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Modulo Order of Operations Calculator

See how expressions like a + b mod c and a mod b × d are parsed. Modulo (%) has the same precedence as multiplication and division — it binds tighter than addition and subtraction — so a + b mod c always means a + (b mod c).
First number
Divisor in first expression (≠ 0)
Addend / grouping test (≠ 0)
Multiplier or second divisor
a + b mod c = a + (b mod c)
16

Modulo binds tighter than addition — evaluated left before the +, just like multiplication

a + b mod c → a + (b mod c)
14 + 2 = 16
a mod b × d → (a mod b) × d
4 × 2 = 8
a mod (b + c) — grouping changes result
6
a mod b + c mod d → (a mod b) + (c mod d)
4 + 1 = 5
Order-of-operations walkthrough
1

Rule: mod (%) has same precedence as × and ÷ — higher than + and −

PEMDAS/BODMAS: … × ÷ % … before + −
2

Evaluate b mod c first (higher precedence than +)

b mod c = 5 mod 3 = 2
3

Then add a

a + (b mod c) = 14 + 2 = 16
4

Grouping a mod (b+c): inner addition runs first

b + c = 8, a mod 8 = 6
=

Compare: without grouping vs with grouping

a mod b = 4 ≠ a mod (b+c) = 6 (usually)
012345678How grouping shifts the remainder
Step by step
  1. 1

    Evaluate b mod c first (higher precedence than +)

    5 mod 3 = 2
    Modulo (%) shares precedence with × and ÷ — it fires before addition.
  2. 2

    Add a to the remainder

    14 + 2 = 16
Results are estimates for general information only and are not professional advice — always verify important results independently before relying on them. Read the full disclaimer.
Quick answer

How does this calculator work?

Modulo (%) has the same precedence as × and ÷ — it is evaluated before + and −, and left-to-right within its tier. So a + b mod c = a + (b mod c), not (a + b) mod c. Use parentheses to override: a mod (b + c) evaluates the addition first, often giving a different result.

Formula
a + b mod c ≡ a + (b mod c) • a mod b × c ≡ (a mod b) × c
How this is calculated

In all mainstream programming languages (C, Java, JavaScript, Python, Go) and in standard mathematical notation, the modulo operator shares the same precedence tier as multiplication (×) and division (÷). That tier is evaluated before addition (+) and subtraction (−), and left-to-right within the same tier.

This means a + b % c is always parsed as a + (b % c) — the modulo fires first on b and c, then the addition uses its result. Similarly, a % b * c is parsed as (a % b) * c, because both % and * have equal precedence and associate left-to-right. To override precedence, use parentheses: a % (b + c) first adds b and c, then takes the modulo with respect to a larger divisor, which will generally give a different result.

A common beginner mistake is writing a + b % c expecting it to mean (a + b) % c. The calculator shows both interpretations with concrete numbers so you can see exactly how the results differ and why grouping matters. All calculations here use the truncated (JS/C) remainder convention so the results match what you would see in a programming context.

Frequently asked questions

Higher. Modulo (%) sits in the same tier as multiplication and division, which is evaluated before addition and subtraction. So 10 + 7 % 3 = 10 + 1 = 11, not 17 % 3 = 2.

Left-to-right, like * and /. So a % b % c is evaluated as (a % b) % c. This is the universal rule across C, Java, JavaScript, Python and most other languages.

Yes — Python's % has the same precedence tier as * and /, so a + b % c is a + (b % c) in Python too. The difference is that Python uses floored division for the remainder value, not truncated — which only affects the sign when inputs are negative.

Also known as

modulo order of operations
mod operator precedence
pemdas with modulo
bodmas remainder operator
modulo before addition
percent operator expression
mod expression evaluation
operator precedence mod

APA

TG we-Calculate Editorial Team. (2026). Modulo Order of Operations Calculator [Online calculator]. TG we-Calculate. https://we-calculate.com/calculator/modulo-order-of-operations-calculator

Chicago

TG we-Calculate Editorial Team. "Modulo Order of Operations Calculator." TG we-Calculate. 2026. https://we-calculate.com/calculator/modulo-order-of-operations-calculator.

IEEE

TG we-Calculate Editorial Team, "Modulo Order of Operations Calculator," TG we-Calculate, 2026. [Online]. Available: https://we-calculate.com/calculator/modulo-order-of-operations-calculator

BibTeX

@misc{wecalculate_modulo_order_of_operations_calculator, title = {Modulo Order of Operations Calculator}, author = {{TG we-Calculate Editorial Team}}, howpublished = {\url{https://we-calculate.com/calculator/modulo-order-of-operations-calculator}}, year = {2026}, note = {TG we-Calculate} }

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