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Zuletzt aktualisiert: 1. August 2026
Modulo Operations with Negative Numbers
Ersteller
Dharmendra SinghPrüfer
Ersteller
Dharmendra SinghPrüfer
Quick Answer
This calculator computes modulo for negative numbers using three conventions at once: truncated (JavaScript/C-style), floored (Python-style), and Euclidean (always non-negative), helping compare how they diverge for negative operands.
Enter a dividend and divisor, and the calculator compares truncated, floored, and Euclidean modulo results side by side.
Ersteller
Dharmendra SinghPrüfer
Ersteller
Dharmendra SinghPrüfer
Formel
truncatedMod = a % n; flooredMod = a - n*floor(a/n); euclideanMod = ((a % n) + |n|) % |n|
Wobei:
- a=Dividend, may be negative
- n=Divisor, may be negative
Rechenbeispiele
Negative dividend
Compare -7 mod 3 across conventions.
- 1Truncated: -7 % 3 = -1
- 2Floored: -7 - 3*floor(-7/3) = 2
- 3Euclidean: always non-negative, so 2
Negative divisor
Compare 7 mod -3 across conventions.
- 1Truncated: 7 % -3 = 1
- 2Floored: 7 - (-3)*floor(7/-3) = -2
- 3Euclidean: 1
Both negative
Compare -7 mod -3 across conventions.
- 1Truncated: -7 % -3 = -1
- 2Floored: -1
- 3Euclidean: 2
Positive values agree
Compare 7 mod 3, where all conventions match.
- 1Truncated: 7 % 3 = 1
- 2Floored: 1
- 3Euclidean: 1
Einführung
When negative numbers are involved, "modulo" can mean different things in different programming languages. This calculator computes the three most common conventions side by side so you can see exactly how they differ.
Why Negative Modulo Isn't Universal
Unlike modulo of two positive numbers, the sign of the result for negative operands depends on the convention chosen. JavaScript, Java, and C use truncated division; Python uses floored division; and many textbooks define a strictly non-negative Euclidean remainder.
Truncated modulo keeps the same sign as the dividend
Floored modulo keeps the same sign as the divisor
Euclidean modulo is always between 0 and the absolute value of the divisor
How the Calculator Works
The calculator computes all three conventions from the same inputs: the raw % operator for truncated modulo, a floor-based formula for floored modulo, and a sign correction for Euclidean modulo.
Both a and n must be finite numbers
The divisor n cannot be zero
All three results are computed and returned together
Input Guide
Enter the dividend a and the divisor n; either or both can be negative.
- 1
a: the dividend, e.g. -7
- 2
n: the divisor, e.g. 3
Output Guide
The calculator returns all three modulo conventions so you can compare them directly.
- 1
truncatedMod: result matching JavaScript, Java, and C's % operator
- 2
flooredMod: result matching Python's % operator
- 3
euclideanMod: the always non-negative remainder
How to Use This Calculator
Enter any dividend and divisor, then compare the three outputs to see how conventions diverge for negative values.
Try a negative dividend with a positive divisor
Try a positive dividend with a negative divisor
Compare all three outputs when both are negative
Common Mistakes
Mixing up conventions between programming languages is the most common source of negative-modulo bugs.
Assuming a language's % always returns a non-negative value
Porting code between languages without checking modulo conventions
Entering a zero divisor, which is undefined for all conventions
Practical Uses
Understanding these conventions matters when porting code, working with circular data structures, or teaching modular arithmetic.
Debugging sign differences when porting code between languages
Wrapping array indices safely regardless of sign
Teaching the different definitions of modular arithmetic
FAQ
What is truncated modulo?
Truncated modulo (used by JavaScript, Java, and C) keeps the same sign as the dividend; for example -7 % 3 equals -1.
What is floored modulo?
Floored modulo (used by Python) keeps the same sign as the divisor; for example -7 mod 3 equals 2 in Python.
What is Euclidean modulo?
Euclidean modulo always returns a non-negative remainder between 0 and the absolute value of the divisor, regardless of sign.
Why do different languages give different answers for the same inputs?
Each language chooses a different mathematical convention for handling negative operands, even though they agree completely for positive inputs.
Which convention should I use?
Use whichever convention matches your target programming language or the mathematical definition your problem requires; the Euclidean convention is often preferred when a non-negative result is required.
Do all three conventions agree for positive numbers?
Yes, when both the dividend and divisor are positive, truncated, floored, and Euclidean modulo all produce the same result.
Can the divisor be zero?
No, all three modulo conventions are undefined when the divisor is zero, so the calculator returns a validation error.
Is Euclidean modulo ever negative?
No, by definition Euclidean modulo is always in the range from 0 up to (but not including) the absolute value of the divisor.