NumPy is Python’s go-to library for numerical computing , especially with large datasets and arrays. Its math functions are vectorized, which means you can apply operations to entire arrays without loops — making them fast and powerful.
Why Use NumPy for Math?
Element-wise operations on arrays
Handles multi-dimensional data
Functions are vectorized (fast & efficient)
Seamless with machine learning , data analysis , and scientific computing
📦 Importing NumPy
import numpy as np
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Note:
The following are the most-used functions only, checkout the complete list on numpy.org .
🔢 Arithmetic Functions
Function
Description
np.add(x1, x2)Element-wise addition
np.subtract(x1, x2)Element-wise subtraction
np.multiply(x1, x2)Element-wise multiplication
np.divide(x1, x2)Element-wise division
np.power(x1, x2)x1 raised to the power of x2
np.mod(x1, x2)Element-wise modulo
📐 Trigonometric Functions
Function
Description
np.sin(x)Sine
np.cos(x)Cosine
np.tan(x)Tangent
np.arcsin(x)Inverse sine
np.arccos(x)Inverse cosine
np.arctan(x)Inverse tangent
np.arctan2(y, x)Arctangent of y/x
np.hypot(x, y)√(x² + y²)
np.degrees(x)Radians → degrees
np.radians(x)Degrees → radians
📊 Exponentials & Logarithms
Function
Description
np.exp(x)e ** x
np.expm1(x)e ** x - 1
np.log(x)Natural log (base e)
np.log2(x)Base-2 logarithm
np.log10(x)Base-10 logarithm
np.log1p(x)log(1 + x) (accurate for small x)
🧠 Rounding, Absolute, and Sign Functions
Function
Description
np.round(x)Round to nearest integer
np.floor(x)Round down
np.ceil(x)Round up
np.trunc(x)Truncate decimal
np.abs(x)Absolute value
np.sign(x)Sign of x (-1, 0, or 1)
📐 Aggregates & Reductions
Function
Description
np.sum(x)Sum of all elements
np.prod(x)Product of all elements
np.mean(x)Average value
np.std(x)Standard deviation
np.var(x)Variance
np.max(x)Maximum value
np.min(x)Minimum value
🔍 Comparisons & Logical Checks
Function
Description
np.isfinite(x)Finite check
np.isinf(x)Infinite check
np.isnan(x)NaN check
np.isclose(x1, x2)Check if values are close
np.equal(x1, x2)Element-wise equality
📏 Linear Algebra (Bonus)
Function
Description
np.dot(x1, x2)Dot product
np.matmul(x1, x2)Matrix multiplication
np.linalg.inv(x)Inverse of a matrix
np.linalg.det(x)Determinant
np.linalg.eig(x)Eigenvalues and eigenvectors
💡 Constants
Constant
Description
np.piπ
np.eEuler’s number
np.infInfinity
np.nanNot a number
⚙️ Practical NumPy Example
You can run it and see the output online here: pythononline.net/#qBOCl4
import numpy as np
arr = np . array ([ 1 , 2 , 3 , 4 ])
arr2 = np . array ([ 4 , 3 , 2 , 1 ])
# Arithmetic
print ( " Add: " , np . add ( arr , arr2 ))
print ( " Subtract: " , np . subtract ( arr , arr2 ))
print ( " Multiply: " , np . multiply ( arr , arr2 ))
print ( " Divide: " , np . divide ( arr , arr2 ))
print ( " Power: " , np . power ( arr , 2 ))
print ( " Mod: " , np . mod ( arr , 3 ))
# Trigonometry
print ( " sin(pi/2): " , np . sin ( np . pi / 2 ))
print ( " cos(0): " , np . cos ( 0 ))
print ( " tan(pi/4): " , np . tan ( np . pi / 4 ))
print ( " arcsin(1): " , np . arcsin ( 1 ))
print ( " arccos(0): " , np . arccos ( 0 ))
print ( " arctan(1): " , np . arctan ( 1 ))
print ( " arctan2(1, 1): " , np . arctan2 ( 1 , 1 ))
print ( " hypot(3, 4): " , np . hypot ( 3 , 4 ))
print ( " degrees(pi): " , np . degrees ( np . pi ))
print ( " radians(180): " , np . radians ( 180 ))
# Exponentials & logs
print ( " exp(1): " , np . exp ( 1 ))
print ( " expm1(1e-5): " , np . expm1 ( 1e-5 ))
print ( " log(e): " , np . log ( np . e ))
print ( " log2(8): " , np . log2 ( 8 ))
print ( " log10(1000): " , np . log10 ( 1000 ))
print ( " log1p(1e-5): " , np . log1p ( 1e-5 ))
# Absolute, rounding
print ( " abs(-5): " , np . abs ( - 5 ))
print ( " sign(-3): " , np . sign ( - 3 ))
print ( " round(3.1415): " , np . round ( 3.1415 ))
print ( " floor(3.9): " , np . floor ( 3.9 ))
print ( " ceil(3.1): " , np . ceil ( 3.1 ))
print ( " trunc(3.8): " , np . trunc ( 3.8 ))
# Aggregates
print ( " sum: " , np . sum ( arr ))
print ( " prod: " , np . prod ( arr ))
print ( " mean: " , np . mean ( arr ))
print ( " std: " , np . std ( arr ))
print ( " var: " , np . var ( arr ))
print ( " max: " , np . max ( arr ))
print ( " min: " , np . min ( arr ))
# Comparisons
print ( " isfinite([1, np.inf]): " , np . isfinite ([ 1 , np . inf ]))
print ( " isinf([1, np.inf]): " , np . isinf ([ 1 , np . inf ]))
print ( " isnan([1, np.nan]): " , np . isnan ([ 1 , np . nan ]))
print ( " isclose(1.0, 1.00001): " , np . isclose ( 1.0 , 1.00001 ))
print ( " equal([1, 2], [1, 3]): " , np . equal ([ 1 , 2 ], [ 1 , 3 ]))
# Constants
print ( " pi: " , np . pi )
print ( " e: " , np . e )
print ( " inf: " , np . inf )
print ( " nan: " , np . nan )
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NumPy offers a rich set of fast, vectorized math functions that go far beyond Python’s built-ins. Whether you're handling basic arithmetic, advanced trigonometry, or high-performance numerical computations, NumPy is an essential tool.
Keep this cheat sheet handy as a quick reference to power up your data science, machine learning, or scientific computing projects!
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