C math.h Library Reference

?Why Use math.h?

C only provides basic arithmetic (+, -, *, /). For anything more complex, you need math.h!

•

Trig

sin, cos, tan

•

Power

pow, sqrt, exp

•

Log

log, log10

Round

ceil, floor

01Introduction to math.h

What is math.h?

<math.h> provides mathematical functions for trigonometry, logarithms, powers, rounding, and more.

Link Math Library

On Linux/GCC, you must link with -lm:
gcc program.c -o program -lm

Category	Functions
Power/Root	pow, sqrt, cbrt, hypot
Trigonometry	sin, cos, tan, asin, acos, atan
Logarithm	log, log10, log2, exp
Rounding	ceil, floor, round, trunc
Other	fabs, fmod, fmax, fmin

02Power and Root Functions

Function	Prototype	Description
pow()	double pow(double base, double exp)	base raised to exp (x^y)
sqrt()	double sqrt(double x)	Square root (√x)
cbrt()	double cbrt(double x)	Cube root (∛x)
hypot()	double hypot(double x, double y)	Hypotenuse √(x²+y²)

power_root.c

1#include <stdio.h>
2#include <math.h>
3
4int main() {
5    // Power
6    printf("2^10 = %.0f\n", pow(2, 10));      // 1024
7    printf("5^3 = %.0f\n", pow(5, 3));        // 125
8    
9    // Square root
10    printf("√16 = %.0f\n", sqrt(16));         // 4
11    printf("√2 = %.4f\n", sqrt(2));           // 1.4142
12    
13    // Cube root
14    printf("∛27 = %.0f\n", cbrt(27));         // 3
15    
16    // Hypotenuse (Pythagorean theorem)
17    printf("hypot(3,4) = %.0f\n", hypot(3, 4)); // 5
18    
19    return 0;
20}

03Trigonometric Functions

Radians, Not Degrees!

All trig functions use radians. Convert: radians = degrees × (π / 180)

Function	Prototype	Description
sin()	double sin(double x)	Sine (x in radians)
cos()	double cos(double x)	Cosine
tan()	double tan(double x)	Tangent
asin()	double asin(double x)	Arc sine (inverse)
acos()	double acos(double x)	Arc cosine
atan()	double atan(double x)	Arc tangent
atan2()	double atan2(double y, double x)	Arc tangent of y/x

trig_functions.c

1#include <stdio.h>
2#include <math.h>
3
4#define PI 3.14159265358979323846
5
6int main() {
7    // Convert degrees to radians
8    double deg = 45.0;
9    double rad = deg * (PI / 180.0);
10    
11    printf("sin(45°) = %.4f\n", sin(rad));  // 0.7071
12    printf("cos(45°) = %.4f\n", cos(rad));  // 0.7071
13    printf("tan(45°) = %.4f\n", tan(rad));  // 1.0000
14    
15    // Inverse trig (returns radians)
16    double angle = asin(0.5);  // 30° in radians
17    printf("asin(0.5) = %.4f rad = %.1f°\n", 
18           angle, angle * (180.0 / PI));
19    
20    // Use M_PI constant (if available)
21    printf("sin(π/2) = %.4f\n", sin(M_PI / 2));  // 1.0000
22    
23    return 0;
24}

04Exponential and Logarithmic

Function	Prototype	Description
exp()	double exp(double x)	e^x (e = 2.718...)
log()	double log(double x)	Natural log (ln x)
log10()	double log10(double x)	Base-10 log
log2()	double log2(double x)	Base-2 log

log_functions.c

1#include <stdio.h>
2#include <math.h>
3
4int main() {
5    // Exponential
6    printf("e^1 = %.4f\n", exp(1));     // 2.7183
7    printf("e^2 = %.4f\n", exp(2));     // 7.3891
8    
9    // Natural logarithm (base e)
10    printf("ln(e) = %.4f\n", log(M_E)); // 1.0000
11    printf("ln(10) = %.4f\n", log(10)); // 2.3026
12    
13    // Base-10 logarithm
14    printf("log10(100) = %.4f\n", log10(100));  // 2.0000
15    printf("log10(1000) = %.4f\n", log10(1000)); // 3.0000
16    
17    // Base-2 logarithm
18    printf("log2(8) = %.4f\n", log2(8));   // 3.0000
19    printf("log2(1024) = %.4f\n", log2(1024)); // 10.0000
20    
21    return 0;
22}

