostream>
#include <numbers>
using namespace std;

int main() {
    cout << "\xCF\x80: " << std::numbers::pi << endl;  // pi
    cout << "e: " << std::numbers::e << endl;           // Euler's number

    // Pre-C++20 fallback
    constexpr double PI = 3.141592653589793;
    constexpr double E  = 2.718281828459045;
    cout << "pi (fallback): " << PI << "\n";
    cout << "e  (fallback): " << E  << "\n";
    return 0;
}

Output

π: 3.14159
e: 2.71828

Practical Math Examples

Examples of math in everyday programs:

Example

#include <iostream>
#include <cmath>
using namespace std;

int main() {
    // Circle area
    constexpr double PI = 3.141592653589793;
    double radius = 5.0;
    double area = PI * pow(radius, 2);
    cout << "Circle area: " << area << endl;

    // Compound interest
    double principal = 1000.0;
    double rate = 0.05;
    int years = 10;
    double amount = principal * pow(1 + rate, years);
    cout << "Investment after " << years << " years: " << amount;
    return 0;
}

Output

Circle area: 78.5398
Investment after 10 years: 1628.89

Best Practices

- Prefer double over float for greater precision

- Be aware of floating-point rounding errors

- Use parentheses to clarify complex expressions

- For advanced needs, consider libraries like Boost.Math

- Always initialize variables before using them in calculations

C++ Math Operations

Introduction to C++ Math

C++ provides a wide range of mathematical operations using both built-in operators and the library. These tools allow you to perform everything from simple arithmetic to advanced calculations.

The header includes functions for common operations, while arithmetic operators handle fundamental math directly.

Basic Arithmetic Operators

ℹ️ Note: Integer division discards the fractional part. Use floating-point operands to preserve decimals.

Operator	Operation	Example	Result
+	Addition	5 + 2	7
-	Subtraction	5 - 2	3
*	Multiplication	5 * 2	10
/	Division	5.0 / 2	2.5
%	Modulus (remainder)	5 % 2	1
++	Increment	x++ (x starts 5)	x becomes 6
--	Decrement	x-- (x starts 5)	x becomes 4

Common Math Functions

The library provides many helpful functions for numerical calculations:

⚠️ Warning: Remember to #include <cmath> before using these functions.

Function	Description	Example	Result
sqrt(x)	Square root	sqrt(25)	5
pow(x,y)	x raised to the power y	pow(2,3)	8
abs(x)	Absolute value	abs(-5)	5
ceil(x)	Round upward	ceil(3.2)	4
floor(x)	Round downward	floor(3.8)	3
round(x)	Round to nearest	round(3.5)	4
fmod(x,y)	Floating-point remainder	fmod(5.5,2)	1.5

Trigonometric Functions

C++ includes standard trigonometric functions that use radians:

Example

#include <iostream>
#include <cmath>
using namespace std;

int main() {
    constexpr double PI = 3.141592653589793;
    double angle = 45.0;
    double radians = angle * PI / 180.0;

    cout << "sin(45°): " << sin(radians) << endl;
    cout << "cos(45°): " << cos(radians) << endl;
    cout << "tan(45°): " << tan(radians) << endl;
    return 0;
}

Output

sin(45°): 0.707107
cos(45°): 0.707107
tan(45°): 1

ℹ️ Note: M_PI is not part of the C++ standard. Prefer a constant you define yourself (as shown) or C++20's std::numbers::pi.

Exponential and Logarithmic Functions

For exponents and logarithms, offers several functions:

Example

#include <iostream>
#include <cmath>
using namespace std;

int main() {
    cout << "exp(1): " << exp(1) << endl;     // e^1
    cout << "log(10): " << log(10) << endl;   // Natural logarithm
    cout << "log10(100): " << log10(100) << endl; // Base-10 logarithm
    return 0;
}

Output

exp(1): 2.71828
log(10): 2.30259
log10(100): 2

Random Number Generation

Modern C++ (C++11 and later) provides robust random number facilities in :

Example

#include <iostream>
#include <random>
using namespace std;

int main() {
    random_device rd;
    mt19937 gen(rd());
    uniform_int_distribution<> dist(1, 6);

    cout << "Dice roll: " << dist(gen) << endl;

    uniform_real_distribution<> float_dist(0.0, 1.0);
    cout << "Random float: " << float_dist(gen);
    return 0;
}

ℹ️ Note: This method is preferred over rand()/srand() due to better randomness quality.

Mathematical Constants

C++20 introduced standardized mathematical constants in . Before that, implementations often provided macros like M_PI, which are not portable.

⚠️ Warning: Prefer std::numbers (C++20). On older standards, define your own constants; do not rely on non-standard macros like M_PI/M_E.

Example

// C++20 (preferred)
#include <iostream>
#include <numbers>
using namespace std;

int main() {
    cout << "\xCF\x80: " << std::numbers::pi << endl;  // pi
    cout << "e: " << std::numbers::e << endl;           // Euler's number

    // Pre-C++20 fallback
    constexpr double PI = 3.141592653589793;
    constexpr double E  = 2.718281828459045;
    cout << "pi (fallback): " << PI << "\n";
    cout << "e  (fallback): " << E  << "\n";
    return 0;
}

Output

π: 3.14159
e: 2.71828

Practical Math Examples

Examples of math in everyday programs:

Example

#include <iostream>
#include <cmath>
using namespace std;

int main() {
    // Circle area
    constexpr double PI = 3.141592653589793;
    double radius = 5.0;
    double area = PI * pow(radius, 2);
    cout << "Circle area: " << area << endl;

    // Compound interest
    double principal = 1000.0;
    double rate = 0.05;
    int years = 10;
    double amount = principal * pow(1 + rate, years);
    cout << "Investment after " << years << " years: " << amount;
    return 0;
}

Output

Circle area: 78.5398
Investment after 10 years: 1628.89

Best Practices

- Prefer double over float for greater precision

- Be aware of floating-point rounding errors

- Use parentheses to clarify complex expressions

- For advanced needs, consider libraries like Boost.Math

- Always initialize variables before using them in calculations

C++ Basics

C++ Functions

C++ Classes

C++ Quiz

C++ Math Operations

Introduction to C++ Math

Basic Arithmetic Operators

Common Math Functions

Trigonometric Functions

Exponential and Logarithmic Functions

Random Number Generation

Mathematical Constants

Practical Math Examples

Best Practices

C++ Math Operations

Introduction to C++ Math

Basic Arithmetic Operators

Common Math Functions

Trigonometric Functions

Exponential and Logarithmic Functions

Random Number Generation

Mathematical Constants

Practical Math Examples

Best Practices