Using math.isclose() to Compare Floats in Python

Comparing floating-point numbers in Python using the standard equality operator (==) frequently leads to unexpected bugs due to hardware-level binary representation errors. The purpose of Python's math.isclose() function is to safely compare two floating-point numbers by checking if they are "close" to each other within an acceptable margin of error. This article explains why floating-point inaccuracies happen, how math.isclose() works, and how to use it effectively in your code.

The Problem with Direct Float Comparison

Computers represent floating-point numbers in base-2 (binary) according to the IEEE 754 standard. Because certain base-10 fractions (like 0.1 or 0.2) cannot be represented cleanly in finite binary digits, small rounding inaccuracies occur.

For example:

print(0.1 + 0.2 == 0.3)  # Outputs: False
print(0.1 + 0.2)         # Outputs: 0.30000000000000004

Because 0.1 + 0.2 evaluates to slightly more than 0.3, testing equality with == returns False.

The Solution: math.isclose()

Introduced in Python 3.5, math.isclose() determines whether two values are considered equal by verifying if the difference between them falls within a specified tolerance threshold.

The function signature is:

math.isclose(a, b, *, rel_tol=1e-09, abs_tol=0.0)

The parameters function as follows:

• a and b: The two numeric values being compared.
• rel_tol (Relative Tolerance): The maximum allowed difference relative to the larger absolute value of a or b. The default value is 1e-09, meaning the values must match within 9 decimal places. This is ideal for most general comparisons where numbers vary in scale.
• abs_tol (Absolute Tolerance): A fixed maximum difference regardless of the magnitude of the numbers. The default is 0.0. This parameter is necessary when comparing values that are very close to zero.

Practical Example

Here is how math.isclose() resolves standard floating-point equality errors:

import math

a = 0.1 + 0.2
b = 0.3

# Standard equality fails
print(a == b)  # False

# math.isclose succeeds
print(math.isclose(a, b))  # True

When to Use abs_tol

When comparing numbers near zero, relative tolerance alone is often insufficient. For instance, comparing 1e-10 to 0.0 will fail with the default rel_tol because the relative difference relative to the larger number is 100%. In such cases, define abs_tol:

import math

# Fails with default parameters
print(math.isclose(1e-10, 0.0))  # False

# Succeeds with an explicit absolute tolerance
print(math.isclose(1e-10, 0.0, abs_tol=1e-9))  # True

Conclusion

Direct equality (==) should almost never be used with floating-point calculations in Python. By using math.isclose(), you account for underlying binary precision limitations, ensuring your conditional checks and tests behave reliably and as expected.