05Rounding Functions

Function	Prototype	Description
ceil()	double ceil(double x)	Round up ⌈x⌉
floor()	double floor(double x)	Round down ⌊x⌋
round()	double round(double x)	Round to nearest
trunc()	double trunc(double x)	Truncate (toward 0)

rounding.c

1#include <stdio.h>
2#include <math.h>
3
4int main() {
5    double x = 3.7, y = -3.7;
6    
7    printf("Value    ceil   floor  round  trunc\n");
8    printf("%.1f     %.0f     %.0f     %.0f     %.0f\n", 
9           x, ceil(x), floor(x), round(x), trunc(x));
10    printf("%.1f    %.0f    %.0f    %.0f    %.0f\n", 
11           y, ceil(y), floor(y), round(y), trunc(y));
12    
13    // Output:
14    // Value    ceil   floor  round  trunc
15    // 3.7      4      3      4      3
16    // -3.7    -3     -4     -4     -3
17    
18    return 0;
19}

Output

Value ceil floor round trunc

3.7 4 3 4 3

-3.7 -3 -4 -4 -3

06Other Useful Functions

Function	Prototype	Description
fabs()	double fabs(double x)	Absolute value \|x\|
fmod()	double fmod(double x, double y)	Floating-point modulo
fmax()	double fmax(double x, double y)	Maximum of x, y
fmin()	double fmin(double x, double y)	Minimum of x, y

other_math.c

1#include <stdio.h>
2#include <math.h>
3
4int main() {
5    // Absolute value
6    printf("fabs(-5.5) = %.1f\n", fabs(-5.5));  // 5.5
7    
8    // Floating-point modulo
9    printf("fmod(5.3, 2) = %.1f\n", fmod(5.3, 2));  // 1.3
10    
11    // Max and Min
12    printf("fmax(3.5, 2.1) = %.1f\n", fmax(3.5, 2.1));  // 3.5
13    printf("fmin(3.5, 2.1) = %.1f\n", fmin(3.5, 2.1));  // 2.1
14    
15    return 0;
16}

07Math Constants

Constant	Value	Description
M_PI	3.14159...	π (pi)
M_E	2.71828...	e (Euler's number)
M_SQRT2	1.41421...	√2
M_LN2	0.69314...	ln(2)

Note

These constants may require #define _USE_MATH_DEFINESbefore including math.h on some compilers (MSVC).

!Code Pitfalls: Common Mistakes & What to Watch For

Copied code often provides math.h code that compiles but fails to link because it doesn't mention the -lm flag.

If you search online to "calculate the square root of a number," it will correctly include <math.h> and use sqrt(). But when you compile with gcc program.c, you get "undefined reference to sqrt." The Code rarely mentions you need gcc program.c -lm.

The Trap: Online sources focus on source code, not build systems. They might also use M_PI without mentioning that it requires #define _USE_MATH_DEFINES on MSVC, or compare floating-point results directly instead of using epsilon-based comparisons.

The Reality: On Unix-like systems, always link with -lm when using math.h. Never compare floats with ==; use fabs(a - b) < epsilon. Check for NaN and infinity using isnan() and isinf().

08bCommon Math Library Mistakes

Forgetting to Link -lm

Unlike other standard library functions, math.h functions require explicitly linking the math library. Always add -lm at the END of your gcc command: gcc program.c -o program -lm

Using Degrees Instead of Radians

All trigonometric functions use radians, not degrees. To convert:radians = degrees * M_PI / 180.0. A 90-degree angle is M_PI / 2 radians.

