C++ Math Functions: Using the cmath Library

When your program needs to compute square roots, raise numbers to powers, round values, or do any serious math, you reach for <cmath> — the C++ math library. It provides all the standard mathematical functions you’d find on a scientific calculator, and they’re straightforward to use.

Including the cmath Header

All the functions in this article require this include:

#include <cmath>

The functions live in the std namespace, so you’ll call them as std::sqrt(), std::pow(), and so on.

Square Root: std::sqrt

#include <iostream>
#include <cmath>

int main() {
    double result = std::sqrt(25.0);
    std::cout << result << "\n"; // 5

    std::cout << std::sqrt(2.0) << "\n"; // 1.41421
    std::cout << std::sqrt(0.0) << "\n"; // 0

    // Negative input gives NaN
    std::cout << std::sqrt(-1.0) << "\n"; // -nan or nan
    return 0;
}

sqrt takes a double and returns a double. Always pass a non-negative number. If you need complex square roots, you’d use <complex> instead.

Power: std::pow

pow(base, exponent) raises base to the power of exponent:

#include <iostream>
#include <cmath>

int main() {
    std::cout << std::pow(2, 10)  << "\n"; // 1024 (2^10)
    std::cout << std::pow(3, 3)   << "\n"; // 27   (3^3)
    std::cout << std::pow(4, 0.5) << "\n"; // 2    (square root of 4)
    std::cout << std::pow(2, -1)  << "\n"; // 0.5  (1/2)
    return 0;
}

Note: pow returns a double, so pow(2, 10) gives 1024.0. If you need an integer result, cast it:

int result = static_cast<int>(std::pow(2, 10)); // 1024

Absolute Value: std::abs

abs returns the non-negative value of a number — it removes the sign:

#include <iostream>
#include <cmath>

int main() {
    std::cout << std::abs(-7.5) << "\n"; // 7.5
    std::cout << std::abs(3.0)  << "\n"; // 3
    std::cout << std::abs(-42)  << "\n"; // 42 (works for int too)
    return 0;
}

Rounding Functions: floor, ceil, round

These three handle different styles of rounding:

• std::floor(x) — rounds down to the nearest integer (toward negative infinity)
• std::ceil(x) — rounds up to the nearest integer (toward positive infinity)
• std::round(x) — rounds to the nearest integer (0.5 rounds up)

#include <iostream>
#include <cmath>

int main() {
    double x = 3.7;
    std::cout << std::floor(x) << "\n"; // 3
    std::cout << std::ceil(x)  << "\n"; // 4
    std::cout << std::round(x) << "\n"; // 4

    double y = 3.2;
    std::cout << std::floor(y) << "\n"; // 3
    std::cout << std::ceil(y)  << "\n"; // 4
    std::cout << std::round(y) << "\n"; // 3

    double z = -2.5;
    std::cout << std::floor(z) << "\n"; // -3
    std::cout << std::ceil(z)  << "\n"; // -2
    std::cout << std::round(z) << "\n"; // -3 (rounds away from zero)
    return 0;
}

These return double — to get an int, use static_cast<int>(std::floor(x)).

Floating-Point Modulo: std::fmod

The regular % operator works for integers. For floating-point remainder, use std::fmod:

#include <iostream>
#include <cmath>

int main() {
    std::cout << std::fmod(10.5, 3.0) << "\n"; // 1.5 (10.5 = 3×3 + 1.5)
    std::cout << std::fmod(7.0, 2.5)  << "\n"; // 2.0 (7.0 = 2×2.5 + 2.0)
    return 0;
}

Logarithms: std::log and std::log10

• std::log(x) — natural logarithm (base e)
• std::log2(x) — logarithm base 2
• std::log10(x) — logarithm base 10

#include <iostream>
#include <cmath>

int main() {
    std::cout << std::log(std::exp(1.0)) << "\n"; // 1 (ln(e) = 1)
    std::cout << std::log10(100.0) << "\n";        // 2
    std::cout << std::log2(8.0)    << "\n";        // 3
    return 0;
}

Trigonometry: sin, cos, tan

These functions take angles in radians, not degrees:

#include <iostream>
#include <cmath>

int main() {
    const double PI = std::acos(-1.0); // a portable way to get pi

    std::cout << std::sin(PI / 2) << "\n"; // 1.0 (sin 90°)
    std::cout << std::cos(0)      << "\n"; // 1.0 (cos 0°)
    std::cout << std::tan(PI / 4) << "\n"; // 1.0 (tan 45°)
    return 0;
}

To convert degrees to radians: radians = degrees * PI / 180.0

Quick Reference: Common cmath Functions

Complete Example: Pythagorean Theorem Calculator

#include <iostream>
#include <cmath>

int main() {
    double a, b;
    std::cout << "Enter side a: ";
    std::cin >> a;
    std::cout << "Enter side b: ";
    std::cin >> b;

    double c = std::sqrt(std::pow(a, 2) + std::pow(b, 2));
    std::cout << "Hypotenuse c = " << c << "\n";

    return 0;
}

Sample run:

Enter side a: 3
Enter side b: 4
Hypotenuse c = 5

Related Articles

• C++ Variables and Data Types: A Complete Beginner’s Guide
• C++ Random Numbers: How to Generate Them Correctly
• C++ Functions Tutorial: How to Write and Use Functions
• C++ Calculator Program: A Beginner Project with Full Code

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