C math.h Tutorial | sqrt, pow, sin, cos, log Explained

📖 What you'll learn on this page

✅ Must-know essentials

Include <math.h> and link with -lm
Use sqrt, pow, sin, cos, log, and exp
Trig functions take radians, not degrees

⭐ Read if you have time

M_PI and M_E constants
fabs, floor, ceil, and round
Handling NaN and Inf

What are Elementary Functions?

C ships with a familiar set of math functions: square roots, trigonometric functions, exponentials, logarithms, and more. To use them, include <math.h>.

How to use them: (1) add #include <math.h> at the top, (2) call functionName(arg), and (3) the return value is almost always a double.

    #include<stdio.h>

    #include<math.h>  // ← required!

    int main(void){

      double x = 2.0;

      printf("sqrt(%.1f) = %f\n", x, sqrt(x));

      return 0;

    }

Compile note: On Linux and Mac, gcc may require the -lm option to link the math library: gcc prog.c -lm. Visual Studio doesn't need it.

Main Math Functions

All of these become available once you #include <math.h>. Arguments and return values are essentially always double.

Function	Purpose	Example	Result
sqrt(x)	Square root √x	sqrt(9.0)	3.0
pow(x, y)	Power x^y	pow(2.0, 10.0)	1024.0
fabs(x)	Absolute value \|x\|	fabs(-3.7)	3.7
sin(x)	Sine (radians)	sin(3.14159/2)	1.0
cos(x)	Cosine (radians)	cos(0.0)	1.0
tan(x)	Tangent (radians)	tan(3.14159/4)	≈ 1.0
exp(x)	Exponential e^x	exp(1.0)	≈ 2.71828
log(x)	Natural log ln(x)	log(2.71828)	≈ 1.0
log10(x)	Common log log₁₀(x)	log10(1000.0)	3.0
ceil(x)	Round up	ceil(2.3)	3.0
floor(x)	Round down	floor(2.7)	2.0

sqrt — Square Root

Our first function. sqrt(x) returns the square root of x (√x).

    #include<stdio.h>

    #include<math.h>

    int main(void){

      double a = 2.0;

      printf("sqrt(%.1f) = %f\n", a, sqrt(a));

      // -> sqrt(2.0) = 1.414214

      // Pythagorean theorem: c = sqrt(a^2 + b^2)

      double b = 3.0, c = 4.0;

      double hyp = sqrt(b*b + c*c);

      printf("hypotenuse = %f\n", hyp);

      // -> hypotenuse = 5.000000

      return 0;

    }

Note: Passing a negative number to sqrt returns NaN (Not a Number). It's safer to check the sign beforehand.

Trigonometric Functions (sin / cos / tan)

C's trig functions take radians, not degrees. Convert degrees to radians with rad = deg * M_PI / 180.0.

sin(θ)

sin(0) = 0
sin(π/2) = 1
sin(π) = 0

cos(θ)

cos(0) = 1
cos(π/2) = 0
cos(π) = -1

tan(θ)

tan(0) = 0
tan(π/4) ≈ 1
tan(π/2) = ∞

    #include<math.h>

    // degrees -> radians

    double deg = 45.0;

    double rad = deg * M_PI / 180.0;

    printf("sin(45 deg) = %f\n", sin(rad)); // -> 0.707107

    printf("cos(45 deg) = %f\n", cos(rad)); // -> 0.707107

    printf("tan(45 deg) = %f\n", tan(rad)); // -> 1.000000

M_PI is a pi constant (3.14159...) defined in math.h. You could write #define PI 3.14159 yourself, but M_PI is more precise.

Function Calculator — Try It

Try the math functions right in your browser. Pick a function and enter a value to see the result.

x =

The result will appear here.

Write Your Own — Math Functions

A program that uses trig functions and square roots to compute the hypotenuse and angles of a right triangle.

#include<stdio.h>
#include<math.h>

int main(void){
  double a = 3.0;
  double b = 4.0;
  double c = sqrt(a*a + b*b);
  printf("a=%.1f, b=%.1f\n", a, b);
  printf("hypotenuse c = %f\n", c);

  double deg = 30.0;
  double rad = deg * 3.14159 / 180.0;
  printf("sin(%.0f) = %f\n", deg, sin(rad));
  printf("cos(%.0f) = %f\n", deg, cos(rad));

  printf("pow(2,10) = %.0f\n", pow(2.0, 10.0));
  printf("log(100) = %f\n", log10(100.0));
  return 0;
}

💡 More ideas to try

Compute pow(2, 10), sqrt(2), and log(M_E)
Try trig special values like sin(M_PI/2) and cos(0)
Compare fabs, floor, ceil, and round
Drop -lm and watch the linker error appear

Review Quiz

Check your understanding.

Q1. Which header do you need to use math functions?

stdlib.h

math.h

string.h

Math functions like sqrt, pow, sin, and cos are declared in math.h. You may also need the -lm option when compiling on Linux or Mac.

Q2. What is the result of pow(2, 3)?

pow(2, 3) returns 2 raised to the 3rd power, which is 8. pow returns a double.

Q3. What is the result of sqrt(16)?

4.0

8.0

256.0

sqrt returns the square root. √16 = 4.0.

Lesson 26: Elementary Functions (math.h)