Integer Division in Math Functions

Passing integers where doubles are expected can cause issues.pow(2, 3) works, butsqrt(1/2) gives 0 because 1/2 is integer division! Use sqrt(1.0/2.0) instead.

09Frequently Asked Questions

Q:Why do I get "undefined reference to sqrt"?

A: You need to link the math library! Add -lm when compiling:gcc program.c -lm -o program. The -lm flag links the math library.

Q:How do I check if a number is NaN or infinity?

A: Use isnan(x)and isinf(x) macros from math.h. These return non-zero if x is NaN or infinity respectively. Never compare NaN with ==; use isnan() since NaN != NaN by definition.

Q:What's the difference between fmod() and %?

A: The % operator works only with integers.fmod(x, y) computes the floating-point remainder of x/y. For example, fmod(5.5, 2.0) returns 1.5, which you can't do with %.

Q:What's the difference between abs() and fabs()?

A: abs() (from stdlib.h) works on integers, fabs() (from math.h) works on floating-point numbers. Using abs() on a float truncates to integer first — always use fabs() for doubles!

Q:Do sin() and cos() use degrees or radians?

A: Radians! To convert degrees to radians: radians = degrees * M_PI / 180. For example, sin(90°) is sin(90 * M_PI / 180), which equals 1.0.

Q:M_PI is undefined — how do I fix it?

A: M_PI is a POSIX extension, not standard C. Add #define _USE_MATH_DEFINESBEFORE including math.h on MSVC, or define it yourself:#define M_PI 3.14159265358979323846

09Summary

Key Functions

Power/Root:

pow, sqrt, cbrt, hypot

Trig:

sin, cos, tan, asin, acos, atan

Log/Exp:

log, log10, log2, exp

Rounding:

ceil, floor, round, trunc

10Practical Tips for Math in C

Comparing Floating Point Numbers

Never use == to compare floats due to precision errors. Instead, check if the difference is within an acceptable epsilon:

#define EPSILON 1e-9
if (fabs(a - b) < EPSILON) { /* equal */ }

Checking for Special Values

Use isnan(x) to check for Not-a-Number and isinf(x) for infinity. These arise from operations like 0.0/0.0 (NaN) or 1.0/0.0 (infinity). Always validate inputs before mathematical operations to avoid unexpected results.

Performance Considerations

Math functions can be computationally expensive. For performance-critical code, consider: using lookup tables for trig functions, approximations like fast inverse square root, or SIMD instructions for bulk operations. Profile before optimizing—modern CPUs have fast hardware math units.

Type-Generic Math (C11)

C11 introduced <tgmath.h> which provides type-generic macros. Instead of choosing between sinf(), sin(), and sinl(), you can just use sin()and it automatically selects the right version based on the argument type.

Handle Domain Errors

Functions like sqrt(-1) or log(0)produce domain errors. Check inputs before calling, or check for NaN/infinity in results usingisnan() and isinf().

Know Your Precision Limits

Floating-point has limited precision. After many operations, errors accumulate. Usedouble instead of float for better precision, and be aware that some exact decimal values cannot be represented exactly in binary floating-point.

?Why Use math.h?

C only provides basic arithmetic (+, -, *, /). For anything more complex, you need math.h!

•

Trig

sin, cos, tan

•

Power

pow, sqrt, exp

•

Log

log, log10

Round

ceil, floor

01Introduction to math.h

What is math.h?

<math.h> provides mathematical functions for trigonometry, logarithms, powers, rounding, and more.

