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Dernière mise à jour : 1 août 2026
Modulo in the Order of Operations
Créateurs
Dharmendra SinghRéviseurs
Créateurs
Dharmendra SinghRéviseurs
Quick Answer
This calculator evaluates arithmetic expressions containing the modulo operator by parsing them with standard operator precedence, treating % at the same level as multiplication and division and evaluating left to right.
Enter an expression with modulo, and the calculator evaluates it using the same precedence rules as multiplication and division.
Créateurs
Dharmendra SinghRéviseurs
Créateurs
Dharmendra SinghRéviseurs
Formule
Evaluate using precedence: parentheses, then unary minus, then * / % (left to right), then + - (left to right)
Où :
- %=Modulo operator, same precedence as multiplication and division
Exemples résolus
Modulo with addition and multiplication
Evaluate 8 + 12 % 5 * 2.
- 112 % 5 = 2 (same precedence as *, evaluated left to right)
- 22 * 2 = 4
- 38 + 4 = 12
Parentheses before modulo
Evaluate (10 + 5) % 4.
- 1Parentheses first: 10 + 5 = 15
- 215 % 4 = 3
- 3Report the result
Equal-precedence operators left to right
Evaluate 2 + 3 * 4 % 5.
- 13 * 4 = 12 (evaluated before % since it comes first, left to right)
- 212 % 5 = 2
- 32 + 2 = 4
Unary minus with modulo
Evaluate -7 % 3.
- 1Apply the unary minus to 7 first
- 2-7 % 3 = -1 using the truncated convention
- 3Report the result
Introduction
Modulo doesn't have its own special rule in the order of operations — it shares precedence with multiplication and division. This calculator evaluates full expressions so you can see exactly where % fits in.
Where Does Modulo Fit in PEMDAS/BODMAS?
Modulo (%) is evaluated at the same precedence level as multiplication and division. Within that level, operators are applied left to right, just like * and /.
Parentheses are always evaluated first
% shares precedence with * and /, evaluated left to right
+ and - are evaluated last, also left to right
How the Calculator Works
The calculator tokenizes the expression and parses it with a recursive-descent algorithm that mirrors standard operator precedence, including support for parentheses and unary minus.
Only digits, + - * / % ( ) and whitespace are accepted
Division or modulo by zero is rejected with an error
Unary minus is supported before a number or parenthesis
Input Guide
Type a full arithmetic expression using +, -, *, /, %, parentheses, and numbers.
- 1
expression: an arithmetic expression, e.g. 8 + 12 % 5 * 2
Output Guide
The calculator returns the evaluated result and echoes back the expression it evaluated.
- 1
result: the numeric value of the expression
- 2
expression: the exact expression that was evaluated
How to Use This Calculator
Type any expression containing %, then compare the result with your own step-by-step evaluation.
Include parentheses to force a different evaluation order
Use spaces freely between numbers and operators
Check the result against manual PEMDAS/BODMAS steps
Common Mistakes
Many people assume modulo is always evaluated last, but it actually shares precedence with multiplication and division.
Assuming modulo always happens after multiplication and division
Forgetting that equal-precedence operators run left to right
Leaving out parentheses when a different order is intended
Practical Uses
Understanding modulo precedence matters for programming, spreadsheet formulas, and math education.
Debugging expressions in programming languages that use %
Teaching PEMDAS/BODMAS with a less common operator
Verifying formulas that mix modulo with other operators
FAQ
Does modulo come before or after multiplication?
Modulo shares the same precedence level as multiplication and division, so among those three, whichever appears first (left to right) is evaluated first.
What operators does this calculator support?
It supports addition, subtraction, multiplication, division, modulo, parentheses, and unary minus.
What happens if I divide or take modulo by zero?
The calculator returns a validation error because both operations are undefined when the divisor is zero.
Can I use parentheses to change the order?
Yes, parentheses are always evaluated first, just like in standard PEMDAS/BODMAS rules.
Why is my hand-calculated answer different?
Double check that you applied % at the same step as * and /, evaluating strictly left to right rather than saving it for last.
Can I use negative numbers in the expression?
Yes, a leading minus sign is treated as unary negation and works correctly with modulo.
What characters are not allowed?
Any character other than digits, decimal points, + - * / % ( ) and spaces will cause a validation error.