Python evaluates arithmetic expressions using its grammar, operator precedence, and the values you provide. To find an unknown such as x in an equation, use a symbolic or numerical solving tool; ordinary Python arithmetic does not infer unknown values.
How Python evaluates a mathematical expression
An expression combines values, names, and operators. Python first groups operators according to its precedence rules, then evaluates the expression. The Python 3.14.8 language reference states, “Python evaluates expressions from left to right.” That evaluation order is distinct from precedence: precedence determines how an expression is grouped, while evaluation order determines the sequence in which its parts are evaluated.
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Parentheses make the intended grouping explicit. For example, 2 * (3 + 4) evaluates the addition first and returns 14. Without the parentheses, multiplication has higher precedence than addition, so 2 * 3 + 4 returns 10.
Common arithmetic operators
+and-perform addition and subtraction.*and/perform multiplication and true division. Dividing two integers with/produces a float.//performs floor division: it rounds the quotient down toward negative infinity, rather than truncating toward zero. For example,-7 // 2is-4.%returns the remainder. For floor division and modulo, Python documents the relationshipx == (x // y) * y + (x % y).**raises a value to a power. Exponentiation has a documented right-to-left associativity exception among Python’s operators; use parentheses if the grouping might be unclear.
Division or modulo by zero raises ZeroDivisionError. These descriptions concern Python’s built-in numeric types: custom types can define operator behavior, and operators such as + also work on some nonnumeric values. See the Python language reference on evaluation order and its operator precedence table.
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Evaluating an expression is not solving an equation
When you write 2 * (3 + 4), every operand is known, so Python can calculate a value. An equation such as x**2 = 2 asks for a value of x that makes both sides equal. Use a symbolic mathematics library or a numerical method for that job.
Use SymPy for symbolic or numerical solutions
SymPy’s solving guide describes solve() and solveset() as tools that seek exact symbolic solutions. For a numerical approximation, it recommends nsolve(). For example, the guide shows nsolve(cos(x) - x, x, 2) producing an approximation near 0.739085133215161; that result depends on the equation and starting value supplied.
Symbolic results can preserve exact values. Use SymPy’s symbolic pi when an exact expression involving π matters; passing the approximate math.pi value from Python’s standard library instead gives the solver a numeric input. SymPy’s evalf() method can approximate a symbolic result at a requested precision; see the solving guide and the SymPy numerical evaluation documentation.
Not every equation has a closed-form solution, and a symbolic solver may not have an implemented method for a particular form. A failed symbolic solve therefore does not, by itself, prove that no solution exists. A numerical method or a different mathematical formulation may be appropriate.
Independent reader supportYour contribution helps us test, update, and keep practical guides available for everyone.Handling arithmetic entered as text
Python code and a string containing Python code are different inputs. If an application receives an expression as text, choosing a way to interpret it is also a security decision.
Why eval() is unsuitable for untrusted input
eval() evaluates a Python expression in a namespace, and Python warns that it can execute arbitrary code. Do not pass user-supplied or otherwise untrusted text to it. Setting __builtins__ to a restricted value does not make it a security mechanism. The warning and behavior are documented in the Python built-in functions documentation.
What ast.literal_eval() can and cannot do
ast.literal_eval() accepts Python literals and container displays, including numbers, strings, tuples, lists, dictionaries, sets, booleans, None, and Ellipsis. It does not evaluate general arithmetic expressions such as 1 + 2, or expressions involving indexing. Although it does not execute arbitrary Python code, the AST documentation warns that relatively small inputs can still exhaust memory or the C stack, crash a process, or consume excessive CPU. It is not a universal safe parser for hostile input.
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If an application must accept user-entered arithmetic, define a narrow grammar and explicitly allow only the operators and values the feature needs. Enforce input-size, complexity, and resource limits, or select a purpose-built expression parser with those controls. Neither eval() nor ast.literal_eval() should be treated as a general-purpose solution for untrusted arithmetic strings.
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