Link Math Library

On Linux/GCC, you must link with -lm:
gcc program.c -o program -lm

Category	Functions
Power/Root	pow, sqrt, cbrt, hypot
Trigonometry	sin, cos, tan, asin, acos, atan
Logarithm	log, log10, log2, exp
Rounding	ceil, floor, round, trunc
Other	fabs, fmod, fmax, fmin

02Power and Root Functions

Function	Prototype	Description
pow()	double pow(double base, double exp)	base raised to exp (x^y)
sqrt()	double sqrt(double x)	Square root (√x)
cbrt()	double cbrt(double x)	Cube root (∛x)
hypot()	double hypot(double x, double y)	Hypotenuse √(x²+y²)

power_root.c

1#include <stdio.h>
2#include <math.h>
3
4int main() {
5    // Power
6    printf("2^10 = %.0f\n", pow(2, 10));      // 1024
7    printf("5^3 = %.0f\n", pow(5, 3));        // 125
8    
9    // Square root
10    printf("√16 = %.0f\n", sqrt(16));         // 4
11    printf("√2 = %.4f\n", sqrt(2));           // 1.4142
12    
13    // Cube root
14    printf("∛27 = %.0f\n", cbrt(27));         // 3
15    
16    // Hypotenuse (Pythagorean theorem)
17    printf("hypot(3,4) = %.0f\n", hypot(3, 4)); // 5
18    
19    return 0;
20}

03Trigonometric Functions

Radians, Not Degrees!

All trig functions use radians. Convert: radians = degrees × (π / 180)

Function	Prototype	Description
sin()	double sin(double x)	Sine (x in radians)
cos()	double cos(double x)	Cosine
tan()	double tan(double x)	Tangent
asin()	double asin(double x)	Arc sine (inverse)
acos()	double acos(double x)	Arc cosine
atan()	double atan(double x)	Arc tangent
atan2()	double atan2(double y, double x)	Arc tangent of y/x

trig_functions.c

1#include <stdio.h>
2#include <math.h>
3
4#define PI 3.14159265358979323846
5
6int main() {
7    // Convert degrees to radians
8    double deg = 45.0;
9    double rad = deg * (PI / 180.0);
10    
11    printf("sin(45°) = %.4f\n", sin(rad));  // 0.7071
12    printf("cos(45°) = %.4f\n", cos(rad));  // 0.7071
13    printf("tan(45°) = %.4f\n", tan(rad));  // 1.0000
14    
15    // Inverse trig (returns radians)
16    double angle = asin(0.5);  // 30° in radians
17    printf("asin(0.5) = %.4f rad = %.1f°\n", 
18           angle, angle * (180.0 / PI));
19    
20    // Use M_PI constant (if available)
21    printf("sin(π/2) = %.4f\n", sin(M_PI / 2));  // 1.0000
22    
23    return 0;
24}

04Exponential and Logarithmic

Function	Prototype	Description
exp()	double exp(double x)	e^x (e = 2.718...)
log()	double log(double x)	Natural log (ln x)
log10()	double log10(double x)	Base-10 log
log2()	double log2(double x)	Base-2 log

log_functions.c

1#include <stdio.h>
2#include <math.h>
3
4int main() {
5    // Exponential
6    printf("e^1 = %.4f\n", exp(1));     // 2.7183
7    printf("e^2 = %.4f\n", exp(2));     // 7.3891
8    
9    // Natural logarithm (base e)
10    printf("ln(e) = %.4f\n", log(M_E)); // 1.0000
11    printf("ln(10) = %.4f\n", log(10)); // 2.3026
12    
13    // Base-10 logarithm
14    printf("log10(100) = %.4f\n", log10(100));  // 2.0000
15    printf("log10(1000) = %.4f\n", log10(1000)); // 3.0000
16    
17    // Base-2 logarithm
18    printf("log2(8) = %.4f\n", log2(8));   // 3.0000
19    printf("log2(1024) = %.4f\n", log2(1024)); // 10.0000
20    
21    return 0;
22}

