C math.h Functions

The math.h library is C's scientific calculator, with things like angles, logarithms, powers and rounding. It does the math the simple operators cannot.

In this page:

Trigonometric Functions
Logarithmic Functions
Exponential Functions
Rounding with round()
Power and Square Root

Syntax

#include <math.h>

sin(radians);
cos(radians);
log(number);
log10(number);

Trigonometric Functions

sin() and cos() compute the sine and cosine of an angle, but they expect that angle expressed in radians rather than degrees, so converting degrees to radians (multiplying by pi/180) before calling them is a common source of subtle bugs for anyone used to working in degrees.

Example: Trigonometric Functions

// Include standard input/output (printf, scanf)
#include <stdio.h>
// Include math functions (sqrt, pow, ...)
#include <math.h>
// Program execution starts in main()
int main() {
	// Declare radians and set it to 0
	double radians = 0;
	// Print formatted text to the screen
	printf("%.1f", cos(radians));
	// Return 0 to signal that the program finished successfully
	return 0;
}

Logarithmic Functions

log() computes the natural logarithm, using base e, while log10() computes the common logarithm, using base 10 — picking the wrong one silently gives a mathematically different (and usually wrong-looking) result, so it's worth double-checking which base your formula actually calls for.

Example: Logarithmic Functions

// Include standard input/output (printf, scanf)
#include <stdio.h>
// Include math functions (sqrt, pow, ...)
#include <math.h>
// Program execution starts in main()
int main() {
	// Print formatted text to the screen
	printf("%.2f %.2f", log(2.718281828), log10(100.0));
	// Return 0 to signal that the program finished successfully
	return 0;
}

Exponential Functions

exp() raises the mathematical constant e to the power of the given argument, effectively computing the inverse operation of log(). It shows up frequently in growth and decay formulas, such as exponential smoothing or compound interest calculations.

Example: Exponential Functions

// Include standard input/output (printf, scanf)
#include <stdio.h>
// Include math functions (sqrt, pow, ...)
#include <math.h>
// Program execution starts in main()
int main() {
	// Print formatted text to the screen
	printf("%.2f", exp(1.0));
	// Return 0 to signal that the program finished successfully
	return 0;
}

Rounding with round()

round() rounds a floating-point value to the nearest whole number, and specifically rounds a value that sits exactly halfway between two integers away from zero (so 2.5 becomes 3, and -2.5 becomes -3), which differs from some other rounding conventions you may have seen elsewhere.

Example: Rounding with round()

// Include standard input/output (printf, scanf)
#include <stdio.h>
// Include math functions (sqrt, pow, ...)
#include <math.h>
// Program execution starts in main()
int main() {
	// Print formatted text to the screen
	printf("%.0f %.0f", round(2.5), round(-2.5));
	// Return 0 to signal that the program finished successfully
	return 0;
}

Power and Square Root

pow() raises a base value to an arbitrary exponent, handling cases like fractional or negative exponents that a plain loop of repeated multiplication can't easily express, while sqrt() computes a value's non-negative square root directly and is more efficient than calling pow(x, 0.5) for that specific case.

Example: Power and Square Root

// Include standard input/output (printf, scanf)
#include <stdio.h>
// Include math functions (sqrt, pow, ...)
#include <math.h>
// Program execution starts in main()
int main() {
	// Print formatted text to the screen
	printf("%.1f %.1f", pow(2, 3), sqrt(16.0));
	// Return 0 to signal that the program finished successfully
	return 0;
}

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