Modulo Order Of Operations
Learn how modulo (%) fits into order of operations (PEMDAS/BODMAS). Evaluate mixed expressions and discover modulo precedence vs multiplication and division.
About This Calculator
The Modulo Order of Operations Calculator helps you understand how the modulo operator (%) interacts with standard arithmetic operations. Whether you are a student learning PEMDAS, a programmer debugging an expression, or a math enthusiast curious about remainder operations, this tool evaluates any arithmetic expression while respecting operator precedence rules.
In standard order of operations, the modulo operator shares the same precedence as multiplication and division. This means expressions are evaluated in this order: parentheses first, then exponents, then modulo, multiplication, and division from left to right, followed by addition and subtraction from left to right. For example, 10 + 12 % 5 x 2 evaluates as 10 + (12 % 5) x 2 = 10 + 2 x 2 = 10 + 4 = 14.
It is important to note that the % operator in most programming languages is technically a remainder operator rather than a true mathematical modulo. For positive numbers they produce identical results, but for negative dividends the remainder can be negative while true modulo always returns a non-negative result. Our calculator uses JavaScript's built-in remainder operator, consistent with how most programming languages handle the % symbol.
Regional Notes: The order of operations is universally taught though the acronym varies by region. In the United States, PEMDAS (Parentheses, Exponents, Multiplication/Division, Addition/Subtraction) is standard. In the United Kingdom and other Commonwealth countries, BODMAS (Brackets, Orders, Division/Multiplication, Addition/Subtraction) or BIDMAS is used. In India, BODMAS (Brackets, Of, Division, Multiplication, Addition, Subtraction) is commonly taught. Despite the different acronyms, the underlying hierarchy is identical worldwide.
Frequently Asked Questions
Where does modulo fit in the order of operations?
In most programming languages, the modulo operator (%) has the same precedence as multiplication and division. It is evaluated after parentheses and exponents but before addition and subtraction, working from left to right.
How do you evaluate 2 x 3 % 4?
The expression 2 x 3 % 4 evaluates to 2. First compute 2 x 3 = 6, then 6 % 4 = 2. Since modulo has the same precedence as multiplication, operations are performed left to right.
How do you evaluate 7 + 5 % 3?
The expression 7 + 5 % 3 evaluates to 9. The modulo operation 5 % 3 = 2 is computed first since modulo has higher precedence than addition, then 7 + 2 = 9.
Is the modulo operator the same as the remainder operator?
In mathematics, modulo always returns a non-negative remainder (0 <= r < n). In programming languages like JavaScript, the % operator is technically a remainder operator that can return negative values when the dividend is negative. For positive numbers, modulo and remainder are identical.
Does the modulo operator work with decimal numbers?
Modulo is traditionally defined for integers, but our calculator supports decimal numbers within expressions. For example, 10.5 % 3 returns the remainder when dividing 10.5 by 3.
Can I use parentheses in my expressions?
Yes, you can use parentheses to override the default order of operations. For example, 10 % (3 + 2) evaluates the addition in parentheses first, giving 10 % 5 = 0.
What happens when I divide by zero in an expression?
Division by zero or modulo by zero results in an undefined value. Our calculator safely catches such cases and does not display a result, preventing errors and NaN values.
Is this calculator free to use?
Yes, all calculators on Calculy are completely free to use with no registration or login required. You can also share your calculations via URL for easy reference.