05Rounding Functions

Function	Prototype	Description
ceil()	double ceil(double x)	Round up ⌈x⌉
floor()	double floor(double x)	Round down ⌊x⌋
round()	double round(double x)	Round to nearest
trunc()	double trunc(double x)	Truncate (toward 0)

rounding.c

1#include <stdio.h>
2#include <math.h>
3
4int main() {
5    double x = 3.7, y = -3.7;
6    
7    printf("Value    ceil   floor  round  trunc\n");
8    printf("%.1f     %.0f     %.0f     %.0f     %.0f\n", 
9           x, ceil(x), floor(x), round(x), trunc(x));
10    printf("%.1f    %.0f    %.0f    %.0f    %.0f\n", 
11           y, ceil(y), floor(y), round(y), trunc(y));
12    
13    // Output:
14    // Value    ceil   floor  round  trunc
15    // 3.7      4      3      4      3
16    // -3.7    -3     -4     -4     -3
17    
18    return 0;
19}

Output

Value ceil floor round trunc

3.7 4 3 4 3

-3.7 -3 -4 -4 -3

06Other Useful Functions

Function	Prototype	Description
fabs()	double fabs(double x)	Absolute value \|x\|
fmod()	double fmod(double x, double y)	Floating-point modulo
fmax()	double fmax(double x, double y)	Maximum of x, y
fmin()	double fmin(double x, double y)	Minimum of x, y

other_math.c

1#include <stdio.h>
2#include <math.h>
3
4int main() {
5    // Absolute value
6    printf("fabs(-5.5) = %.1f\n", fabs(-5.5));  // 5.5
7    
8    // Floating-point modulo
9    printf("fmod(5.3, 2) = %.1f\n", fmod(5.3, 2));  // 1.3
10    
11    // Max and Min
12    printf("fmax(3.5, 2.1) = %.1f\n", fmax(3.5, 2.1));  // 3.5
13    printf("fmin(3.5, 2.1) = %.1f\n", fmin(3.5, 2.1));  // 2.1
14    
15    return 0;
16}

07Math Constants

Constant	Value	Description
M_PI	3.14159...	π (pi)
M_E	2.71828...	e (Euler's number)
M_SQRT2	1.41421...	√2
M_LN2	0.69314...	ln(2)

Note

These constants may require #define _USE_MATH_DEFINESbefore including math.h on some compilers (MSVC).

!Code Pitfalls: Common Mistakes & What to Watch For

Copied code often provides math.h code that compiles but fails to link because it doesn't mention the -lm flag.

The Reality: On Unix-like systems, always link with -lm when using math.h. Never compare floats with ==; use fabs(a - b) < epsilon. Check for NaN and infinity using isnan() and isinf().

08bCommon Math Library Mistakes

Forgetting to Link -lm

Unlike other standard library functions, math.h functions require explicitly linking the math library. Always add -lm at the END of your gcc command: gcc program.c -o program -lm

Using Degrees Instead of Radians

All trigonometric functions use radians, not degrees. To convert:radians = degrees * M_PI / 180.0. A 90-degree angle is M_PI / 2 radians.

Integer Division in Math Functions

Passing integers where doubles are expected can cause issues.pow(2, 3) works, butsqrt(1/2) gives 0 because 1/2 is integer division! Use sqrt(1.0/2.0) instead.

09Frequently Asked Questions

Q:Why do I get "undefined reference to sqrt"?

A: You need to link the math library! Add -lm when compiling:gcc program.c -lm -o program. The -lm flag links the math library.

Q:How do I check if a number is NaN or infinity?

A: Use isnan(x)and isinf(x) macros from math.h. These return non-zero if x is NaN or infinity respectively. Never compare NaN with ==; use isnan() since NaN != NaN by definition.

Q:What's the difference between fmod() and %?

A: The % operator works only with integers.fmod(x, y) computes the floating-point remainder of x/y. For example, fmod(5.5, 2.0) returns 1.5, which you can't do with %.

Q:What's the difference between abs() and fabs()?

