How to Check If a Number Is Close to Another in Python

When working with floating-point numbers in Python, testing for equality using == is often unreliable. Due to how computers represent decimal numbers in binary (IEEE 754 standard), simple arithmetic like 0.1 + 0.2 does not exactly equal 0.3.

This guide explains why direct comparisons fail and how to use math.isclose() and absolute difference calculations to correctly determine if two numbers are "close enough" to be considered equal.

The Problem: Floating-Point Inaccuracy

Computers store numbers in binary. Some decimal fractions (like 0.1) cannot be represented exactly in binary, leading to tiny precision errors that accumulate during calculations.

num1 = 0.1 + 0.2
num2 = 0.3

print(f"num1: {num1:.17f}")
print(f"num2: {num2:.17f}")

if num1 == num2:
    print("Equal")
else:
    print("Not Equal")

Output:

num1: 0.30000000000000004
num2: 0.29999999999999999
Not Equal

Method 1: Using math.isclose (Recommended)

Introduced in Python 3.5, the math.isclose() function is the robust, standard way to compare floating-point numbers. It checks if two values are within a relative or absolute tolerance of each other.

import math

val_a = 0.1 + 0.2
val_b = 0.3

if math.isclose(val_a, val_b):
    print(f"{val_a} is close to {val_b}")
else:
    print("Values differ significantly.")

Output:

0.30000000000000004 is close to 0.3

Customizing Tolerance

You can adjust strictness using rel_tol (relative tolerance) and abs_tol (absolute tolerance).

import math

a = 10.0
b = 10.05

print(f"Default check: {math.isclose(a, b)}")

print(f"Relaxed check: {math.isclose(a, b, rel_tol=0.05)}")

Output:

Default check: False
Relaxed check: True

Method 2: Calculating Absolute Difference

If you are using an older version of Python or need a simple, specific threshold logic without importing modules, you can calculate the absolute difference.

The logic is: |a - b| <= tolerance.

val_a = 0.1 + 0.2
val_b = 0.3
tolerance = 1e-9  # 0.000000001

difference = abs(val_a - val_b)

if difference <= tolerance:
    print("Approximately Equal")
else:
    print("Not Equal")

Output:

Approximately Equal

Method 3: Checking Arrays with NumPy

If you are working with data science libraries, you likely have arrays of numbers rather than scalars. Standard Python functions won't work on arrays directly. Use numpy.isclose().

import numpy as np

data_calculated = np.array([0.1 + 0.2, 1.0 / 3.0])
data_expected = np.array([0.3, 0.3333333333333333])

matches = np.isclose(data_calculated, data_expected)

print(f"Matches: {matches}")
print(f"All close? {np.all(matches)}")

Output:

Matches: [ True  True]
All close? True

Conclusion

To check if numbers are close in Python:

1. Use math.isclose(a, b) for standard scalar comparisons. It is robust, explicit, and handles tolerances automatically.
2. Use abs(a - b) <= tol only if you need a quick, manual implementation without imports.
3. Use numpy.isclose(arr1, arr2) when working with lists or arrays of data.
4. Avoid == for floats, as it requires bit-for-bit equality which is rarely achieved in computed values.