The math module in Python provides access to mathematical functions defined by the C standard. It includes functions for basic arithmetic, trigonometry, logarithms, and more, as well as constants like pi and e.
Table of Contents
- Introduction
- Constants
- Number-theoretic and Representation Functions
ceilcopysignfabsfactorialfloorfmodfrexpfsumgcdisfiniteisinfisnanldexpmodftrunc
- Power and Logarithmic Functions
expexpm1loglog1plog2log10powsqrt
- Trigonometric Functions
acosasinatanatan2cossintan
- Angular Conversion
degreesradians
- Hyperbolic Functions
acoshasinhatanhcoshsinhtanh
- Special Functions
erferfcgammalgamma
- Examples
- Real-World Use Case
- Conclusion
- References
Introduction
The math module provides a comprehensive set of mathematical functions and constants. These functions are optimized for performance and provide a reliable foundation for numerical calculations.
Constants
pi
The mathematical constant π.
import math
print(math.pi) # 3.141592653589793
e
The mathematical constant e.
print(math.e) # 2.718281828459045
tau
The mathematical constant τ, which is 2π.
print(math.tau) # 6.283185307179586
inf
A floating-point positive infinity.
print(math.inf) # inf
nan
A floating-point “not a number” value.
print(math.nan) # nan
Number-theoretic and Representation Functions
ceil
Returns the ceiling of x, the smallest integer greater than or equal to x.
print(math.ceil(4.2)) # 5
copysign
Returns a float with the magnitude of x but the sign of y.
print(math.copysign(3, -1)) # -3.0
fabs
Returns the absolute value of x.
print(math.fabs(-5.3)) # 5.3
factorial
Returns the factorial of x, an exact integer.
print(math.factorial(5)) # 120
floor
Returns the floor of x, the largest integer less than or equal to x.
print(math.floor(4.8)) # 4
fmod
Returns the remainder of x / y.
print(math.fmod(7, 3)) # 1.0
frexp
Returns the mantissa and exponent of x as the pair (m, e).
print(math.frexp(8)) # (0.5, 4)
fsum
Returns an accurate floating-point sum of values in the iterable.
print(math.fsum([0.1, 0.2, 0.3])) # 0.6
gcd
Returns the greatest common divisor of the integers a and b.
print(math.gcd(8, 12)) # 4
isfinite
Returns True if x is neither an infinity nor a NaN, and False otherwise.
print(math.isfinite(5)) # True
print(math.isfinite(math.inf)) # False
isinf
Returns True if x is a positive or negative infinity, and False otherwise.
print(math.isinf(math.inf)) # True
print(math.isinf(5)) # False
isnan
Returns True if x is a NaN (not a number), and False otherwise.
print(math.isnan(math.nan)) # True
print(math.isnan(5)) # False
ldexp
Returns x * (2**i). This is essentially the inverse of frexp.
print(math.ldexp(0.5, 4)) # 8.0
modf
Returns the fractional and integer parts of x.
print(math.modf(4.5)) # (0.5, 4.0)
trunc
Returns the truncated integer value of x.
print(math.trunc(4.7)) # 4
Power and Logarithmic Functions
exp
Returns e raised to the power of x.
print(math.exp(2)) # 7.38905609893065
expm1
Returns e raised to the power of x, minus 1.
print(math.expm1(1)) # 1.718281828459045
log
Returns the natural logarithm of x.
print(math.log(2.718281828459045)) # 1.0
log1p
Returns the natural logarithm of 1 + x.
print(math.log1p(1)) # 0.6931471805599453
log2
Returns the base-2 logarithm of x.
print(math.log2(8)) # 3.0
log10
Returns the base-10 logarithm of x.
print(math.log10(100)) # 2.0
pow
Returns x raised to the power of y.
print(math.pow(2, 3)) # 8.0
sqrt
Returns the square root of x.
print(math.sqrt(16)) # 4.0
Trigonometric Functions
acos
Returns the arc cosine of x, in radians.
print(math.acos(1)) # 0.0
asin
Returns the arc sine of x, in radians.
print(math.asin(0)) # 0.0
atan
Returns the arc tangent of x, in radians.
print(math.atan(1)) # 0.7853981633974483
atan2
Returns atan(y / x), in radians.
print(math.atan2(1, 1)) # 0.7853981633974483
cos
Returns the cosine of x, in radians.
print(math.cos(math.pi / 4)) # 0.7071067811865476
sin
Returns the sine of x, in radians.
print(math.sin(math.pi / 2)) # 1.0
tan
Returns the tangent of x, in radians.
print(math.tan(math.pi / 4)) # 1.0
Angular Conversion
degrees
Converts angle x from radians to degrees.
print(math.degrees(math.pi)) # 180.0
radians
Converts angle x from degrees to radians.
print(math.radians(180)) # 3.141592653589793
Hyperbolic Functions
acosh
Returns the inverse hyperbolic cosine of x.
print(math.acosh(1)) # 0.0
asinh
Returns the inverse hyperbolic sine of x.
print(math.asinh(0)) # 0.0
atanh
Returns the inverse hyperbolic tangent of x.
print(math.atanh(0)) # 0.0
cosh
Returns the hyperbolic cosine of x.
print(math.cosh(0)) # 1.0
sinh
Returns the hyperbolic sine of x.
print(math.sinh(0)) # 0.0
tanh
Returns the hyperbolic tangent of x.
print(math.tanh(0)) # 0.0
Special Functions
erf
Returns the error function of x.
print(math.erf(0)) # 0.0
erfc
Returns the complementary error function of
x.
print(math.erfc(0)) # 1.0
gamma
Returns the Gamma function of x.
print(math.gamma(5)) # 24.0
lgamma
Returns the natural logarithm of the absolute value of the Gamma function of x.
print(math.lgamma(5)) # 3.1780538303479458
Examples
Calculating the Hypotenuse
Calculate the length of the hypotenuse of a right-angled triangle.
import math
def hypotenuse(a, b):
return math.sqrt(a**2 + b**2)
print(hypotenuse(3, 4)) # 5.0
Area of a Circle
Calculate the area of a circle given its radius.
import math
def area_of_circle(radius):
return math.pi * radius ** 2
print(area_of_circle(5)) # 78.53981633974483
Real-World Use Case
Compound Interest Calculation
Calculate the compound interest on an investment.
import math
def compound_interest(principal, rate, times_compounded, years):
return principal * (1 + rate / times_compounded) ** (times_compounded * years)
principal = 1000
rate = 0.05
times_compounded = 4
years = 10
print(compound_interest(principal, rate, times_compounded, years)) # 1647.00949769028
Conclusion
The math module in Python provides a wide range of mathematical functions and constants that are essential for various calculations and scientific computing. By utilizing these functions, you can perform complex mathematical operations with ease and precision.