A: abs() (from stdlib.h) works on integers, fabs() (from math.h) works on floating-point numbers. Using abs() on a float truncates to integer first — always use fabs() for doubles!

Q:Do sin() and cos() use degrees or radians?

A: Radians! To convert degrees to radians: radians = degrees * M_PI / 180. For example, sin(90°) is sin(90 * M_PI / 180), which equals 1.0.

Q:M_PI is undefined — how do I fix it?

A: M_PI is a POSIX extension, not standard C. Add #define _USE_MATH_DEFINESBEFORE including math.h on MSVC, or define it yourself:#define M_PI 3.14159265358979323846

09Summary

Key Functions

Power/Root:

pow, sqrt, cbrt, hypot

Trig:

sin, cos, tan, asin, acos, atan

Log/Exp:

log, log10, log2, exp

Rounding:

ceil, floor, round, trunc

10Practical Tips for Math in C

Comparing Floating Point Numbers

Never use == to compare floats due to precision errors. Instead, check if the difference is within an acceptable epsilon:

#define EPSILON 1e-9
if (fabs(a - b) < EPSILON) { /* equal */ }

Checking for Special Values

Performance Considerations

Type-Generic Math (C11)

Handle Domain Errors

Functions like sqrt(-1) or log(0)produce domain errors. Check inputs before calling, or check for NaN/infinity in results usingisnan() and isinf().

What You Will Learn

?Why Use math.h?

01Introduction to math.h

What is math.h?

Link Math Library

02Power and Root Functions

03Trigonometric Functions

Radians, Not Degrees!

04Exponential and Logarithmic

05Rounding Functions

06Other Useful Functions

07Math Constants

Note

!Code Pitfalls: Common Mistakes & What to Watch For

Copied code often provides math.h code that compiles but fails to link because it doesn't mention the -lm flag.

08bCommon Math Library Mistakes

Forgetting to Link -lm

Using Degrees Instead of Radians

Integer Division in Math Functions

09Frequently Asked Questions

Q:Why do I get "undefined reference to sqrt"?

Q:How do I check if a number is NaN or infinity?

Q:What's the difference between fmod() and %?

Q:What's the difference between abs() and fabs()?

Q:Do sin() and cos() use degrees or radians?

Q:M_PI is undefined — how do I fix it?

09Summary

Key Functions

10Practical Tips for Math in C

Comparing Floating Point Numbers

Checking for Special Values

Performance Considerations

Type-Generic Math (C11)

Handle Domain Errors

Know Your Precision Limits

Test Your Knowledge

Related Tutorials

C string.h Library Reference

C ctype.h Library Reference

C stdio.h Library Reference

Have Feedback?

What You Will Learn

?Why Use math.h?

01Introduction to math.h

What is math.h?

Link Math Library

02Power and Root Functions

03Trigonometric Functions

Radians, Not Degrees!

04Exponential and Logarithmic

05Rounding Functions

06Other Useful Functions

07Math Constants

Note

!Code Pitfalls: Common Mistakes & What to Watch For

Copied code often provides math.h code that compiles but fails to link because it doesn't mention the -lm flag.

08bCommon Math Library Mistakes

Forgetting to Link -lm

Using Degrees Instead of Radians

Integer Division in Math Functions

09Frequently Asked Questions

Q:Why do I get "undefined reference to sqrt"?

Q:How do I check if a number is NaN or infinity?

Q:What's the difference between fmod() and %?

Q:What's the difference between abs() and fabs()?

Q:Do sin() and cos() use degrees or radians?

Q:M_PI is undefined — how do I fix it?

09Summary

Key Functions

10Practical Tips for Math in C

Comparing Floating Point Numbers

Checking for Special Values

Performance Considerations

Type-Generic Math (C11)

Handle Domain Errors

Know Your Precision Limits

Test Your Knowledge

Related Tutorials

C string.h Library Reference

C ctype.h Library Reference